Question

Escape velocity from the Moon is approximately 5500 miles per hour = 2.45 x 103m/s. At certain spots on the surface of the Moon, the temperature of the surface material reaches 800K. Suppose a molecule of hydrogen (m= 3.33x 0-27kg) were to hit the surface of the Moon and reach a speed equal to the root-mean-square (rms) speed for this temperature. `
What would be the velocity or root-mean-square speed (Vrms) of the Hydrogen molecule?
Will the Hydrogen molecule manage to escape?

Answer 1

$\begin{aligned} v_{rms} &= \sqrt{\dfrac{3kT}{m}}\\ \\ v_{rms} &= \sqrt{\dfrac{3×1.38×10^{-23}×800}{3.33×10^{-27}}}\\ \\ v_{rms} &= \sqrt{10,036,363.6}\\ v_{rms} &= 3168ms^{-1} \end{aligned}$

The Hydrogen molecule should be able to manage to escape due to its root mean square speed being higher than the velocity needed to escape from the moon.