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