Question

The key feature of Bohr's theory of spectrum of hydrogen atom is the quantization of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantized rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr's quantization condition.

A diatomic molecule has moment of inertia $I$. By Bohr's quantization condition its rotational energy in the $n ^{\text {th }}$ level $( n =0$ is not allowed) is

• A. $\frac{1}{ n ^{2}}\left(\frac{ h ^{2}}{8 \pi^{2} I }\right)$
• B. $\frac{1}{ n }\left(\frac{ h ^{2}}{8 \pi^{2} I }\right)$
• C. $n \left(\frac{ h ^{2}}{8 \pi^{2} I }\right)$
• D. $n^{2}\left(\frac{ h ^{2}}{8 \pi^{2} I }\right)$

Answer 1

Answer: (D)

$L =\frac{ nh }{2 \pi}$
$K . E .=\frac{ L ^{2}}{2 I }=\left(\frac{ nh }{2 \pi}\right)^{2} \frac{1}{2 I }$