Physics Book - User contributions [en]

Quantized energy levels

2015-12-03T03:32:06Z

Wporter8:

Created by Keller Porter

The nucleus of each every atom creates an electric field, and it is composed of different levels, or stationary orbits, and each one requires a different energy level for an electron to reside there. The electrons in this electric field are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]]
[[File:emission spectrum.jpg|thumb|right|An emission spectrum graph for hydrogen.]]

If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. This process creates something called an absorption spectrum. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. 

===Atom Energy Stability===

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

[[File:Bohr atom.gif|thumb|right|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces. The base energy level, called the ground state, is the first stationary orbit. From there, there can be many more levels. The energy of each level can be denoted <math>E_n</math>, <math>n=1,2,3...</math>. At the ground state, the energy required to free the electron is greatest. It requires a specific level of energy to excite an electron to another energy level, and energy can be released to bring the electron back down to the ground state. 

===Energy Level Calculations===

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground level energy of <math>E_R = 13.6eV</math>. With Rydberg's constant, the initial formula for energy levels can be altered to include this. This new formula is: 
<math>E_n = \frac{-E_R}{n^2}</math>

===Basic Level Calculation===

Find the energy level for the level <math>n=6</math>. 
 Solution: <math>E_6 = \frac{-13.6}{6^2} = -.378eV</math>

===Level Change Calculation===

Will an electron with energy <math>E_{electron} = 10.4eV</math> be able to bump a hydrogen electron in the ground state to the second level? 
 Solution: <math>E_1 = \frac{-13.6}{1} = -13.6eV</math> 
<math>E_2 = \frac{-13.6}{2^2} = \frac{-13.6}{4} = -3.4eV</math> 
<math>E_2 - E_1 = -3.4eV - -13.6eV = 10.2eV</math>, so it requires <math>10.2eV</math> to bump an electron from the ground state to the second level. 
<math>10.4eV \ge 10.2eV</math> 
Yes, the electron has enough energy to bump the electron from the ground state to the second energy level.

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-03T03:30:54Z

Wporter8: /* Example: Hydrogen Model */

Created by Keller Porter

The nucleus of each every atom creates an electric field, and it is composed of different levels, or stationary orbits, and each one requires a different energy level for an electron to reside there. The electrons in this electric field are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]]
[[File:emission spectrum.jpg|thumb|right|An emission spectrum graph for hydrogen.]]

If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. This process creates something called an absorption spectrum. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. 

===Atom Energy Stability===

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

[[File:Bohr atom.gif|thumb|right|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces. The base energy level, called the ground state, is the first stationary orbit. From there, there can be many more levels. The energy of each level can be denoted <math>E_n</math>, <math>n=1,2,3...</math>. At the ground state, the energy required to free the electron is greatest. It requires a specific level of energy to excite an electron to another energy level, and energy can be released to bring the electron back down to the ground state. 

===Energy Level Calculations===

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground level energy of <math>E_R = 13.6eV</math>. With Rydberg's constant, the initial formula for energy levels can be altered to include this. This new formula is: 
<math>E_n = \frac{-E_R}{n^2}</math>

===Basic Level Calculation===

Find the energy level for the level <math>n=6</math>. 
 Solution: <math>E_6 = \frac{-13.6}{6^2}</math>

===Level Change Calculation===

Will an electron with energy <math>E_{electron} = 10.4eV</math> be able to bump a hydrogen electron in the ground state to the second level? 
 Solution: <math>E_1 = \frac{-13.6}{1} = -13.6eV</math> 
<math>E_2 = \frac{-13.6}{2^2} = \frac{-13.6}{4} = -3.4eV</math> 
<math>E_2 - E_1 = -3.4eV - -13.6eV = 10.2eV</math>, so it requires <math>10.2eV</math> to bump an electron from the ground state to the second level. 
<math>10.4eV \gre 10.2eV</math> 
Yes, the electron has enough energy to bump the electron from the ground state to the second energy level.

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-03T03:17:39Z

Wporter8: /* References */

Created by Keller Porter

The nucleus of each every atom creates an electric field, and it is composed of different levels, or stationary orbits, and each one requires a different energy level for an electron to reside there. The electrons in this electric field are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]]
[[File:emission spectrum.jpg|thumb|right|An emission spectrum graph for hydrogen.]]

If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. This process creates something called an absorption spectrum. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. 

===Atom Energy Stability===

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

[[File:Bohr atom.gif|thumb|right|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces. The base energy level, called the ground state, is the first stationary orbit. From there, there can be many more levels. The energy of each level can be denoted <math>E_n</math>, <math>n=1,2,3...</math>. At the ground state, the energy required to free the electron is greatest. It requires a specific level of energy to excite an electron to another energy level, and energy can be released to bring the electron back down to the ground state. 

===Energy Level Calculations===

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground energy of <math>E_1 = 13.6eV</math>. This is a good way to practice the principles of quantized energy levels. With Rydberg's constant, the initial formula for energy levels can be altered. This new formula is: 
<math>E_n = \frac{-E_r}{n^2}</math>

===Simple===
===Middling===
===Difficult===

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-03T03:16:52Z

Wporter8: /* References */

Created by Keller Porter

The nucleus of each every atom creates an electric field, and it is composed of different levels, or stationary orbits, and each one requires a different energy level for an electron to reside there. The electrons in this electric field are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]]
[[File:emission spectrum.jpg|thumb|right|An emission spectrum graph for hydrogen.]]

If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. This process creates something called an absorption spectrum. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. 

===Atom Energy Stability===

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

[[File:Bohr atom.gif|thumb|right|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces. The base energy level, called the ground state, is the first stationary orbit. From there, there can be many more levels. The energy of each level can be denoted <math>E_n</math>, <math>n=1,2,3...</math>. At the ground state, the energy required to free the electron is greatest. It requires a specific level of energy to excite an electron to another energy level, and energy can be released to bring the electron back down to the ground state. 

===Energy Level Calculations===

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground energy of <math>E_1 = 13.6eV</math>. This is a good way to practice the principles of quantized energy levels. With Rydberg's constant, the initial formula for energy levels can be altered. This new formula is: 
<math>E_n = \frac{-E_r}{n^2}</math>

===Simple===
===Middling===
===Difficult===

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - *http://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - *http://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

File:Level change.jpg

2015-12-03T03:15:18Z

Wporter8:

Quantized energy levels

2015-12-03T03:14:50Z

Wporter8:

Created by Keller Porter

The nucleus of each every atom creates an electric field, and it is composed of different levels, or stationary orbits, and each one requires a different energy level for an electron to reside there. The electrons in this electric field are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized. Quantization is a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight that were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]]
[[File:emission spectrum.jpg|thumb|right|An emission spectrum graph for hydrogen.]]

If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. This process creates something called an absorption spectrum. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. 

===Atom Energy Stability===

In 1911, Rutherford came up with his model for the atom. It used all the same components of an atom that we know exist today, but it had one glaring issue. His model lacked stability. Classical electromagnetic theory said that the electrons surrounding the nucleus would quickly collapse because they were emitting electromagnetic waves, causing them to lose energy. If this were true, then the atom as we know it would not be able to exist. 

[[File:Bohr atom.gif|thumb|right|This is a model of the Bohr atom. It shows different levels for the electrons to orbit the nucleus.]]

 Bohr's model of the atom solved this problem. He proposed that the laws of classical mechanics must be reconsidered. His model said that the electron cloud had stationary orbits, a specific set of orbits for electrons. This differed from the assumption that the electron cloud was just a continuum where the electrons were free to orbit the nucleus. His model was similar to the solar system in that electrons orbit the nucleus like planets orbit the sun. Electrons are held in place by electrostatic forces, and planets are held in place by gravitational forces. The base energy level, called the ground state, is the first stationary orbit. From there, there can be many more levels. The energy of each level can be denoted <math>E_n</math>, <math>n=1,2,3...</math>. At the ground state, the energy required to free the electron is greatest. It requires a specific level of energy to excite an electron to another energy level, and energy can be released to bring the electron back down to the ground state. 

===Energy Level Calculations===

The energy of each level can be found using the formula: 
<math>E_n = \frac{-2\pi^2me^4Z^2}{n^2h^2}</math>
 where <math>m</math> is the mass of an electron, <math>e</math> is the magnitude of the electric charge, <math>n</math> is the quantum number, <math>h</math> is Planck's constant, and <math>Z</math> is the atomic number of the atom. This gives the energy for a specific atom at each energy level. The value will always be negative because electrons in the electron cloud are in a bounded state, so the potential energy is negative. 

[[File:level change.jpg|thumb|left|This represents the different levels that electrons can jump between provided they acquire energy from either another electron or a photon.]]

 While the value for each energy level is set in place, the energy of each individual electron can change. This can happen either by an interaction with another electron or a photon. For an electron, they can jump from the ground state to the fourth level if <math>E_{particle} \ge E_4-E_1</math>

==Example: Hydrogen Model==

Research done by Johannes Rydberg showed that hydrogen has a ground energy of <math>E_1 = 13.6eV</math>. This is a good way to practice the principles of quantized energy levels. With Rydberg's constant, the initial formula for energy levels can be altered. This new formula is: 
<math>E_n = \frac{-E_r}{n^2}</math>

===Simple===
===Middling===
===Difficult===

==Implications==

Until quantization of atomic energy levels occurred, there were a few different experiments that had already been performed that did not make sense. Once researchers discovered the actual way electrons make up the electron cloud as well as the mechanisms that help them jump from level to level, these experiments could be explained. Readings for these three experiments can be found below.

#[https://en.wikipedia.org/wiki/Black-body_radiation Blackbody Radiation]
#[https://en.wikipedia.org/wiki/Photoelectric_effect Photoelectric Effect]
#[https://en.wikipedia.org/wiki/Emission_spectrum Emission Spectra of Atoms]

==References==

*http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html
*http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_1.html
*http://www.colorado.edu/UCB/AcademicAffairs/ArtsSciences/physics/TZD/PageProofs1/TAYL05-144-167.I.pdf
*"Emission spectrum-H" by Merikanto, Adrignola - File:Emission spectrum-H.png. Licensed under CC0 via Commons - *https://commons.wikimedia.org/wiki/File:Emission_spectrum-H.svg#/media/File:Emission_spectrum-H.svg
*"Fraunhofer lines" by Fraunhofer_lines.jpg: nl:Gebruiker:MaureenVSpectrum-sRGB.svg: PhroodFraunhofer_lines_DE.svg: *Fraunhofer_lines.jpg: Saperaud 19:26, 5. Jul. 2005derivative work: Cepheiden (talk)derivative work: Cepheiden (talk) - Fraunhofer_lines.jpgSpectrum-sRGB.svgFraunhofer_lines_DE.svg. Licensed under Public Domain via Commons - https://commons.wikimedia.org/wiki/File:Fraunhofer_lines.svg#/media/File:Fraunhofer_lines.svg
*http://venables.asu.edu/quant/Dinesh/Bohratom2.html (bohr atom)
*"Energy levels" by SVG: Hazmat2 Original: Rozzychan - This file was derived from: Energylevels.png. Licensed under CC BY-SA 3.0 via Commons - *https://commons.wikimedia.org/wiki/File:Energy_levels.svg#/media/File:Energy_levels.svg

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-03T03:04:45Z

Wporter8:

Quantized energy levels

2015-12-03T02:53:11Z

Wporter8:

Quantized energy levels

2015-12-03T02:50:50Z

Wporter8:

Quantized energy levels

2015-12-03T02:40:08Z

Wporter8: /* Energy Calculations */

Quantized energy levels

2015-12-03T02:39:18Z

Wporter8:

Quantized energy levels

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Wporter8:

Quantized energy levels

2015-12-03T02:26:03Z

Wporter8:

Quantized energy levels

2015-12-03T02:24:00Z

Wporter8:

Quantized energy levels

2015-12-03T02:21:32Z

Wporter8:

Quantized energy levels

2015-12-03T02:16:27Z

Wporter8:

Quantized energy levels

2015-12-03T02:07:50Z

Wporter8:

File:Bohr atom.gif

2015-12-03T02:06:27Z

Wporter8: Model of a Bohr Atom, showing different electron orbits.

Model of a Bohr Atom, showing different electron orbits.

Quantized energy levels

2015-12-03T02:03:44Z

Wporter8:

Quantized energy levels

2015-12-03T01:54:44Z

Wporter8:

Quantized energy levels

2015-12-03T01:53:25Z

Wporter8:

Quantized energy levels

2015-12-03T01:17:59Z

Wporter8:

Quantized energy levels

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Wporter8:

Quantized energy levels

2015-12-03T00:36:56Z

Wporter8:

Quantized energy levels

2015-12-02T23:37:00Z

Wporter8:

Quantized energy levels

2015-12-02T23:25:44Z

Wporter8:

Created by Keller Porter

Each atom has an electron cloud, and the electron cloud is composed of levels, each one requiring a different energy level for an electron to reside there. The electrons in an electron cloud are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized, or a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight there were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]][[File:emission spectrum.jpg|thumb|right|An emission spectrum graph for hydrogen.]]

This is known as an absorption spectrum. If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. This is important because it sets up the basis for the way electrons in the electron cloud change from one level to the next. Atoms have a base energy level, called the ground state. At the ground state, the energy required to free the electron is greatest.

===A Computational Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-02T21:56:56Z

Wporter8:

Created by Keller Porter

Each atom has an electron cloud, and the electron cloud is composed of levels, each one requiring a different energy level for an electron to reside there. The electrons in an electron cloud are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized, or a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight there were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]][[File:emission spectrum.jpg|thumb|right|An emission spectrum graph for hydrogen.]]

This is known as an absorption spectrum. If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines. This is important because it sets up the basis for the way electrons in the electron cloud change from one level to the next. Atoms have a base energy level, called the ground state. At the ground state, the energy required to free the electron is greatest. Since the nucleus

===A Computational Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-02T21:45:16Z

Wporter8:

Created by Keller Porter

Each atom has an electron cloud, and the electron cloud is composed of levels, each one requiring a different energy level for an electron to reside there. The electrons in an electron cloud are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized, or a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight there were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]][[File:emission spectrum.jpg|thumb|right|An emission spectrum graph for hydrogen.]]

This is known as an absorption spectrum. If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines.

===A Computational Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

File:Emission spectrum.jpg

2015-12-02T21:44:33Z

Wporter8: An emission spectrum of hydrogen.

An emission spectrum of hydrogen.

Quantized energy levels

2015-12-02T21:44:03Z

Wporter8:

Created by Keller Porter

Each atom has an electron cloud, and the electron cloud is composed of levels, each one requiring a different energy level for an electron to reside there. The electrons in an electron cloud are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized, or a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight there were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]][[File:emission spectrum.jpg]]

This is known as an absorption spectrum. If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines.

===A Computational Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-02T21:43:16Z

Wporter8:

Created by Keller Porter

Each atom has an electron cloud, and the electron cloud is composed of levels, each one requiring a different energy level for an electron to reside there. The electrons in an electron cloud are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized, or a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight there were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. 

[[File:Absorption spectrum.jpg|thumb|right|A typical absorption spectrum graph.]]

This is known as an absorption spectrum. If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines.

===A Computational Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

File:Absorption spectrum.jpg

2015-12-02T21:39:05Z

Wporter8: Example of a typical absorption spectrum.

Example of a typical absorption spectrum.

Quantized energy levels

2015-12-02T21:26:10Z

Wporter8:

Created by Keller Porter

Each atom has an electron cloud, and the electron cloud is composed of levels, each one requiring a different energy level for an electron to reside there. The electrons in an electron cloud are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized, or a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight there were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. This is known as an absorption spectrum. If light is shone through a gas, the gas will absorb the specific wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light or a diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. Similarly, if this same gas was heated to the right temperature, it would emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines.

===A Computational Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-02T21:22:50Z

Wporter8:

Created by Keller Porter

Each atom has an electron cloud, and the electron cloud is composed of levels, each one requiring a different energy level for an electron to reside there. The electrons in an electron cloud are in a bound state, requiring energy to be removed from their current energy level. These energy levels are considered quantized, or a transition from a classical understanding of physical principles to a more modern understanding.

===Background===

In the 1814, Joseph von Fraunhofer and William Hyde Wollaston discovered that when viewed closely, the spectrum from sunlight contained dark lines. These lines represented wavelengths of sunlight there were not reaching us. These wavelengths were being absorbed by the sun's atmosphere. This is known as an absorption spectrum. If light is shone through a gas, the gas will absorb the wavelengths characteristic of the atoms in the gas. If the light were to be put through a prism of light diffraction grating, then there would be absorption lines, or places where the wavelength of light had been absorbed into the gas. Similarly, if a gas is heated to the right temperature, it can emit the same wavelengths that it absorbed before. Putting this emitted light through a prism or diffraction grating would create an emission spectrum. This is the opposite of an absorption spectrum because it shows the emission lines from the gas instead of the absorption lines.

===A Computational Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings. How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-02T21:05:01Z

Wporter8:

Quantized energy levels

2015-12-02T20:58:29Z

Wporter8:

Quantized energy levels

2015-12-02T20:44:31Z

Wporter8:

Created by Keller Porter

Each atom has an electron cloud, and the electron cloud is composed of levels, each one requiring a different energy level for an electron to reside there.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-02T20:43:51Z

Wporter8:

Claimed by wporter8

Each atom has an electron cloud, and the electron cloud is composed of levels, each one requiring a different energy level for an electron to reside there.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-02T20:42:58Z

Wporter8: /* The Main Idea */

Claimed by wporter8

==The Main Idea==

Each atom has an electron cloud, and the electron cloud is composed of levels, each one requiring a different energy level for an electron to reside there.

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-02T04:10:24Z

Wporter8:

Claimed by wporter8

==The Main Idea==

State, in your own words, the main idea for this topic
Electric Field of Capacitor

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Quantized energy levels

2015-12-02T03:59:04Z

Wporter8:

Claimed by wporter8