Walker, Halliday & Resnick — The Kinetic Theory of Gases: Problem 47

47 At what temperature does the rms speed of (a) $H_2$ (molecular hydrogen) and (b) $O_2$ (molecular oxygen) equal the escape speed from Earth (Table 13-2)? At what temperature does the rms speed of (c) $H_2$ and (d) $O_2$ equal the escape speed from the Moon (where the gravitational acceleration at the surface has magnitude $0.16g$)? Considering the answers to parts (a) and (b), should there be much (e) hydrogen and (f) oxygen high in Earth’s upper atmosphere, where the temperature is about $1000 \text{ K}$?