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{"ops":[{"insert":"When two quantum energy levels, E1 and E2 of an atom are separated by an energy gap \u0394E = E2 - E1, and a large number of such atoms are in thermal equilibrium at temperature T, then the relative number of atoms N1 and N2 in the two energy levels are given by the Boltzmann ratio N2\/N1 = e-\u0394E\/kT. Evaluate this ratio for the following cases: (a) transition occurs at the frequency of 3100 MHz, and the temperature is 300 K. What is the fractional population difference (N2-N1)\/ N1?\n(b) Consider the same situation, except that \u03bd = 9000 MHz and the temperature is 4 K. What is (N2-N1)\/ N1?\n(c) Calculate the Boltzmann ratio N2\/ N1 for \u03bb = 5500 Ao , and T = 300 K.\n(d) What temperature required to make (N2 equal to 8 % of N1) in part (c) ?\n"}]}
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