Question

Moon has no atmosphere because
$\left( a \right)$ It is a satellite of earth
$\left( b \right)$ It doesn’t have a population
$\left( c \right)$ It is colder than earth
$\left( d \right)$ r.m.s velocity of all the gases is more than the escape velocity from its surface

Answer 1

Hint So to answer this question we should have the knowledge of the root mean square velocity and also the concept of escape velocity, and we also know that the escape velocity is very less as compared to the root mean square velocity. So by using these concepts, we can conclude the answer.

Complete Step by Step Solution The speed (the minimum velocity with which a body is to be projected thus to escape the gravitational pull) on the surface of the moon may be a heap of less, not precisely the RMS speed (Root Mean square speed) of the particles of gas at the surface temperature of the moon. So the molecules can escape and thus the moon cannot hold an environment. Escape velocity will be given by the expression as- $\sqrt 2 gr$
The moon’s surface temperature cycles between$- {155^ \circ }c{\text{ and 10}}{{\text{0}}^ \circ }c$. With the increase in the temperature then, in comparison to the escape velocity the molecule's speed is much more.
The size of the moon compared to earth is extremely small and thus its gravitational acceleration is very small $1.62m{s^{ - 2}}$. This force brings about exceptionally little break speed from its surface, which is considerably more modest than the r.m.s speed from its surface, which is significantly more modest than the r.m.s velocity of all the gases. Thus the moon has no atmosphere.

Therefore, the option $\left( d \right)$ is correct.

Note If the Moon suddenly got an atmosphere, it would be blown off in a few million years, with some of it settling on each of the other planets. Winds would be a feature of the moon for a while, and dust would fly until all the light material is lifted and redistributed. Its appearance would change dramatically and wind erosion would affect current features.