Why is there no atmosphere on the Moon? Explain it in terms of escape velocity.

(N/A) The escape velocity of a body on the surface of a planet is given by $v_{e} = \sqrt{\frac{2GM}{R}}$.
For the Moon,the escape velocity is $(v_{e})_{\text{moon}} = \sqrt{\frac{2GM_{m}}{R_{m}}}$.
Given the mass of the Moon $M_{m} \approx 7.36 \times 10^{22} \text{ kg}$ and its radius $R_{m} \approx 1.74 \times 10^{6} \text{ m}$,the escape velocity is calculated as:
$(v_{e})_{\text{moon}} \approx 2.38 \text{ km/s}$.
The root mean square velocity of gas molecules at the surface temperature of the Moon is higher than this escape velocity. Because the thermal velocity of the gas molecules exceeds the escape velocity of the Moon,the gas molecules easily escape the Moon's gravitational pull. Consequently,the Moon cannot retain an atmosphere.