Explain why

(a) there is no atmosphere on moon.

(b) there is fall in temperature with altitude.

(a) We know that

acceleration due to gravity (g’) on the surface of moon is one-sixth of acceleration due to gravity on surface of earth.

Since

Escape velocity is given by

Hence the escape velocity on moon is much less as compared to earth.

Now, with respect to earth, since moon and earth are at nearly equal distance from each other, the amount of air molecules are same on both planets.

Therefore, rms speed of molecules on both the planet are same. Some of the molecules among them have speed greater than the escape speed and they escape the surface of moon. Hence, over a long period of time many molecules continue to escape from surface of moon and it becomes atmosphere free.

(b) As the gas molecule begin to rise, their gravitational potential energy increases due to increase in their height. We know that energy of a gas molecule is conserved. Therefore, as potential energy increases, kinetic energy starts decreasing

The kinetic energy of gas is given by formula

Where T is the temperature

Hence, as Kinetic energy decreases, the temperature of gas molecules starts decreasing and there is fall in temperature.