SKEDSOFT

Physics For Engineers - 1

Expression for Einstein’s coefficient: By rearranging the terms, we get

From Boltzmann’s law, we know that the ratio of the population densities N1 and N2in the ground state E1 and excited state E1 respectively is given by,

Using this in the equation of Eν, we get

By comparing the above two equations, we get

 

The equality B12 = B21 implies that the probability of induced absorption is equal to that of stimulated emission. Hence we can use simply A andB to denote the Einstein’s coefficients. With this our equation for the energy density at thermal equilibrium takes the form,