Physics - Modern Physics Question with Solution | TestHub

According to Bohr's quantisation condition, the angular momentum is given by $L=\frac{nh}{2\pi }$.

For the second orbit, $n=2$.

$L=\frac{2h}{2\pi }=\frac{h}{\pi }$

The rotational kinetic energy of a diatomic molecule is given by $K=\frac{L^2}{2I}$, where $I$ is the moment of inertia.

Substituting the value of $L$, we get:

$K=\frac{1}{2I}{\left(\frac{h}{\pi }\right)}^2=\frac{h^2}{2I{\pi }^2}$

Answer: $\frac{h^2}{2I{\pi }^2}$