Energy Relationships in Absorption and Emission

[Alex Nguyen 3I]

How is the energy that energizes an electron related to the photon that is emitted if it is ejected. How is the incoming energy related to the energy of an electron if it is not ejected but moves from an energy level to another?

[Nathan Danielsen 1G]

If a photon has enough energy to remove an electron from a material then no electromagnetic radiation will be emitted. Electrons emit EM radiation when they move down energy levels, so an electron that has escaped completely will not move back down energy levels, and therefore will not emit EM radiation. If the energy of the photon exceeds the energy required to remove the electron, that excess energy is translated into the kinetic energy of the emitted electron, as the electron absorbs the entire photon's energy. If a photon does not have enough energy to remove an electron, it will still excite it, moving it to a higher energy level. More energy will move the electron to a higher energy level. By the time the electron moves back down to its ground state, it will have released the same amount of EM energy as it absorbed from the initial photon. Even if the electron takes multiple jumps, the total energy released will still be the same. For example: When the electron goes from n=3 to n=2, and then from n=2 to n=1. The two EM waves will have the same total energy as when the electron moves from n=3 to n=1. I hope you find this helpful.

[Chem_Mod]

Nathan is relative right in all things except for the fact that the photon absorbed must have EXACTLY the energy to remove the electron for the hydrogen atom. If the energy that holds the electron is -13.6 eV and you supplied a photon with 13.7 eV, you will not get an electron that is more energetic but the photon will have just passed through. This is because the energy levels are discrete in the hydrogen atom which is verified by the observation of discrete spectral lines in its spectrum.

In the photoelectric effect, on the other hand, the material does not have discrete energy levels as they are compounds and macroscopic objects. Each individual atom in the material has different energy levels which combines and blurs the overall energy spectrum. Thus, in the photoelectric effect, photon absorption can occur from a continuous spectrum of photon energy levels.