Question

There is no atmosphere on the moon because

• A. It receives light from the sun.
• B. It revolves around the earth.
• C. The escape velocity of gas molecules is greater than their root mean square velocity.
• D. It is closer to the earth.

Answer 1

The correct option is C

The escape velocity of gas molecules is greater than their root mean square velocity.

Explanation for the correct option:
We know that the mass of the moon ($M_{moon}$) = $7.4\times {10}^{22}$ kg, the radius of the moon ($R_{moon}$) = $1.75\times {10}^6$ m, and $G=6.67\times {10}^{-11}{\mathrm{Nm}}^2/{\mathrm{kg}}^2.$

So the escape velocity of the moon is given as,

⇒$v_e=\sqrt{\frac{2G{M}_{moon}}{R_{moon}}}$

⇒ $v_e$ = $2.38$km/s

There is no atmosphere on the moon because the escape velocity is less than the average square velocity of the gas molecules on the moon. Therefore, all gas molecules escape.

Hence, option (C) is correct.