Emission occurs when a substance goes from a higher energy state to a lower energy state, giving off a photon whose energy is equal to the difference in the energies of the states:
ΔE ≡ Ef - Ei = hν
In 1917, Albert Einstein defined a rate of spontaneous emission as
rate of spontaneous emission = A · c
where c is the concentration of absorbers in the upper energy state and A is the Einstein coefficient of spontaneous emission and is given by
where:
e—charge on electron, 1.6022×10-19C
ε0—permittivity of free space, 8.8542×10-12C2/J·m
me—mass of the electron, 9.1094×10-31 kg
Einstein also demonstrated that there is also a rate of stimulated emission:
where B' is the Einstein coefficient of stimulated emission and ρ(ν) is the density of radiation having frequency ν. Einstein was able to show that B' = B, the coefficient of stimulated absorption. Further, the ratio of spontaneous emission to stimulated emission is proportional to ν3:
The higher the frequency of light involved, the greater the rate of spontaneous emission over stimulated emission.
