A simple model of spontaneous emission consists of an atom which may be in two electronic energy states, the ground state (1) and the excited state (2), with energies E_{1} and E_{2} respectively.
If the atom is in the excited state, it may spontaneously decay into the ground state, releasing the difference in energies between the two states as a photon. The photon will have frequency ν and energy hν, given by:
where h is Planck's constant.
An energy level diagram illustrating the process is shown below:
Before emission After emission O  E2  Atom in  excited state  ~~~>  Photon hν  V  O E1 Atom in ground state
In a group of such atoms, if the number of atoms in the excited state is given by N, the rate at which spontaneous emission occurs is given by:
where A_{21} is a proportionality constant for this particular transistion in this particular atom. (The constant is referred to as an Einstein A coefficient.) The rate of emission is thus proportional to the number of atoms in the excited state, N.
The above equation can be solved to give:
where N(0) is the inital number of atoms in the excited state, and τ_{21} is the lifetime of the transition, τ_{21} = (A_{21})^{1}.
It can be seen that spontaneous emission occurs in a way rather similar to the decay of radioactive particles, in particular that the lifetime is analogous to a halflife.
See also absorption, stimulated emission, laser science.
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