IGNOU BPHCT 137 2026 - An atomic system consisting of two energy levels, with population of h

Question

An atomic system consisting of two energy levels, with population of higher energy level less than that of the lower level, is in thermal equilibrium. Show that the absorption of radiation dominates stimulated emission if radiation of appropriate frequency is introduced into the system. Comment on the consequences of this fact for laser action.

19 Jan 2026

Answer :

Word Count : 468

In an atomic system with two energy levels, let the lower energy level be (E_1) and the higher energy level be (E_2). Denote the populations of these levels as (N_1) and (N_2) respectively, where (N_2 < N_1) because the system is in thermal equilibrium. According to Boltzmann statistics, the population ratio is given by [ \frac{N_2}{N_1} = e^{-(E_2 - E_1)/kT} < 1 ] where (k) is Boltzmann’s constant and (T) is the absolute temperature. When electromagnetic radiation of frequency (\nu = (E_2 - E_1)/h) is introduced, the system can undergo three types of transitions: absorption, spontaneous emission, and stimulated emission. The rate of absorption (R_{abs}) is proportional to the number of atoms in the lower state (N_1) and the energy density of the radiation (u(\nu)): [ R_{abs} = B_{12} N_1 u(\nu) ] where (B_{12}) is the

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