All Problems Properties of Atoms. Spectra.
Problem 6.130
Atomic hydrogen is in thermodynamic equilibrium with its radiation. Find: (a) the ratio of probabilities of induced and spontaneous radiations of the atoms from the level \(2 P\) at a temperature \(T=3000 \mathrm{~K}\) (b) the temperature at which these probabilities become equal.
6.130. (a) \(P_{\text {ind }} / P_{s p}=1 /\left(\mathbf{e}^{\hbar \omega / k T}-1\right) \approx 10^{-34}, \quad\) where \(\quad \omega=\) \(=3 / 4 R\) (b) \(T=1.7 \cdot 10^{5} \mathrm{~K}\)