Einstein coefficients

The Einstein coefficients are three coefficients associated with a material that absorbs and emits EMR that Albert Einstein developed in his analysis of emission and absorption, based upon the (current at the time) Bohr model of the atom. Einstein presumed that an atom at some excitation level has a probability of absorbing a passing photon of a compatible wavelength, and has some probability of emitting one at random (spontaneous emission). (This presumption was consistent with the Bohr model and is implied by current theory.) His analysis showed that to function as a black body, yet avoid breaking the laws of thermodynamics (that thermal emission from a gas cannot raise another gas to a higher temperature), there must exist stimulated emission. He defined the three coefficients as part of his analysis; given two successive levels of atomic excitation (labeling the lower level as "1" and the higher level as "2", but not implying which pair of levels this refers to):

• A₂₁ - probably that an atom some excited level will spontaneously emit a photon, falling from level 2 to level 1.
• B₁₂ - probability that a passing photon will be absorbed by an atom at level 1, increasing it to level 2.
• B₂₁ - probability that a passing photon will stimulate an atom at level 2 to emit a photon and fall to level 1.

Without a B₂₁ (i.e., if it were zero), then absorption would depend on both the number of photons passing through and the number of unexcited atoms, while emission would depend only on the number of excited atoms, and the thermodynamic equilibrium that defines a black body would not be spontaneously achieved.