Question

For a two level system, suppose N2 = 10N1, where N1 and N2 denote the number of atoms (per unit volume) in level 1 and level 2 respectively. The transition between these two levels corresponds to the frequency of 5x104 Hz. Calculate the ratio of spontaneous emission and stimulated emission. Also calculate the temperature required to produce this population inversion.

Answer 1

The the ratio of spontaneous emission and stimulated emission:

$$\frac{A_{21}}{B_{12}}=\frac{2h\nu^3}{c^3}=\frac{2(6.6\cdot10^{-34})(5\cdot10^{4})^3}{(3\cdot10^{8})^3}=6.1\cdot10^{-45}\frac{Js}{m^3}$$

$$kT=h\nu\\(1.38\cdot10^{-23})T=(6.6\cdot10^{-34})(5\cdot10^{4})\\T=2.4\cdot10^{-6}\ K$$