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 E1 and E2 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:
An energy level diagram illustrating the process is shown below:
\r\n Before emission After emission\r\n\r\n --------O--------- ------------------ E2\r\n | Atom in\r\n | excited state \r\n | ~~~>\r\n | Photon hν\r\n | \r\n V \r\n ------------------ ---------O-------- E1\r\n Atom in ground state\r\n
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:
The above equation can be solved to give:
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 half-life.
See also absorption, stimulated emission, laser science.