Question

Moon has no atmosphere because

• A. It is far away from the surface of the earth
• B. Its surface temperature is 10⁰C
• C. the RMS velocity of all the gas molecules is more than the escape velocity of the moon's surface
• D. the escape velocity of the moon's surface is more than the RMS velocity of all molecules

Answer 1

The correct option is C

the RMS velocity of all the gas molecules is more than the escape velocity of the moon's surface

Explanation:

1. The moon's escape velocity is much less than the root mean square (RMS) velocity of gas molecules on the moon.
2. Therefore, the molecules of gas escape from the moon’s surface.
3. The gravitational field is weak on the surface of the moon. Hence, the moon doesn’t have an atmosphere.
4. Escape velocity can be given as $V_{esc}=\sqrt{2gR}$
5. where $V_{esc}$=escape velocity, $g$= acceleration due to gravity on the surface of the celestial body, $R$= radius of the celestial body.
6. For earth, it is about $11200\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$. But for moon, it is less. i.e. $2400\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$ approximately.
7. The temperature of moon’s surface is between $-155°C$ and $100°C$. The speed of molecules becomes more than the escape velocity as the temperature increases.
8. Therefore, RMS velocity of all the gas molecules is more than the escape velocity of the moon’s surface.

Hence, the correct option is option C.