Physics Book - User contributions [en]

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2022-04-25T04:09:47Z

Zach Shapiro: {{Information | Description = | Source = | Date = | Author = | Permission = }} Category:

== Summary ==
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2022-04-25T04:06:58Z

Zach Shapiro:

Electronic Energy Levels and Photons

2022-04-25T04:02:54Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

====Photon as a Wave====
One demonstration of how photons act as waves is the double-slit experiment. When a beam of light/photons is shot at a panel with 2 slits in it, a striped pattern is formed on the other side. This is due to the wave-like interference between the two beams of light that are created by the two slits. Where the stripes themselves appear, the light waves are constructively interfering, or adding together. Between the stripes is darkness due to the destructive interference of the light waves.

[[File:Two-Slit Experiment Light.svg|thumb|Double-Slit Experiment Light]]

By measuring the distance y between the stripes of light, this phenomenon can also be used to determine the wavelength of the photons as long as the distance d between the slits is known as well as the distance x between the slitted panel and the wall.

<math>\lambda = \frac{y*d}{x}</math>

[[File:Untitled drawing.jpg|thumb|Double-Slit Experiment]]

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.

<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

https://www.millersville.edu/physics/experiments/089/

https://courses.lumenlearning.com/austincc-physics2/chapter/27-3-youngs-double-slit-experiment/

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T04:02:33Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

====Photon as a Wave====
One demonstration of how photons act as waves is the double-slit experiment. When a beam of light/photons is shot at a panel with 2 slits in it, a striped pattern is formed on the other side. This is due to the wave-like interference between the two beams of light that are created by the two slits. Where the stripes themselves appear, the light waves are constructively interfering, or adding together. Between the stripes is darkness due to the destructive interference of the light waves.

[[File:Two-Slit Experiment Light.svg|thumb|Double-Slit Experiment Light]]

By measuring the distance y between the stripes of light, this phenomenon can also be used to determine the wavelength of the photons as long as the distance d between the slits is known as well as the distance x between the slitted panel and the wall.

<math>\lambda = \frac{y*d}{x}</math>

[[File:Untitled drawing.jpg|thumb|Double-Slit Experiment]

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.

<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

https://www.millersville.edu/physics/experiments/089/

https://courses.lumenlearning.com/austincc-physics2/chapter/27-3-youngs-double-slit-experiment/

[[Category:Energy]]

File:Untitled drawing.jpg

2022-04-25T04:00:28Z

Zach Shapiro:

Electronic Energy Levels and Photons

2022-04-25T03:55:27Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

====Photon as a Wave====
One demonstration of how photons act as waves is the double-slit experiment. When a beam of light/photons is shot at a panel with 2 slits in it, a striped pattern is formed on the other side. This is due to the wave-like interference between the two beams of light that are created by the two slits. Where the stripes themselves appear, the light waves are constructively interfering, or adding together. Between the stripes is darkness due to the destructive interference of the light waves.

[[File:Two-Slit Experiment Light.svg|thumb|Double-Slit Experiment Light]]

By measuring the distance y between the stripes of light, this phenomenon can also be used to determine the wavelength of the photons as long as the distance d between the slits is known as well as the distance x between the slitted panel and the wall.

<math>\lambda = \frac{y*d}{x}</math>

[[File:/Users/zach/Downloads/Untitled drawing-3.pdf|thumb|Double-Slit Experiment Light]]

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.

<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

https://www.millersville.edu/physics/experiments/089/

https://courses.lumenlearning.com/austincc-physics2/chapter/27-3-youngs-double-slit-experiment/

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T03:48:38Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

====Photon as a Wave====
One demonstration of how photons act as waves is the double-slit experiment. When a beam of light/photons is shot at a panel with 2 slits in it, a striped pattern is formed on the other side. This is due to the wave-like interference between the two beams of light that are created by the two slits. Where the stripes themselves appear, the light waves are constructively interfering, or adding together. Between the stripes is darkness due to the destructive interference of the light waves.

[[File:Two-Slit Experiment Light.svg|thumb|Double-Slit Experiment Light]]

By measuring the distance y between the stripes of light, this phenomenon can also be used to determine the wavelength of the photons as long as the distance d between the slits is known as well as the distance x between the slitted panel and the wall.

<math>\lambda = \frac{y*d}{x}</math>

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.

<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

https://www.millersville.edu/physics/experiments/089/

https://courses.lumenlearning.com/austincc-physics2/chapter/27-3-youngs-double-slit-experiment/

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T03:48:24Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

====Photon as a Wave====
One demonstration of how photons act as waves is the double-slit experiment. When a beam of light/photons is shot at a panel with 2 slits in it, a striped pattern is formed on the other side. This is due to the wave-like interference between the two beams of light that are created by the two slits. Where the stripes themselves appear, the light waves are constructively interfering, or adding together. Between the stripes is darkness due to the destructive interference of the light waves.

[[File:Two-Slit Experiment Light.svg|thumb|Two-Slit Experiment Light]]

By measuring the distance y between the stripes of light, this phenomenon can also be used to determine the wavelength of the photons as long as the distance d between the slits is known as well as the distance x between the slitted panel and the wall.

<math>\lambda = \frac{y*d}{x}</math>

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.

<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

https://www.millersville.edu/physics/experiments/089/

https://courses.lumenlearning.com/austincc-physics2/chapter/27-3-youngs-double-slit-experiment/

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T03:45:16Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

====Photon as a Wave====
One demonstration of how photons act as waves is the double-slit experiment. When a beam of light/photons is shot at a panel with 2 slits in it, a striped pattern is formed on the other side. This is due to the wave-like interference between the two beams of light that are created by the two slits. Where the stripes themselves appear, the light waves are constructively interfering, or adding together. Between the stripes is darkness due to the destructive interference of the light waves.

[[File:Two-Slit Experiment Electrons.svg|thumb|Two-Slit Experiment Electrons]]

By measuring the distance y between the stripes of light, this phenomenon can also be used to determine the wavelength of the photons as long as the distance d between the slits is known as well as the distance x between the slitted panel and the wall.

<math>\lambda = \frac{y*d}{x}</math>

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.

<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

https://www.millersville.edu/physics/experiments/089/

https://courses.lumenlearning.com/austincc-physics2/chapter/27-3-youngs-double-slit-experiment/

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T03:42:24Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

====Photon as a Wave====
One demonstration of how photons act as waves is the double-slit experiment. When a beam of light/photons is shot at a panel with 2 slits in it, a striped pattern is formed on the other side. This is due to the wave-like interference between the two beams of light that are created by the two slits. Where the stripes themselves appear, the light waves are constructively interfering, or adding together. Between the stripes is darkness due to the destructive interference of the light waves.

By measuring the distance y between the stripes of light, this phenomenon can also be used to determine the wavelength of the photons as long as the distance d between the slits is known as well as the distance x between the slitted panel and the wall.

<math>\lambda = \frac{y*d}{x}</math>

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.

<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

https://www.millersville.edu/physics/experiments/089/

https://courses.lumenlearning.com/austincc-physics2/chapter/27-3-youngs-double-slit-experiment/

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T03:41:27Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

====Photon as a Wave====
One demonstration of how photons act as waves is the double-slit experiment. When a beam of light/photons is shot at a panel with 2 slits in it, a striped pattern is formed on the other side. This is due to the wave-like interference between the two beams of light that are created by the two slits. Where the stripes themselves appear, the light waves are constructively interfering, or adding together. Between the stripes is darkness due to the destructive interference of the light waves.

By measuring the distance between the stripes of light, this phenomenon can also be used to determine the wavelength of the photons as long as the distance d between the slits is known as well as the distance x between the slitted panel and the wall.
<math>\lambda = y*d/x</math>

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.

<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

https://www.millersville.edu/physics/experiments/089/

https://courses.lumenlearning.com/austincc-physics2/chapter/27-3-youngs-double-slit-experiment/

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T03:20:23Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.

<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

https://www.millersville.edu/physics/experiments/089/

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T03:18:30Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.

<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T03:18:09Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.
<math>\hbar = \frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T03:17:50Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.

<math>\Delta x \Delta p \approx \hbar \ge \frac{\hbar}{2}</math>

In this equation, <math>\hbar</math> is the reduced plank's constant.
<math>\hbar = frac{h}{2\pi}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T03:14:01Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===Uncertainty===
Due to the wave-particle duality of photons, they must obey the Heisenberg uncertainty principle, which states that the more accurately the location of the photon is defined, the less accurately the momentum can be defined. The reverse is true as well.
<math>\delta x \delta p \approx \hbar \ge \frac{\hbar}{2}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:51:49Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c}{\lambda}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:51:18Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

<math>E=p*c=\frac{h*c/\lambda</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:51:05Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum and energy of a photon can be calculated using the following equations, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>
<math>E=p*c=\frac{h*c/\lambda</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:48:31Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum of a photon can be calculated using the following equation, where <math>\lambda</math> is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:47:48Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum of a photon can be calculated using the following equation, where \lambda is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^{−34} J⋅Hz^{−1}</math>)

<math>p=\frac{h}{\lambda}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:47:28Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum of a photon can be calculated using the following equation, where \lambda is the wavelength (or the inverse of the frequency) and h is plank's constant (<math>6.62607015×10^−34 J⋅Hz^−1</math>)

<math>p=\frac{h}{\lambda}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:46:26Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum of a photon can be calculated using the following equation, where \lambda is the wavelength (or the inverse of the frequency) and h is plank's constant (6.62607015×10−34 J⋅Hz−1)

<math>p=\frac{h}{\lambda}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:43:44Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

<math>p=\frac{h}{\lambda}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:43:07Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

<math>p=\frac{h}{\Lambda}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:42:35Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

<math>p=\frac{h}{l}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:42:02Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

<math>\p=h/l</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:41:28Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

<math>\sum_{i=0}^\infty 2^{-i}</math>

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:40:59Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c +

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:38:12Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

{{math|''E'' {{=}} ''mc''{{sup|2}}}}

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:36:12Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

[[File:/Users/zach/Downloads/chart.png]]
{{math|1=''E'' = ''mc''{{sup|2}}}}
{{nowrap|''E'' {{=}} ''mc''<sup>2</sup>}}

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:34:46Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

[[File:/Users/zach/Downloads/chart.png]]
{{math|1=''E'' = ''mc''{{sup|2}}}}

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:31:17Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

[[File:/Users/zach/Downloads/chart.png]]

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:30:59Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

[[/Users/zach/Downloads/chart.png]]

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:30:47Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum

/Users/zach/Downloads/chart.png

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:29:56Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum equation E = h/lambda/Users/zach/Downloads/chart.png

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T02:26:20Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===Energy and Momentum===

Since photons move at the speed of light, their energy and momentum must be calculated relativistically. The momentum equation E = h/lambda

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T01:59:16Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/photon2

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T01:58:29Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

The following program is a computational model of the electron of a hydrogen atom releasing a photon and jumping from the second energy level to the first. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-25T01:35:41Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

===A Computational Model of the Bohr Hydrogen Atom===
The following program is a computational model of the electron of a hydrogen atom absorbing a photon and jumping from the first energy level to the second. The speed of the photon (the yellow sphere) has been greatly scaled back for visual purposes.
https://www.glowscript.org/#/user/zachshap88/folder/MyPrograms/program/idk

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-24T18:24:37Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. Photons are the fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-24T18:23:35Z

Zach Shapiro:

Zachary Shapiro Spring 2022

In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. A photon is a fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-24T18:23:26Z

Zach Shapiro:

Zachary Shapiro Spring 2022
In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. A photon is a fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (299,792,458 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Electronic Energy Levels and Photons

2022-04-24T18:22:45Z

Zach Shapiro:

Zachary Shapiro Spring 2022
In a classical Bohr model, electrons have discrete quantities of energy, called energy levels, as they orbit the central nucleus. An atom is thought to contain several "shells" in which electrons orbit the nucleus, and each shell represents a different energy level. Which shell an electron is currently in is denoted by the principal quantum number (n = 1,2,3...). Lower principal quantum numbers represent an electron shell that has a lower energy level and is closer to the nucleus.
Electrons can transfer to a higher energy level by absorbing energy (usually in the form of a photon). However, the electron will eventually return to its ground state, releasing a photon in the process. A photon is a fundamental unit of electromagnetic radiation and are responsible for the phenomenon of light. They are considered to be massless and thus travel at the speed of light (3x10^8 m/s).

==The Main Ideas==
===The Quantized Nature of Electronic Energy Levels===

Electrons can be excited by absorbing energy from photons. Electrons can only be excited to certain electronic energy levels. Each electronic energy level is a number that represents the sum of the kinetic and potential energy (K+U). Because the electronic potential energy between the positive protons in the nucleus and the surrounding negative electrons will always be negative, the value of K+U will be negative. Because electrons are only stable at those energy levels, an electron can only absorb certain quantized energies from photons. Once the electron absorbs a photon, it is excited by the energy. After the electron is excited, it drops down and releases a photon with the energy difference between the two energy levels. It can drop to any energy level below it, and thus the resulting photons can be of several energies. If the photon gained is the the opposite of the K+U value for the energy level, then the electron is said to have been ionized. The ionization energy of an atom is the energy needed to ionize an electron that is at rest.

===The Nature of a Photon===

A photon falls neither in the category of a particle nor in the category of a wave. A photon behaves like a particle with a velocity, however it has no mass, and ceases to exist once its energy is absorbed. It can be created or destroyed at anytime, and thus cannot truly be considered as being a particle. It can be imagined as a elementary package of energy. It is a product of the wave-particle duality of light, which states that light behaves both as a particle was well as a wave. The relationship between the frequency of the wave of light and the energy contained in the photon can be described using Planck's Constant.

===A Mathematical Model of the Bohr Hydrogen Atom===

For example, the electronic energy levels for a hydrogen atom can be modeled by the equation: <math>{\frac{-13.6}{N^2}} = {K+U}</math> where '''N''' is the energy level. N=1 is the rest energy level; N=2 is the the first excited energy level; and N=3 is the second level, etc. This formula gives energy levels in terms of electron volts (eV). If you substitute values of N into the equation you can build the atom shown. As the value of N increases, the space between each energy level decreases. The energy difference between the rest energy level and the first excited energy level is the largest. Because the energy of the rest energy level is -13.6 eV, the ionization energy of an electron at rest in a hydrogen atom is 13.6 eV. In other words, if the electron at rest absorbs a photon with 13.6 eV, the electron is "freed" from the atom. In this atom, the difference between the the first (-13.6 eV) and second (-3.4 eV) energy level is 10.2 eV. This means that a photon needs to have a minimum energy of 10.2 eV to be absorbed by the electron and excite it.
[[File:hydrogen.png|200px|thumb|left|Hydrogen and its energy levels]]

==Examples==

===Photon Absorption===

If a hypothetical ion had the first 4 energy levels of -4, -2.3, -1.9, and -.8 eV, and an electron at rest was struck by a photon with 2.2 eV of energy, what is the highest excited state the electron could be at? How much energy would the photon leave with, if at all?

First, check the amount of energy need to go from the rest energy level to the first excited energy level: -2.3-(-4)= 1.7. 2.2>1.7, so the electron will be excited to at least this state. If 1.7 eV is absorbed, then 2.2-1.7= .5 eV is remaining. Then check if this sufficient to raise it one more energy level. -1.9-(-2.3)= .4. .5 is greater than .4, so the photon also has sufficient energy to raise it to the second energy level. after raising it to the second excited level, the photon has .5-.4= .1 eV of energy remaining. This .1 eV is not sufficient to raise it to the third excited energy level. So, the photon will be at the second excited energy level, and the photon will have .1 eV of energy remaining.

===Photon Emission===

If electrons of energy 12.8 eV are incident on a gas of hydrogen atoms in their ground state, what are the energies of the photons that are emitted by the excited gas?

First, determine that the difference between the rest energy level (-13.6 eV) and the 3rd excited state (-.85 eV) IS 12.75 eV, and the remaining .05 eV is not sufficient to raise it another energy level. Then consider the different paths the electron could take back to its rest position, and calculate the energies of the corresponding photon emissions. Firstly, the electron could return one energy level at a time, releasing a a photon each drop. The differences between each energy level are: 10.2, 1.89, and .66 eV. Alternatively, the electron could drop from the the fourth energy level directly back to the first. This photon would have an energy equal to the difference between the 2 energy levels: 12.75 eV. Also, it could drop from 4th to 2nd to 1st, and the photon that would be emitted between the 4th and 2nd is 2.55. We have already accounted for the drop between the 2nd and 1st. Lastly, the electron could go from 4th to 3rd to 1st. The drop from 4th to 3rd has already been accounted for, and the difference between the 3rd and l is 12.09. In conclusion, all the possible energies for the emitted photons, from highest to lowest are: 12.75, 12.09, 10.2,2.55,1.89, and .66 eV.

==Historical Context==

In the development of atomic theory, Rutherford discovered that atoms have a nucleus through his famous gold foil experiment. Then, Niels Bohr conjectured that electrons only travel in distinct energy levels around the nucleus. In 1913, Niels Bohr proposed a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well defined quantities. Electrons should move around the nucleus but only in prescribed orbits. When jumping from one orbit to another with lower energy, a light quantum is emitted. Bohr's theory could explain why atoms emitted light in fixed wavelengths.

== See also ==

[[Photons]],
[[Bohr Model]],
[[Electronic Energy Levels]]

===External links===

http://physics.about.com/od/quantumphysics/f/quantumoptics.htm
http://dev.physicslab.org/document.aspx?doctype=3&filename=atomicnuclear_bohrmodelderivation.xml

==References==

https://www.youtube.com/watch?v=Y0048AI5uEQ

Matter and Interactions. 4th Edition.

http://www.nobelprize.org/nobel_prizes/physics/laureates/1922/bohr-facts.html

[[Category:Energy]]

Main Page

2022-04-24T17:45:59Z

Zach Shapiro: /* Special Relativity */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">

==Physics 1==
===Week 1===
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====GlowScript 101====
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*[[Python Syntax]]
*[[GlowScript]]
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====VPython====

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*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

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====Vectors and Units====
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*[[Vectors]]
*[[SI Units]]
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====Interactions====
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*[[Types of Interactions and How to Detect Them]]
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====Velocity and Momentum====
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*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
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</div>

===Week 2===
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====Momentum and the Momentum Principle====
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*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

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====Iterative Prediction with a Constant Force====
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*[[Iterative Prediction]]
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===Week 3===
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====Analytic Prediction with a Constant Force====
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*[[Kinematics]]
*[[Projectile Motion]]
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====Iterative Prediction with a Varying Force====
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*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
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===Week 4===
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====Fundamental Interactions====
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*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
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===Week 5===
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====Properties of Matter====
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*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
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===Week 6===
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====Identifying Forces====
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*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
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====Curving Motion====
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*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
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</div>

===Week 7===
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====Energy Principle====
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*[[Energy of a Single Particle]]
*[[Kinetic Energy]]
*[[Work/Energy]]
*[[The Energy Principle]]
*[[Conservation of Energy]]
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</div>

===Week 8===
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====Work by Non-Constant Forces====
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*[[Work Done By A Nonconstant Force]]
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====Potential Energy====
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*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
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====Multiparticle Systems====
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*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
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</div>

===Week 10===
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====Choice of System====
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*[[System & Surroundings]]
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====Thermal Energy, Dissipation, and Transfer of Energy====
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*[[Thermal Energy]]
*[[Specific Heat]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
*[[The Third Law of Thermodynamics]]
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</div>
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====Rotational and Vibrational Energy====
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*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
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===Week 11===
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====Different Models of a System====
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*[[Point Particle Systems]]
*[[Real Systems]]
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====Friction====
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*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
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===Week 12===
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====Conservation of Momentum====
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*[[Conservation of Momentum]]
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====Collisions====
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*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
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===Week 13===
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====Rotations====
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*[[Rotational Kinematics]]
*[[Eulerian Angles]]
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====Angular Momentum====
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*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
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===Week 14===
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====Analyzing Motion with and without Torque====
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*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
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===Week 15===
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====Introduction to Quantum Concepts====
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*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Electron transitions]]
*[[Entropy]]
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==Physics 2==
===Week 1===
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====3D Vectors====

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*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
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====Electric field====
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*[[Electric Field]]
*[[Electric Field and Electric Potential]]
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====Electric force====
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*[[Electric Force]]
*[[Lorentz Force]]
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====Electric field of a point particle====
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*[[Point Charge]]
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====Superposition====
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*[[Superposition Principle]]
*[[Superposition principle]]
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====Dipoles====
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*[[Electric Dipole]]
*[[Magnetic Dipole]]
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===Week 2===
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====Interactions of charged objects====
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*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
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====Tape experiments====
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*[[Polarization]]
*[[Electric Polarization]]
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====Polarization====
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*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
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===Week 3===
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====Conductors and Insulators====
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*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
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====Charging and Discharging====
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*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
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===Week 4===
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====Field of a charged rod====
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*[[Field of a Charged Rod|Charged Rod]]
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====Field of a charged ring/disk/capacitor====
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*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
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====Field of a charged sphere====
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*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
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===Week 5===
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====Potential energy====
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*[[Potential Energy]]
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</div>

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====Electric potential====
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*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
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====Sign of a potential difference====
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*[[Sign of a Potential Difference]]
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====Potential at a single location====
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*[[Electric Potential]]
*[[Potential Difference at One Location]]
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====Path independence and round trip potential====
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*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
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===Week 6===
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====Electric field and potential in an insulator====
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*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
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====Moving charges in a magnetic field====
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*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
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====Biot-Savart Law====
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*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
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</div>
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====Moving charges, electron current, and conventional current====
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*[[Moving Point Charge]]
*[[Current]]
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===Week 7===
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====Magnetic field of a wire====
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*[[Magnetic Field of a Long Straight Wire]]
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</div>

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====Magnetic field of a current-carrying loop====
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*[[Magnetic Field of a Loop]]
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====Magnetic field of a Charged Disk====
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*[[Magnetic Field of a Disk]]
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====Magnetic dipoles====
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*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
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====Atomic structure of magnets====
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*[[Atomic Structure of Magnets]]
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===Week 8===
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====Steady state current====
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*[[Steady State]]
*[[Non Steady State]]
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</div>

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====Kirchoff's Laws====
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*[[Kirchoff's Laws]]
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</div>

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====Electric fields and energy in circuits====
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*[[Electric Potential Difference]]
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</div>

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====Macroscopic analysis of circuits====
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*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
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====Electric field and potential in circuits with capacitors====
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*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

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====Magnetic forces on charges and currents====
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*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

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====Electric and magnetic forces====
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*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

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====Velocity selector====
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*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
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===Week 10===
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====Hall Effect====
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*[[Hall Effect]]
<h1><strong>Alayna Baker Spring 2020</strong></h1>
[[File:Hall Effect 1.jpg]]
[[File:Hall Effect 2.jpg]]

*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

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]]]====Motional EMF====

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*[[Motional Emf]]
<h1><strong>Adeline Boswell Fall 2019</strong></h1>
[[File:Motional EMF Example.jpg]]

*[[Motional Emf using Faraday's Law]]
</div>
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page

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If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"

[[File:MotEMFCR.jpg]]

====Magnetic force====
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*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

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====Magnetic torque====
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*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

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====Gauss's Law====
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*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

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====Ampere's Law====
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*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
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====Semiconductors====
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*[[Semiconductor Devices]]
</div>
</div>

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====Faraday's Law====
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*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

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====Maxwell's equations====
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*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
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====Circuits revisited====
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</div>
</div>

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====Inductors====
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*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
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==== Electromagnetic Radiation ====
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*[[Electromagnetic Radiation]]
</div>
</div>

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====Sparks in the air====
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*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

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====Superconductors====
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*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

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==Physics 3==

===Week 1===
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====Classical Physics====
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</div>
</div>

===Week 2===
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====Special Relativity====
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*[[Frame of Reference]]

*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
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====Photons====
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*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Week 4===
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====Matter Waves====
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*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
</div>
</div>

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====Schrödinger Equation====
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*[[Solution for a Single Free Particle]]
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]
*[[Solution for Simple Harmonic Oscillator (Xuen Zhen)]]
</div>
</div>

===Week 5===
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====Wave Mechanics====
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*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

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====Quantum Mechanics====
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*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

===Week 6===
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====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
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====The Hydrogen Atom====
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*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
*[[Molecules]]
*[[sp Molecular Bonds]]
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
*[[Application of Statistics in Physics]]
*[[Temperature & Entropy]]
</div>
<div class="mw-collapsible-content">

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>

Main Page

2022-04-24T17:42:46Z

Zach Shapiro: /* Special Relativity */

__NOTOC__
= '''Georgia Tech Student Wiki for Introductory Physics.''' =

This resource was created so that students can contribute and curate content to help those with limited or no access to a textbook. When reading this website, please correct any errors you may come across. If you read something that isn't clear, please consider revising it for future students!

Looking to make a contribution?
#Pick one of the topics from intro physics listed below
#Add content to that topic or improve the quality of what is already there.
#Need to make a new topic? Edit this page and add it to the list under the appropriate category. Then copy and paste the default [[Template]] into your new page and start editing.

Please remember that this is not a textbook and you are not limited to expressing your ideas with only text and equations. Whenever possible embed: pictures, videos, diagrams, simulations, computational models (e.g. Glowscript), and whatever content you think makes learning physics easier for other students.

== Source Material ==
All of the content added to this resource must be in the public domain or similar free resource. If you are unsure about a source, contact the original author for permission. That said, there is a surprisingly large amount of introductory physics content scattered across the web. Here is an incomplete list of intro physics resources (please update as needed).
* A physics resource written by experts for an expert audience [https://en.wikipedia.org/wiki/Portal:Physics Physics Portal]
* A wiki written for students by a physics expert [http://p3server.pa.msu.edu/coursewiki/doku.php?id=183_notes MSU Physics Wiki]
* A wiki book on modern physics [https://en.wikibooks.org/wiki/Modern_Physics Modern Physics Wiki]
* The MIT open courseware for intro physics [http://ocw.mit.edu/resources/res-8-002-a-wikitextbook-for-introductory-mechanics-fall-2009/index.htm MITOCW Wiki]
* An online concept map of intro physics [http://hyperphysics.phy-astr.gsu.edu/hbase/hph.html HyperPhysics]
* Interactive physics simulations [https://phet.colorado.edu/en/simulations/category/physics PhET]
* OpenStax intro physics textbooks: [https://openstax.org/details/books/university-physics-volume-1 Vol1], [https://openstax.org/details/books/university-physics-volume-2 Vol2], [https://openstax.org/details/books/university-physics-volume-3 Vol3]
* The Open Source Physics project is a collection of online physics resources [http://www.opensourcephysics.org/ OSP]
* A resource guide compiled by the [http://www.aapt.org/ AAPT] for educators [http://www.compadre.org/ ComPADRE]
* The Feynman lectures on physics are free to read [http://www.feynmanlectures.caltech.edu/ Feynman]
* Final Study Guide for Modern Physics II created by a lab TA [https://docs.google.com/document/d/1_6GktDPq5tiNFFYs_ZjgjxBAWVQYaXp_2Imha4_nSyc/edit?usp=sharing Modern Physics II Final Study Guide]

== Resources ==
* Commonly used wiki commands [https://en.wikipedia.org/wiki/Help:Cheatsheet Wiki Cheatsheet]
* A guide to representing equations in math mode [https://en.wikipedia.org/wiki/Help:Displaying_a_formula Wiki Math Mode]
* A page to keep track of all the physics [[Constants]]
* A listing of [[Notable Scientist]] with links to their individual pages

<div style="float:left; width:30%; padding:1%;">

==Physics 1==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====GlowScript 101====
<div class="mw-collapsible-content">
*[[Python Syntax]]
*[[GlowScript]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====VPython====

<div class="mw-collapsible-content">
*[[VPython]]
*[[VPython basics]]
*[[VPython Common Errors and Troubleshooting]]
*[[VPython Functions]]
*[[VPython Lists]]
*[[VPython Loops]]
*[[VPython Multithreading]]
*[[VPython Animation]]
*[[VPython Objects]]
*[[VPython 3D Objects]]
*[[VPython Reference]]
*[[VPython MapReduceFilter]]
*[[VPython GUIs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Vectors and Units====
<div class="mw-collapsible-content">
*[[Vectors]]
*[[SI Units]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Interactions====
<div class="mw-collapsible-content">
*[[Types of Interactions and How to Detect Them]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Velocity and Momentum====
<div class="mw-collapsible-content">
*[[Newton's First Law of Motion]]
*[[Mass]]
*[[Velocity]]
*[[Speed]]
*[[Speed vs Velocity]]
*[[Relative Velocity]]
*[[Derivation of Average Velocity]]
*[[2-Dimensional Motion]]
*[[3-Dimensional Position and Motion]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Momentum and the Momentum Principle====
<div class="mw-collapsible-content">
*[[Linear Momentum]]
*[[Newton's Second Law: the Momentum Principle]]
*[[Impulse and Momentum]]
*[[Net Force]]
*[[Inertia]]
*[[Acceleration]]
*[[Relativistic Momentum]]

</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Iterative Prediction with a Constant Force====
<div class="mw-collapsible-content">
*[[Iterative Prediction]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">

====Analytic Prediction with a Constant Force====
<div class="mw-collapsible-content">

*[[Kinematics]]
*[[Projectile Motion]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Iterative Prediction with a Varying Force====
<div class="mw-collapsible-content">
*[[Fundamentals of Iterative Prediction with Varying Force]]
*[[Spring_Force]]
*[[Simple Harmonic Motion]]


*[[Iterative Prediction of Spring-Mass System]]
*[[Terminal Speed]]
*[[Predicting Change in multiple dimensions]]
*[[Two Dimensional Harmonic Motion]]
*[[Determinism]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Fundamental Interactions====
<div class="mw-collapsible-content">
*[[Gravitational Force]]
*[[Gravitational Force Near Earth]]
*[[Gravitational Force in Space and Other Applications]]
*[[3 or More Body Interactions]]

*[[Electric Force]]
*[[Introduction to Magnetic Force]]
*[[Strong and Weak Force]]
*[[Reciprocity]]
*[[Conservation of Momentum]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Properties of Matter====
<div class="mw-collapsible-content">
*[[Kinds of Matter]]
*[[Ball and Spring Model of Matter]]
*[[Density]]
*[[Length and Stiffness of an Interatomic Bond]]
*[[Young's Modulus]]
*[[Speed of Sound in Solids]]
*[[Malleability]]
*[[Ductility]]
*[[Weight]]
*[[Hardness]]
*[[Boiling Point]]
*[[Melting Point]]
*[[Change of State]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Identifying Forces====
<div class="mw-collapsible-content">
*[[Free Body Diagram]]
*[[Inclined Plane]]
*[[Compression or Normal Force]]
*[[Tension]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Curving Motion====
<div class="mw-collapsible-content">
*[[Curving Motion]]
*[[Centripetal Force and Curving Motion]]
*[[Perpetual Freefall (Orbit)]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Energy Principle====
<div class="mw-collapsible-content">
*[[Energy of a Single Particle]]
*[[Kinetic Energy]]
*[[Work/Energy]]
*[[The Energy Principle]]
*[[Conservation of Energy]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Work by Non-Constant Forces====
<div class="mw-collapsible-content">
*[[Work Done By A Nonconstant Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential Energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
*[[Potential Energy of Macroscopic Springs]]
*[[Spring Potential Energy]]
*[[Ball and Spring Model]]
*[[Gravitational Potential Energy]]
*[[Energy Graphs]]
*[[Escape Velocity]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Multiparticle Systems====
<div class="mw-collapsible-content">
*[[Center of Mass]]
*[[Multi-particle analysis of Momentum]]
*[[Potential Energy of a Multiparticle System]]
*[[Work and Energy for an Extended System]]
*[[Internal Energy]]
**[[Potential Energy of a Pair of Neutral Atoms]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Choice of System====
<div class="mw-collapsible-content">
*[[System & Surroundings]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Thermal Energy, Dissipation, and Transfer of Energy====
<div class="mw-collapsible-content">
*[[Thermal Energy]]
*[[Specific Heat]]
*[[Calorific Value(Heat of combustion)]]
*[[First Law of Thermodynamics]]
*[[Second Law of Thermodynamics and Entropy]]
*[[Temperature]]
*[[Transformation of Energy]]
*[[The Maxwell-Boltzmann Distribution]]
*[[Air Resistance]]
*[[The Third Law of Thermodynamics]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Rotational and Vibrational Energy====
<div class="mw-collapsible-content">
*[[Translational, Rotational and Vibrational Energy]]
*[[Rolling Motion]]
</div>
</div>

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Different Models of a System====
<div class="mw-collapsible-content">
*[[Point Particle Systems]]
*[[Real Systems]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Friction====
<div class="mw-collapsible-content">
*[[Friction]]
*[[Static Friction]]
*[[Kinetic Friction]]
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====Conservation of Momentum====
<div class="mw-collapsible-content">
*[[Conservation of Momentum]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Collisions====
<div class="mw-collapsible-content">
*[[Newton's Third Law of Motion]]
*[[Collisions]]
*[[Elastic Collisions]]
*[[Inelastic Collisions]]
*[[Maximally Inelastic Collision]]
*[[Head-on Collision of Equal Masses]]
*[[Head-on Collision of Unequal Masses]]
*[[Scattering: Collisions in 2D and 3D]]
*[[Rutherford Experiment and Atomic Collisions]]
*[[Coefficient of Restitution]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Rotations====
<div class="mw-collapsible-content">
*[[Rotational Kinematics]]
*[[Eulerian Angles]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Angular Momentum====
<div class="mw-collapsible-content">
*[[Total Angular Momentum]]
*[[Translational Angular Momentum]]
*[[Rotational Angular Momentum]]
*[[The Angular Momentum Principle]]
*[[Angular Impulse]]
*[[Predicting the Position of a Rotating System]]
*[[The Moments of Inertia]]
*[[Right Hand Rule]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Analyzing Motion with and without Torque====
<div class="mw-collapsible-content">
*[[Torque]]
*[[Torque 2]]
*[[Systems with Zero Torque]]
*[[Systems with Nonzero Torque]]
*[[Torque vs Work]]
*[[Gyroscopes]]
</div>
</div>

===Week 15===
<div class="toccolours mw-collapsible mw-collapsed">
====Introduction to Quantum Concepts====
<div class="mw-collapsible-content">
*[[Bohr Model]]
*[[Energy graphs and the Bohr model]]
*[[Quantized energy levels]]
*[[Electron transitions]]
*[[Entropy]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 2==
===Week 1===
<div class="toccolours mw-collapsible mw-collapsed">
====3D Vectors====

<div class="mw-collapsible-content">
*[[Vectors]]
*[[Right-Hand Rule]]
*[[Right Hand Rule]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Field and Electric Potential]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric force====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric field of a point particle====
<div class="mw-collapsible-content">
*[[Point Charge]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Superposition====
<div class="mw-collapsible-content">
*[[Superposition Principle]]
*[[Superposition principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Dipoles====
<div class="mw-collapsible-content">
*[[Electric Dipole]]
*[[Magnetic Dipole]]
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Interactions of charged objects====
<div class="mw-collapsible-content">
*[[Electric Field]]
*[[Electric Potential]]
*[[Electric Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Tape experiments====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Polarization====
<div class="mw-collapsible-content">
*[[Polarization]]
*[[Electric Polarization]]
*[[Polarization of an Atom]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Conductors and Insulators====
<div class="mw-collapsible-content">
*[[Conductivity and Resistivity]]
*[[Insulators]]
*[[Potential Difference in an Insulator]]
*[[Conductors]]
*[[Polarization of a conductor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Charging and Discharging====
<div class="mw-collapsible-content">
*[[Charge Transfer]]
*[[Electrostatic Discharge]]
*[[Charged Conductor and Charged Insulator]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged rod====
<div class="mw-collapsible-content">
*[[Field of a Charged Rod|Charged Rod]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Field of a charged ring/disk/capacitor====
<div class="mw-collapsible-content">
*[[Charged Ring]]
*[[Charged Disk]]
*[[Charged Capacitor]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Field of a charged sphere====
<div class="mw-collapsible-content">
*[[Charged Spherical Shell]]
*[[Field of a Charged Ball]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Potential energy====
<div class="mw-collapsible-content">
*[[Potential Energy]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric potential====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
*[[Potential Difference in a Uniform Field]]
*[[Potential Difference of Point Charge in a Non-Uniform Field]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Sign of a potential difference====
<div class="mw-collapsible-content">
*[[Sign of a Potential Difference]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Potential at a single location====
<div class="mw-collapsible-content">
*[[Electric Potential]]
*[[Potential Difference at One Location]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Path independence and round trip potential====
<div class="mw-collapsible-content">
*[[Path Independence of Electric Potential]]
*[[Potential Difference Path Independence, claimed by Aditya Mohile]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in an insulator====
<div class="mw-collapsible-content">
*[[Potential Difference in an Insulator]]
*[[Electric Field in an Insulator]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Moving charges in a magnetic field====
<div class="mw-collapsible-content">
*[[Magnetic Field]]
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">
====Biot-Savart Law====
<div class="mw-collapsible-content">
*[[Biot-Savart Law]]
*[[Biot-Savart Law for Currents]]
</div>
</div>
<div class="toccolours mw-collapsible mw-collapsed">

====Moving charges, electron current, and conventional current====
<div class="mw-collapsible-content">
*[[Moving Point Charge]]
*[[Current]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a wire====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Long Straight Wire]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Magnetic field of a current-carrying loop====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Loop]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic field of a Charged Disk====
<div class="mw-collapsible-content">
*[[Magnetic Field of a Disk]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic dipoles====
<div class="mw-collapsible-content">
*[[Magnetic Dipole Moment]]
*[[Bar Magnet]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Atomic structure of magnets====
<div class="mw-collapsible-content">
*[[Atomic Structure of Magnets]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Steady state current====
<div class="mw-collapsible-content">
*[[Steady State]]
*[[Non Steady State]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Kirchoff's Laws====
<div class="mw-collapsible-content">
*[[Kirchoff's Laws]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Electric fields and energy in circuits====
<div class="mw-collapsible-content">
*[[Electric Potential Difference]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Macroscopic analysis of circuits====
<div class="mw-collapsible-content">
*[[Series Circuits]]
*[[Parallel Circuits]]
*[[Parallel Circuits vs. Series Circuits*]]
*[[Loop Rule]]
*[[Node Rule]]
*[[Fundamentals of Resistance]]
*[[Problem Solving]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Electric field and potential in circuits with capacitors====
<div class="mw-collapsible-content">
*[[Charging and Discharging a Capacitor]]
*[[RC Circuit]]
*[[R Circuit]]
*[[AC and DC]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic forces on charges and currents====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[Motors and Generators]]
*[[Applying Magnetic Force to Currents]]
*[[Magnetic Force in a Moving Reference Frame]]
*[[Right-Hand Rule]]
*[[Analysis of Railgun vs Coil gun technologies]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Electric and magnetic forces====
<div class="mw-collapsible-content">
*[[Electric Force]]
*[[Magnetic Force]]
*[[Lorentz Force]]
*[[VPython Modelling of Electric and Magnetic Forces]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Velocity selector====
<div class="mw-collapsible-content">
*[[Lorentz Force]]
*[[Combining Electric and Magnetic Forces]]
</div>
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">

====Hall Effect====
<div class="mw-collapsible-content">
*[[Hall Effect]]
<h1><strong>Alayna Baker Spring 2020</strong></h1>
[[File:Hall Effect 1.jpg]]
[[File:Hall Effect 2.jpg]]

*[[Right-Hand Rule]]
*[[Motional Emf]]
*[[Magnetic Force]]
*[[Magnetic Torque]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

]]]====Motional EMF====

<div class="mw-collapsible-content">
*[[Motional Emf]]
<h1><strong>Adeline Boswell Fall 2019</strong></h1>
[[File:Motional EMF Example.jpg]]

*[[Motional Emf using Faraday's Law]]
</div>
</div>http://www.physicsbook.gatech.edu/Special:RecentChangesLinked/Main_Page

<div class="toccolours mw-collapsible mw-collapsed">

If you have a bar attached to two rails, and the rails are connected by a resistor, you have effectively created a circuit. As the bar moves, it creates an "electromotive force"

[[File:MotEMFCR.jpg]]

====Magnetic force====
<div class="mw-collapsible-content">
*[[Magnetic Force]]
*[[Lorentz Force]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Magnetic torque====
<div class="mw-collapsible-content">
*[[Magnetic Torque]]
*[[Right-Hand Rule]]
</div>
</div>

===Week 12===

<div class="toccolours mw-collapsible mw-collapsed">
====Gauss's Law====
<div class="mw-collapsible-content">
*[[Gauss's Flux Theorem]]
*[[Gauss's Law]]
*[[Magnetic Flux]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Ampere's Law====
<div class="mw-collapsible-content">
*[[Ampere's Law]]
*[[Ampere-Maxwell Law]]
*[[Magnetic Field of Coaxial Cable Using Ampere's Law]]
*[[Magnetic Field of a Long Thick Wire Using Ampere's Law]]
*[[Magnetic Field of a Toroid Using Ampere's Law]]
*[[Magnetic Field of a Solenoid Using Ampere's Law]]
*[[The Differential Form of Ampere's Law]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Semiconductors====
<div class="mw-collapsible-content">
*[[Semiconductor Devices]]
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</div>

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====Faraday's Law====
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*[[Faraday's Law]]
*[[Motional Emf using Faraday's Law]]
*[[Lenz's Law]]

</div>
</div>

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====Maxwell's equations====
<div class="mw-collapsible-content">
*[[Gauss's Law]]
*[[Magnetic Flux]]
*[[Ampere's Law]]
*[[Faraday's Law]]
*[[Maxwell's Electromagnetic Theory]]
</div>
</div>

===Week 14===
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====Circuits revisited====
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</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Inductors====
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*[[Inductors]]
*[[Current in an LC Circuit]]
*[[Current in an RL Circuit]]
</div>
</div>

===Week 15===
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==== Electromagnetic Radiation ====
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*[[Electromagnetic Radiation]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Sparks in the air====
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*[[Sparks in Air]]
*[[Spark Plugs]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Superconductors====
<div class="mw-collapsible-content">
*[[Superconducters]]
*[[Superconductors]]
*[[Meissner effect]]
</div>
</div>
</div>

<div style="float:left; width:30%; padding:1%;">

==Physics 3==

===Week 1===
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====Classical Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 2===
<div class="toccolours mw-collapsible mw-collapsed">
====Special Relativity====
Edited by Zachary Shapiro
<div class="mw-collapsible-content">
*[[Frame of Reference]]

*[[Einstein's Theory of Special Relativity]]
*[[Time Dilation]]
*[[Einstein's Theory of General Relativity]]
*[[Albert A. Micheleson & Edward W. Morley]]
*[[Magnetic Force in a Moving Reference Frame]]
</div>
</div>

===Week 3===
<div class="toccolours mw-collapsible mw-collapsed">
====Photons====
<div class="mw-collapsible-content">
*[[Spontaneous Photon Emission]]
*[[Light Scattering: Why is the Sky Blue]]
*[[Lasers]]
*[[Electronic Energy Levels and Photons]]
*[[Quantum Properties of Light]]
*[[The Photoelectric Effect]]
</div>
</div>

===Week 4===
<div class="toccolours mw-collapsible mw-collapsed">
====Matter Waves====
<div class="mw-collapsible-content">
*[[Wave-Particle Duality]]
*[[Particle in a 1-Dimensional box]]
*[[Heisenberg Uncertainty Principle]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">

====Schrödinger Equation====
<div class="mw-collapsible-content">
*[[Solution for a Single Free Particle]]
*[[Solution for a Single Particle in an Infinite Quantum Well - Darin]]
*[[Solution for a Single Particle in a Semi-Infinite Quantum Well]]
*[[Solution for Simple Harmonic Oscillator (Xuen Zhen)]]
</div>
</div>

===Week 5===
<div class="toccolours mw-collapsible mw-collapsed">
====Wave Mechanics====
<div class="mw-collapsible-content">
*[[Standing Waves]]
*[[Wavelength]]
*[[Wavelength and Frequency]]
*[[Mechanical Waves]]
*[[Transverse and Longitudinal Waves]]
</div>
</div>

<div class="toccolours mw-collapsible mw-collapsed">
====Quantum Mechanics====
<div class="mw-collapsible-content">
*[[Quantum Tunneling through Potential Barriers]]
</div>
</div>

===Week 6===
<div class="toccolours mw-collapsible mw-collapsed">
====Rutherford-Bohr Model====
<div class="mw-collapsible-content">
*[[Rutherford Experiment and Atomic Collisions]]
*[[Bohr Model]]
*[[Quantized energy levels]]
*[[Energy graphs and the Bohr model]]
</div>
</div>

===Week 7===
<div class="toccolours mw-collapsible mw-collapsed">
====The Hydrogen Atom====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
</div>
</div>

===Week 8===
<div class="toccolours mw-collapsible mw-collapsed">
====Many-Electron Atoms====
<div class="mw-collapsible-content">
*[[Quantum Theory]]
*[[Atomic Theory]]
*[[Pauli exclusion principle]]
</div>
</div>

===Week 9===
<div class="toccolours mw-collapsible mw-collapsed">
====Molecules====
<div class="mw-collapsible-content">
</div>
*[[Molecules]]
*[[sp Molecular Bonds]]
</div>

===Week 10===
<div class="toccolours mw-collapsible mw-collapsed">
====Statistical Physics====
<div class="mw-collapsible-content">
</div>
*[[Application of Statistics in Physics]]
*[[Temperature & Entropy]]
</div>
<div class="mw-collapsible-content">

===Week 11===
<div class="toccolours mw-collapsible mw-collapsed">
====Condensed Matter Physics====
<div class="mw-collapsible-content">
</div>
</div>

===Week 12===
<div class="toccolours mw-collapsible mw-collapsed">
====The Nucleus====
<div class="mw-collapsible-content">
*[[Nucleus]]
</div>
</div>

===Week 13===
<div class="toccolours mw-collapsible mw-collapsed">
====Nuclear Physics====
<div class="mw-collapsible-content">
*[[Nuclear Fission]]
*[[Nuclear Energy from Fission and Fusion]]
</div>
</div>

===Week 14===
<div class="toccolours mw-collapsible mw-collapsed">
====Particle Physics====
<div class="mw-collapsible-content">
*[[Elementary Particles and Particle Physics Theory]]
*[[String Theory]]
</div>
</div>
</div>