"Why is there no atmosphere on the Moon" – Explain it in terms of escape velocity

Explanation

`implies` Escape velocity of a body lying on the surface of earth is
`v_(e) = sqrt((2GM_(E))/R_(E))" "...(1)`
`implies` Let mass of moon in `M_(m) ` and radius `R_m` then the body lying on the suface of moon has escape velocity.
`(v_(e))_("moon")= sqrt((2GM_m)/(R_m))" "...(2)`
`implies` Substituting the values of `M_m and R_m` in above equation,
`(M_(m) = 7.36 xx 10^(22) kg`
`R_m = 1856 ` km
` = 1856 xx 10^(3) m)`
`(v_e)_("moon") = 0.23 xx10^(4) m//s`
`(v_(e))_("moon") = 2.3 xx 10^(4) km//s`
`implies` If gas exist on moon the speed of this gas is 2.3 km/s corresponds to the temperature on the moon. This speed is more than the value of escape velocity and hence the gases escapes from the gravitational field of moon and so there is no atmosphere.