Physics - Modern Physics Question with Solution | TestHub

According to Bohr's quantization condition, the angular momentum $L$ of the diatomic molecule is quantized as:

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

The rotational kinetic energy $E$ of a molecule with moment of inertia $I$ is given by:

$E=\frac{L^2}{2I}$

Substituting the value of $L$ into the energy equation:

$E=\frac{1}{2I}{\left(\frac{nh}{2\pi }\right)}^2$

$E=\frac{n^2{h}^2}{8{\pi }^{2}I}=n^2\left(\frac{h^2}{8{\pi }^{2}I}\right)$

Answer: ${\mathrm{n}}^2\left(\frac{{\mathrm{h}}^2}{8{\pi }^2\mathrm{I}}\right)$