Question

Consider a hydrogen atom undergoing a 2P 1S transition. The lifetime tsp of the 2P
state for spontaneous emission is 1.6 ns and the energy difference between the levels is
10.2 eV. Assuming that the refractive index of the medium n0 = 1, the ratio of Einstein
coefficients for stimulated and spontaneous emission   B 21/ A21 is given by

Answer 1

For the given data, we have

$$\frac{B_{21}}{A_{21}}=\frac{\pi^2c^3}{\hbar\omega^3n_0^3}=\frac{\hbar^2\pi^2c^3}{(\Delta E)^3n_0^3}=678\cdot10^9\space\frac{\text{m}^3}{\text{J}\cdot\text{s}}.$$

Do not forget to convert electron-volts to joules!