What happens to excess energy when an electron gets excited by light?

[Richard2001]

TL;DR Summary

I do not understand what happen when in electron in atom gets excited by incident light and a very small amount of excess energy remains. What happens to this excess energy?

Hello,

I am struggerling with this very basic physics problem. I understand that an electron can get excited if the energy of an incident photon is enough to jump to a higher band. If I understand correctly, this will only use up exactely the required energy. What I do not understand is what happens with the leftover energy, especially, if it is very little.

To make it more concrete: Assume hydrogen is excited from n = 1 to n = 2.
If I understand wikipedia and the Rydberg formula correctly, excited the electron would require around 121.57nm.
What would happen if the incident light was of wavelength 121.56nm?
This would result in a excess energy with wavelength 1/(1/121.56nm - 1/121.57nm) = 1.5mm (if I a not mistaken).

So, would this emit microwaves? Wouldn't a lot of things emit mircowaves and radiowaves in sunlight in this case?

 

[Baluncore]

Welcome to PF.

Things get hot when placed in the sunlight, and not only from the IR part of the solar spectrum.

The transition is thermally broadened to accept the available energy. That means there will be no left-over energy, or it will appear as vibrational heat in the chemistry, rather than as another photon.

 

[hutchphd]

TL;DR Summary: I do not understand what happen when in electron in atom gets excited by incident light and a very small amount of excess energy remains. What happens to this excess energy?

What would happen if the incident light was of wavelength 121.56nm?

Another way to think about this is that the energy levels of real atoms are not "perfectly sharp" unless each atom is perfectly isolated. Given any assemblage of matter each atom will see a slightly different environment that is also likely time dependent. Averaging over these variabilities gives a range of possible energies. Also If the hydrogen is a gas the motion can produce Doppler shifts in photon frequencies of absorption.
This is usually formally treated by associating the width of a resonance .

 

[Baluncore]

https://en.wikipedia.org/wiki/Doppler_broadening

 

[DaveC426913]

...the electron would require around 121.57nm.
What would happen if the incident light was of wavelength 121.56nm?...

And (correct me if I'm wrong) another possibility here is that - if that energy discrepancy were sufficiently large - that light would bypass the electron - perhaps many - to the point where it can conceivably pass right through the material and out the other side - IWO the material is transparent to that wavelength of light.

 

[snorkack]

Another way to think about this is that the energy levels of real atoms are not "perfectly sharp" unless each atom is perfectly isolated.

Nor are the energy levels perfectly sharp unless the state is longlived. Heisenberg uncertainty.
What happens when there is a small shortfall of energy?
The 1s state is longlived (it is the ground state)
The 2p state is shortlived (unlike the 2s-1s transition which is forbidden making the 2s state longlived).
Suppose that you irradiate atomic hydrogen with incident light which is selected to be a narrower band than the intrinsic Heisenberg width of the 2p-1s transition, and also is slightly redshifted to fall on the shoulder, not the peak of the hydrogen line.
Will the hydrogen be forced to emit light of the same spectrum as incident light (other than the part transmitted) because of conservation of energy?

 

[hutchphd]

By supposition you have said that the atom is not in an energy eigenstate. So one does not know precisely the energy of the system light+atom. Energy will be conserved but that does not completely constrain the energy of the emiitted light quantum.

 

[snorkack]

By supposition you have said that the atom is not in an energy eigenstate. So one does not know precisely the energy of the system light+atom. Energy will be conserved but that does not completely constrain the energy of the emiitted light quantum.

The atom starts at a long lived, ground state (1s). So we know precisely the energy of atom, and the initial photon.
The absorption forms a shortlived but defined 2p state, whose width exceeds the uncertainty of the initial state.
Now that 2p state exists and eventually decays. To 1p state, whose energy is narrow, and a photon.
Does the reemitted photon have the full width of the intermediate 2p state, or is it constrained to have same energy (and same width) as the initially absorbed photon?