The key feature of Bohr's 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^(th)` level (`n = 0` is not allowed ) is

Options

A. `(1)/(n^(2))((h^(2))/(8pi^(2)I))`
B. `(1)/(n)((h^(2))/(8pi^(2)I))`
C. `n((h^(2))/(8pi^(2)I))`
D. `n^(2)((h^(2))/(8pi^(2)I))`

Answer

D

Explanation

`E_(n)=1/2 I omega^(2)=((I omega)^(2))/(2 I)=((nh//2pi)^(2))/(2 I)=(n^(2)h^(2))/(8pi^(2) I)`