The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the…
The absolute temperature at which the rms speed of a hydrogen molecule is equal to its escape speed from the moon's surface is (where, $R$ is radius of moon is $r, g$ is acceleration due to gravity on Moon's surface, $m$ is mass of hydrogen molecules and $k$ is Boltzmann constant)
$\frac{m g R}{2 k}$
$\frac{2 m g R}{k}$
$\frac{3 m g R}{2 k}$
$\frac{2 m g R}{3 k}$
Solution
$\begin{aligned} & v_{\text {rms }}(\text { hydrogen })=\sqrt{\frac{3 R T}{M}}=\sqrt{\frac{3 k T}{m}} \\ & \text { and } v_{\text {escape }}(\text { moon })=\sqrt{2 g R} \\ & v_{\text {rms }}=v_{\text {escape }} \\ & \Rightarrow \quad \frac{3 k T}{m}=2 g R \Rightarrow T=\frac{2 m g R}{3 k} \\ & \end{aligned}$