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Spontaneous emission

In optics, spontaneous emission is the process by which matter may lose energy, resulting in the creation of a photon.

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:

E2 - E1 = hν ,

where h is Planck's constant.

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:

N / ∂t = - A21N ,

where A21 is a proportionality constant for this particular transistion in this particular atom. (The constant is referred to as an Einstein A co-efficient.) 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:

N(t) = N(0) exp( - t / τ21 ),

where N(0) is the inital number of atoms in the excited state, and τ21 is the lifetime of the transition, τ21 = (A21)-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 half-life.