where, E1 and E2 are energies of atom in the state “1” and “2”. This is absorption of radiation.This is a stimulated process .
The probable rate of occurance of this absorption transition 1 –>2 depends upon the property of states 1 and 2 and is proportional to the energy density u(ν) of the radiation of frequency ν incident on the atom.
The probability of spontaneous emission 2–>1 is determined by the properties of states 2 and 1.
The probability of simulated emission transition 2→1 is proportional to the energy density u(ν)
where, B21 is Einstein coefficient of stimulated emission of radiation.
Relation between spontaneous and stimulated Emission Probabilities:
For equilibrium ,the objective and emission must occur equally. Thus,
Enstein proved thermodynamically that:
According to Boltzmann law the distribution of atoms among different energy states is given by:
where, No = Number of atoms in ground state.
Er = Energy of rth state.
Nr = Number of atoms in rth state.
This is the formula for the ratio between spontaneous and stimulated emission.