A diatomic gas consisting of rigid molecules is at a temperature of 87   ° C . If the moment of…

Recall the formula of the kinetic energy of one molecule in terms of Boltzmann constant and absolute temperature,

$K.E.=\frac{1}{2}KT$, for two rigid molecules, it will be,

$K.E.=2\times \frac{1}{2}KT=KT$, if $I$ is a moment of inertia of body and $\omega$ is the angular velocity then,

$$\begin{gathered} KT=\frac{1}{2}I{\omega }^2 \\ \Rightarrow \omega =\sqrt{\frac{2KT}{I}}=\sqrt{\frac{2\times 1.38\times {10}^{-23}\left(87+273\right)}{2.76\times {10}^{-39}\times {10}^{-7}}}=6\times {10}^{12} \mathrm{rad} {\mathrm{s}}^{-1} \end{gathered}$$