Problems and Solutions on Thermodynamics and Statistical Mechanics

206 Problems d soltltions on Thermodynum'cd d Statisticd Mechanics

Solution:

(a) The moment of inertia of the hydrogen molecule is

and its rotational energy level is

with degeneracy (21 + 1),1 = 0,1,2,... .For ortho-H, 1 = 1,3,5,... ; for
para-H, 1 = 0,2,4,6,.... Thus in hydrogen molecules, the ratio of the
number of ortho-H to that of para-H is

where the coefficient 3 results from spin degeneracy and

(b) When T = 100 K, A = 0.88, since as 1 increases the terms in the

summations decrease rapidly, we need consider only the first two terms.

Hence

se-2~ + ~~-12~

1 + 5e-GA

f=3 = 1.52