Word Count : 468

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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) _______ ______ __________ __________ ______ ________ ______ _____ _______ _____ ______.
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