Question

At what absolute temperature $T$ is the root mean square speed of a hydrogen molecule equal to its Escape velocity from the surface of the moon? The radius of moon $R=g$ is the acceleration due to gravity on moon's surface $m$ is the mass of a hydrogen molecule and $k$ is the Boltzmann constant

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

The root mean square speed is given by

$v_{rms}=\sqrt{\frac{3kT}{m}}$

The escape velocity is given by $v_2=\sqrt{2gR}$

For $v_{rms}=v_e$, we require

$\sqrt{\frac{3kT}{m}}=\sqrt{2gR}$ or $T=\frac{2mgR}{3k}$, which is choice (d)