Halliday, Resnick & Walker — The Kinetic Theory of Gases: Problem 39

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 13.5.1)? 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 \(1000\text{ K}\)?