# Photon and energy level

bloupo
What if an electron at a certain energy level receive a little bit more energy from a photon than the difference between its current energy level and the next one, will it jump to it ?
I see written in textbooks that the photon energy must exactly match the difference between two energy level for the electron to jump from one to the other. So what ? let's say an electron with the difference btw its actual energy level and the next one of 12eV and a photon of 12,4 eV knock on his door , will he just ignore him bc is not exactly 12 or will it jump to the next one and keep some of this energy ??

Thanks

Staff Emeritus
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The electron must have exactly 12 eV of energy to jump to the next energy level. However, I'm not sure if the extra 0.4 eV can be absorbed by the whole atom/molecule in some way. Perhaps this can only occur in molecules or bulk materials since they have far more degrees of freedom and energy levels?

bloupo
thank yo, so the electron will actually jump from one energy level to the other(considering the 12eV difference in energy levels) if it encounters a photon of 12,4 eV right ??

Staff Emeritus
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No, there is no guarantee. If there is nowhere for the extra energy to go, then it will not jump.

Homework Helper
Gold Member
Some of the extra energy can go into exciting translational degrees of freedom of the atom, i.e. the atom also has some kinetic energy after the transition. This probably tends to be washed away to some extent by the Doppler broadening of the spectral lines, which is due to the motion of the atoms before the transition, and is probably a larger effect.

Zarqon
Well, first off, nothing is perfectly monocromatic (or mono energetic), there's a built-in uncertainty in both the source and the electron, and if the width if those distributions overlap then there is still a non-zero probability that the transition occurs. This probability simply rises the closer to resonance you get.

Secondly, an assisted transition can occur, as was mentioned above, and this is when the energy difference is made up for by something else. In gases this is often doppler shifts from atoms increasing or decreasing their speed as a result of the interaction and in solids it is often phonons that can get absorbed or deposited in the process to conserve energy.

Thirdly, even if the energy does not match up in the end, the "transition" can still occur during a sufficiently short time intervall, before the wavefuntion has canceled due to destructive interference. This is usually not referred to as a real transition, but as a "virtual energy level", and this feature is significant in for examlpe two-photon raman transitions which can occur also far off-resonantly.

Staff Emeritus
2022 Award
Well, first off, nothing is perfectly monocromatic (or mono energetic), there's a built-in uncertainty in both the source and the electron, and if the width if those distributions overlap then there is still a non-zero probability that the transition occurs. This probability simply rises the closer to resonance you get.

Interesting. I was not aware that this could occur. Any chance you could elaborate a bit?

Mentor
Interesting. I was not aware that this could occur. Any chance you could elaborate a bit?

Considering an atom, this is simply an expression of the Heisenberg uncertainty principle. Apart from the ground state, all electronic states have a finite lifetime, as an excited electron will eventually decay. This finiteness of ##\Delta t## means that there is an uncertainty ##\Delta E > 0## on the exact energy of the excited state. We say that the state has a certain width in energy, which is inversely proportional to its lifetime.

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