Question

Could you please help me to solve this exercise? I know it is quite long but please try to do as much as your are allowed to do.

Thanks

2. (Average Energy of rotation of a diatomic molecule) The kinetic energy of a diatomic molecule, which revolves around an axis perpendicular to the line that joins the two atoms, is classically given by: 2 2I where L is the angular momentum vector and I is the inertial tensor. In a quantum description this energy can take discrete values El-h21(1 + 1) 21 where the quantum number I determines the value of the module (magnitude) that the angular momentum can acquire 1.2.3.4. For each value of l, there are (21 + 1) different possible quantum states that correspond to the possible discrete spatial orientations of L. Suppose that the diatomic molecule belongs to a gas in equilibrium at the absolute temperature T' a) Calculate the partition function Q (remember that this sum contains a term for each individual state). Assume that KT 》 h2/21, condition that most molecules satisfy at room temperature. Show that the sum in Q can be replaced by an integral, making use of a continuous variable b) Calculate the energy of the molecule using this partition function

Answer 1

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