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I read this in my class textbook, and learnt the reason of absence of Hydrogen from atmosphere and Maxwell distribution curve from Physics stack exchange. But I am unsure of why should the average velocity be greater than 1/6 times escape velocity. Also why do we use average velocity instead of root mean square velocity?

Edit : average speed > 1/6 the escape velocity. The book is given by our coaching for astronomy Olympiads.

Please refer this question: Why doesn't hydrogen gas exist in Earth's atmosphere?

Vardaan Srivastava
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A gas molecule travelling faster than the escape velocity will only escape if it doesn't hit anything to slow it down. However, gas molecules are constantly colliding, so the even if a molecule/atom achieves escape velocity, the chance of it maintaining that velocity all the way to the edge of the atmosphere is tiny.

I vaguely remember a similar claim in one of my courses that the figure 6 x escape velocity is just an approximate rule of thumb to estimate whether the gas has enough energy to escape the planet/atmosphere at a high enough rate, such that that the planet cannot hold on to it over long timescales. As it's just a very rough estimate, it doesn't matter whether it's the average or the RMS velocity.

Rustony
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Probably some confusion or unclear text source. Any gas molecule that is faster than the escape speed will escape. There is nothing about the number six to see here.

rfl
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