Question

2. Suppose there exists an infinite set of energy levels, each having energy ?. = mr(mi + 2)hv m=0,1,2,..,00 and that each energy level possesses a degeneracy of m +1. a. Approximate the partition function summation for these energy levels by an integration. ) Show that after a change of variable x m(m+2) that this integral can be written in the form: b. Show that the closed-form analytic partition function for these energy levels is and that it has a value Z # 6.74 for v # 460 GHz at 298 K. show that this partition function has an internal energy contribution: U nRT. Show that this partition function has an entropy contribution: S nRin Show that the most-probably occupied rotational level for this system is given by the expression: Z-1 and for the conditions of part b.) that this value is: 1.6. 20 c, (%) d. 20 e.

Answer 1

et anininits ard thal each enara degenera mt ↑ a) ヒ7 b) ½了e-a@歼dy Z:

2x h 3 6 74 10 6090,千 0.0(3 54x10 6.3s c) 一ヒ个 ORT d)

n e