Question

There is no atmosphere on the moon because :
A. It is closer to the earth
B. It revolving around the earth
C. It gets light from the sun
D. Here the escape velocity of gas is less than their rms velocity

Answer 1

Hint: - The atmosphere means gas particles.
- On the surface of the earth due to the greater mass gravitational attraction force on any object is greater than on the surface of the moon.
- So, the escape velocity of the earth is greater than that of the moon.
- If rms velocity is larger than then escape velocity then there will be no gas particles in the atmosphere.

Complete step by step solution:
Escape velocity is the lowest velocity that a body must have in order to escape the gravitational attraction of a particular planet.
On the surface of the earth due to greater mass gravitational attraction force on any object is greater than on the surface of the moon.
RMS velocity of a gas is the square root of the average of the square of velocity. So, we can say gas particles travel with rms velocity.

So, where the attraction is greater there gas has to travel faster to escape the attraction. And, where the attraction is less it can escape easily.

So, on the moon gas particles can escape easily. That’s why there is no atmosphere on the moon.

So, the correct option is (d)

Note: The gravitational force between two objects of mass $M$and $m$ separated at a distance $r$, is $F = \dfrac{{GMm}}{{{r^2}}}$-
 The gravitational attraction on the surface of the moon is times of the gravitational force on the surface of the earth.
- rms velocity of a gas molecule at temperature $T$ is $\sqrt {\dfrac{{3RT}}{M}} $ , where $M$ is the molar mass of the gas and $R$ is gas constant.