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Excerpt from Field Guide to Spectroscopy

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:

ΔEEf - 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

e—charge on electron, 1.6022×10-19C
ε0—permittivity of free space, 8.8542×10-12C2/J·m
cspeed of light, 2.9979×10-8 m/s
me—mass of the electron, 9.1094×10-31 kg

Einstein also demonstrated that there is also a rate of stimulated emission:

rate of stimulated emission = B' · ρ(ν) · c

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.


D. W. Ball, Field Guide to Spectroscopy, SPIE Press, Bellingham, WA (2006).

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David W. Ball
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