where, E_{1 }and E_{2} 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.

_{12}is known as Einstein coefficient of absorption of radiation.

**SPONTANEOUS EMISSION :**

^{-8}s).

The probability of spontaneous emission 2–>1 is determined by the properties of states 2 and 1.

_{21}, which is known as Einstein coefficient of spontaneous emission of radiation.

**STIMULATED EMISSION (INDUCED EMISSION)**

*The direction of propogation ,energy, phases of emitted photon is exactly same as that of incident stimulating photon.”*

The probability of simulated emission transition 2→1 is proportional to the energy density u(ν)

where, B_{21} is Einstein coefficient of stimulated emission of radiation.

**Relation between spontaneous and stimulated Emission Probabilities:**

_{1}and N

_{2}be the number of atoms in states 1 and 2 respectively.

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.

Now,

This is the formula for the ratio between spontaneous and stimulated emission.