Photons and Linewidths

Most recent answer: 05/17/2013

Q:
When an electron transitions between two energy levels we say that it emits a photon of energy E=hv, where v is the frequency. But photon is a particle of light. That is it is localized in space. But such a packet is made up of several different frequencies. Then how can it have single frequency?
- Aman Kanojia (age 22)
India
A:

This is a brilliant question. You're absolutely right that if the photon had an exactly defined energy, then its wavefunction would have to be infinitely spread out. So it must have some spread in energies. How can energy be conserved then if it takes away the energy lost in a transition between two well-defined energy levels?

The secret is that the energy levels of the atom or molecule are not absolutely sharply defined. In particular the excited state (e.g. 2p for hydrogen) is not quite a true energy eigenstate, i.e. state with exactly defined energy. You can tell that must be right because exact energy eigenstates never do anything, so one would not emit light! In the full quantum mechanical expression for the energy, including the quantum version of the electromagnetic field, those excited states actually represent a narrow band of energies. The emitted photons share that range, thus conserving energy. That allows them to have a finite extent in space.

In many cases, a less fundamental solution applies. The atoms may be colliding and so forth, which already makes the situation more complicated and creates an energy range. Even in the ideal case, however, there's some little linewidth to those transition lines, keeping things consistent.

Mike W.

 

(not yet checked by Lee, who's traveling)

 


(published on 05/17/2013)

Follow-Up #1: why do excited-state electrons emit photons?

Q:
I am not sure if my question is relevant or it is filled with misconceptions. Please help me out. I learnt that electrons emit photon when they leave their excited state to a lower energy state. My question is what causes the electron to fall to a lower energy state.
- broccoli (age 22)
singapore
A:

That's a very nice but very hard question. We just answered one that's closely related, so I've put it in that thread.  Please follow-up if you want more explanation.

Mike W.


(published on 05/27/2013)