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Step 1: Understand the concept of escape velocity. Escape velocity is the minimum speed an object must reach to break free from a gravitational pull without further propulsion.
Step 2: The Moon has a lower gravity compared to Earth, which means that gases can escape its gravitational influence more easily.
Step 3: The root mean square velocity of gas molecules is a measure of the average speed of gas particles at a given temperature. On the Moon, the average speed of gas molecules can exceed the escape velocity due to its low gravity.
Step 4: Since the escape velocity of gas molecules is greater than their root mean square velocity on the Moon, they can escape into space, resulting in no atmosphere.
Conclusion: Therefore, the reason there is no atmosphere on the Moon is that the escape velocity of gas molecules is lesser than their root mean square velocity here.