Question

A single hydrogen atom, initially in a 2p state, will decay to its 1s state with emission of a photon of wave number k at a rate R1 when it is in a zero-temperature environment. If, however, there are already four photons of wave number k already present, it will decay at a rate R2. What is the ratio R2/R1?

Answer 1

In the Zero Temperature environment,

In the absence of photons Emission is Spontaneous emission.

The rate of emission of a photon is

A is the einstein coefficient of Spontaneous emission

In the presence of photons, the emission is stimulated emission

The rate of emission is

B is the einstein coefficient of stimulated emission

u is energy density

N is the number of atoms in that state

frequency of the photon

The standard formulae