Optical Transitions and light emission
If
we could solve Schrödinger's equation for all the electrons in an
atom, in its lowest energy state, we would have a detailed description
of the electron structure of the atom and its electron energy.
But
Schrödinger's equation tells us that other electron structures and
energies are possible for that atom. The atom may change to one
of these other configurations by the absorption or emission of an amount of energy equal to the difference in the energies of
the two configurations.
A
common mode for the change in atomic energy is the emission or absorption
of a photon (a parcel of electromagnetic radiation, such as light).
This process is called an 'optical transition'.
A photon is a disturbance of the electromagnetic field. The energy in a photon is
where h is Planck's constant, n is frequency, c is the speed of light in vacuum, and l is wavelength. A photon also has a momentum given by
Linewidth
When an atom absorbs a photon it is elevated to an excited state.
This excited state will generally last for a limited time, typically
10^{8} s. The atom can deexcite by emitting a photon.
From Heisenberg's uncertainty principle, the finite lifetime Dt of the excited state means
there will be an uncertainty in the energy of the emitted
photon given by
Combining this with equation (1) above [don't forget to differentiate!]
gives a minimum width of
So the finite lifetime of the excited state means that when we
measure the wavelength of the emitted photon it will have a spread
of wavelengths around the mean value l.
For a line at 450 nm and a lifetime of 10^{8} s,
the minimum (or natural) linewidth is 0.01 pm.
Momentum
A spontaneous optical transition is a sudden and directional process.
It therefore involves the exchange of momentum between the atom
and the exciting photon. In absorption, the atom receives momentum
in the direction of the incoming photon. This is a fundamental aspect
of quantum mechanics, first derived by Einstein and quite different
from classical theories. The direction of emission is random, and
it is only in averaging a large number of such events that emission
appears to be nondirectional with zero momentum as predicted
by classical theories.
First published on the web: 15 February 2000.
Author: Richard Payling
