Electronic Energy Levels and Photons
Short Description of Topic
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]\displaystyle{ {\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.
A Computational Model
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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
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See also
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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.