Because the intensity of a transition to first order is proportional to the population of the originating state, the J value for which the maximum intensity is observed in a rotational€“vibrational spectrum is not generally J = 0. Treat J in the equation

as a continuous variable.

a. Show that

b. Show that setting d(n_J /n₀)/d J = 0 gives the equation

c. Show that the solution of this quadratic equation is

In this problem, we assume that the intensity of the individual peaks is solely determined by the population in the originating state and that it does not depend on the initial and final J values.

Transcribed Image Text:

81e(6j-€0)/knT = (2J + 1)e-ħ³J(J+l)/21k,T no go пу 20J(J+1}/2Ik,T _ (2J + 1)*ħ J(J+1)/27&,T 21 kgT По