Question
Moon has no atmosphere because
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Answer
The escape velocity (the minimum velocity with which a body is to be projected so as to escape from the gravitational pull) on the surface of moon is very much less than the rms velocity of the molecules of gas at the surface temperature of moon. Therefore, the molecules will escape and therefore moon cannot hold an atmosphere.
The expression for escape velocity is $\sqrt{2 gR }$, the value of escape velocity on earth is $11200 \; m / s$. The value of escape velocity on moon is $2400 \; m / s$ (approximately) The moon's surface temperature cycles between $-155^{\circ} C$ and $100^{\circ} C$. As temperature increases the speed of molecules become more than the escape velocity.
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