Chapter 42, Problem 42.39P

(a)

To determine

Why the ratio of the number of molecules in the $l$ th rotational energy level to the number of molecules in the ground rotational level is

$\frac{n_l}{n_0}=\left(2l+1\right)e^{-\left[l\left(l+1\right){\hslash }^2\right]/2IkT}$

(b)

(i)

To determine

The ratio $n_l/n_0$ for a gas of CO molecules at $300\text{ K}$ for $l=1$.

(ii)

To determine

The ratio $n_l/n_0$ for a gas of CO molecules at $300\text{ K}$ for $l=2$.

(iii)

To determine

The ratio $n_l/n_0$ for a gas of CO molecules at $300\text{ K}$ for $l=10$.

(iv)

To determine

The ratio $n_l/n_0$ for a gas of CO molecules at $300\text{ K}$ for $l=20$.

(v)

To determine

The ratio $n_l/n_0$ for a gas of CO molecules at $300\text{ K}$ for $l=50$.

(c)

To determine

The reason why the ratio $n_l/n_0$ first increases and then decreases.