The specific frequencies which can be emitted by some type of atom are the same as the frequencies which can be absorbed by that type of atom. In each case the frequency f is given by hf=EI
, where h is Planck's constant and EI
are the energies of the initial and final states of the atom. Since there are only certain allowed values of those energies, there are only certain allowed frequencies.
Starting with any particular batch of atoms, however, means starting with a particular batch of EI
's, which puts different limits on the emission and absorption. To pick the simplest case, say the atoms are very cold, nearly all in the ground (lowest energy) state, which we'll call E1
. Then they can't emit at all. The possible absorption f's are just those reachable with EI
: e.g. hf = E2
, or E3
etc. where E2
,.. are the possible higher energies. Now say you heat up that batch of atoms. Many of them are in states with higher energy. Now you can get emission spectra
with hf = E2
, or E3
, etc. You can also get some absorption frequencies that weren't available from the coldest state: hf= E3
There are some additional complications. For both emission and absorption, the interaction with light depends on properties of the states beyond the energies. These "selection rules" can effectively eliminate some of the frequencies you calculate from the energy differences from the set of emission and absorption lines.
There's been quite a lot written about how the electron goes from a state with one energy to another. Much of what you might read on the subject is plain wrong. For example, people often say that an electron must always be in a state with definite energy, but that's completely false. If you start with an electron in a state with definite energy and an electromagnetic field is present, the combination of states that the electron is in changes over time. The way it changes can be calculated from the time-dependent Schroedinger equation. Here's a really wonderful illustration of the way that works: http://www.falstad.com/qmatomrad/
The weird thing is that if something comes along to "measure" the electron's energy, we don't see it in some state with a combination of different energies, but only in a state with definite energy. How that comes to be is a controversial topic. We're happy to follow-up.
(published on 04/01/2011)