Matching Photon and Atom Energies

Most recent answer: 04/07/2017

Q:
We are taught that an electron in an atom can absorb an incoming photon and get kicked up to a higher energy level, but something has always puzzled me about that.Let's say we have an atom where the electron needs 3 units of energy to get bumped up to the first excited state from the ground state, but it needs 5 units of energy to get bumped up to the second excited state from the ground state. As I understand it, if a photon comes along that has 4 units of energy, nothing will happen because there is no energy state between the two excited states for the electron to move into. So my question is, how exactly does the photon's energy have to correspond to the difference in the atom's energy levels? If the photon has 3.00001 units of energy, is that close enough to bump the electron to the first excited state? If so, where does the "extra" energy go? If not, how can the process ever work at all since presumably the probability of the photon having exactly the right amount of energy is infinitesimal?
- Bill (age 55)
New York, NY USA
A:

Great question! The answer is a little subtle.

Other than the ground state energy, the energy levels of an atom are not completely precisely defined. The excited states of the atom are not true energy eigenstates, states with single exact energy values. Energy eigenstates persist forever without physically changing. The excited states of atoms don't persist forever. They decay by spontaneously emitting one or more photons. So it's precisely the same interaction with electromagnetism that's needed to allow photon absorption that also makes the states have a small intrinsic energy width, i.e. frequency width.

Here's a site that has some quantitative discussion: http://farside.ph.utexas.edu/teaching/qmech/Quantum/node122.html
http://farside.ph.utexas.edu/teaching/qmech/Quantum/node122.html.

 

In addition to the intrinsic linewidth, several other effects broaden the absorption line. One is Doppler broadening, since in a gas the atoms are moving around with random thermal velocities. Another comes from collisions between the atoms, so that they aren't quite idealized isolated atoms. As a result, light whose frequency in the lab frame differs from the ideal absorption frequency by more than the intrinsic linewidth will still be absorbed by some atoms that happen to be moving with the right velocity to make the frequency almost ideal in their own frame.

Mike W.


(published on 04/07/2017)