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

Answer

D

Explanation

`L=(nh)/(2pi) and KE=L^(2)/(2l)=((nh)/(2pi))=(n^(2)h^(2))/(8pi^(2)I)`
` hv=kE_(n=2)-kE_(n=1)`