Modern Physics 1 Question 29
26. A diatomic molecule has moment of inertia I. By Bohr’s quantization condition its rotational energy in the $n$th level ( $n=0$ is not allowed) is
(2010)
(a) $\frac{1}{n^{2}} \frac{h^{2}}{8 \pi^{2} I}$
(b) $\frac{1}{n} \frac{h^{2}}{8 \pi^{2} I}$
(c) $n \frac{h^{2}}{8 \pi^{2} I}$
(d) $n^{2} \frac{h^{2}}{8 \pi^{2} I}$
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Solution:
- $L=I \omega=\frac{n h}{2 \pi}$
$\therefore \quad \omega=\frac{n h}{2 \pi I}$
$$ K=\frac{1}{2} I \omega^{2}=\frac{1}{2} I \quad \frac{n h}{2 \pi I}{ }^{2}=\frac{n^{2} h^{2}}{8 \pi^{2} I} $$
