Question

A diatomic molecule has moment of inertia $I$. By Bohrs quantization condition its rotational energy in the $n^{th}$ 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

The correct option is D $n^2\left(\frac{h^2}{8{\pi }^{2}I}\right)$

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