determine the einstein relations by upward and

Question

Determine the Einstein relations by upward and downward transition.

While the system is in equilibrium, the upward and downward transition rates should be equal.

N₁ρ(ν) B₁₂= N₂ ρ(ν) B₂₁+ N₂ A₂₁ ........... (1)

Hence ρ(ν) = N₂ A₂₁ / N₁B₁₂- N₂ B₂₁ ........... (2)

The Einstein relations are specified by the equations 3 and 4.

g₁B₁₂= g₂B₂₁ ........ (3)

A₂₁/B₂₁= 8πhν³/c³........ (4)