## RELATION BETWEEN EINSTEIN A AND B COEFFICIENTS

**RELATION BETWEEN EINSTEIN’S A AND B COEFFICIENTS:**** **Let us consider an enclosure containing atoms which are in thermal equilibrium or in steady state. Let N1 and N2 are the number of atoms per unit volume called population in energy levels E_{1} and E_{2}, respectively. Here E_{2} is greater than E_{1}. In thermal equilibrium three processes of transition described above will take place.

** 1. Spontaneous Emission:** According to Einstein the probability of spontaneous emission from energy level E

_{2}to energy level E

_{1}per unit time is denoted by

A21 is called the Einstein’s A coefficient of spontaneous emission of radiation. Thus the number of photons of energy E_{2} – E_{1} emitted per second by spontaneous emission in the system is equal to N_{2}A_{21}.

__ 2. Induced Emission:__ According to Einstein the probability of induced emission from energy level E

_{2 }to energy level E

_{1}per unit time can be written as

Here B_{21} is called the Einstein’s B coefficient of induced emission of radiation and u(ν) is the energy density of the radiation of frequency ν. Then the number of photons of energy hν emitted per second by induced emission in the system is equal to N_{2} B_{21} u(ν).

** 3. Absorption of Radiation: **According to Einstein the probability of absorption of energy for transition from energy level E

_{1}to energy level E

_{2}per unit time can be written as

Here B_{12} is called the Einstein’s B coefficient of absorption of radiation and u(ν) is the energy density of the radiation of frequency ν. Then the number of photons of energy hν absorbed per second in the system is equal to N_{1}B_{12} u(ν).In the thermal equilibrium state (i.e., steady state) total number of photons absorbed per second should be equal to the total number of photons emitted per second. It can be written as

..........eq(1)

According to Maxwell-Boltzmann distribution the number of atoms N_{1} and N_{2} in the energy states E_{1} and E_{2}, respectively, in the steady state at temperature T are given by