What is the relationship between B₂₁ and B₁₂?

Concept:

The Einstein A coefficients are related to the rate of spontaneous emission of light, and the Einstein B coefficients are related to the absorption and stimulated emission of light.

Stimulated and spontaneous emission

• When an optical gain medium is pumped optically or electronically, an electron is pumped (excited) from a lower energy level to an upper energy level.
• The exciting medium is eventually relaxed to some lower energy level by radiating energy – as upper energy levels are generally less stable than lower energy levels – and sometimes the energy radiation takes the form of a photon.

Explanation:

• B₂₁ is the coefficient for the stimulated emission while B₁₂ is the coefficient for stimulated absorption.
• Both the processes are mutually reverse processes and their probabilities are equal.

Therefore, B₁₂ = B₂₁.