(Solution) - Consider a gas of diatomic molecules moment of inertia I -(2025 Original AI-Free Solution)

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Consider a gas of diatomic molecules (moment of inertia I) at an absolute temperature T. If Eg is a ground-state energy and E ex is the energy of an excited state, then the Maxwell-Boltzmann distribution (see Section 38.6) predicts that the ratio of the numbers of molecules in the two states is
(a) Explain why the ratio of the number of molecules in the l th rotational energy level to the number of molecules in the ground (l = 0) rotational level is
(b) Determine the ratio n1/n0 for a gas of CO molecules at 300 K for the cases (i) l = 1; (ii) l = 2; (iii) l = 10;
(iv) l = 20; (v) l = 50. The moment of inertia of the CO molecule is given in Example 42.2 (Section 42.2).
(c) Your results in part (b) show that as I is increased, the ratio n1/n2 first increases and then decreases. Explainwhy.