In sunlight, the Moon's surface reaches about 390 K…

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Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

In sunlight, the Moon's surface reaches about $390$ K. The escape speed from the Moon is $2.38$ km/s. (a) Find the rms speeds of hydrogen ( $2$ g/mol) and oxygen ( $32$ g/mol) at $390$ K. (b) The fraction of molecules faster than a speed $v$ is $\operatorname{erfc}(x) + \dfrac{2x}{\sqrt{\pi}}e^{-x^2}$ , where $x = v/v_{mp}$ . Use the program to find this fraction at the escape speed, for both gases. Which gas does the Moon lose quickly?

Need a reminder? The key ideaShow

\displaystyle v_{rms} = \sqrt{\frac{3RT}{M}}, \quad v_{avg} = \sqrt{\frac{8RT}{\pi M}}, \quad v_{mp} = \sqrt{\frac{2RT}{M}}

with $M$ in kg/mol. The ratio is $v_{mp} : v_{avg} : v_{rms} = 1 : 1.128 : 1.225$ .

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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