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

Answer

D