A particle near earth's surface traveling faster than about 11 km/s has enough kinetic energy to completely escape from the earth, despite earth's gravitational pull. Molecules in the upper atmosphere that are moving faster than this will therefore escape if they do not suffer any collisions on the way out. (a) The temperature of earth's upper atmosphere is actually quite high, around 1000 K. Calculate the probability of a nitrogen molecule at this temperature moving faster than 11 km/s, and comment on the result.
(b) Repeat the calculation for a hydrogen molecule (H2) and for a helium atom, and discuss the implications.
(c) Escape speed from the moon's surface is only about 2.4 km/s. Explain why the moon has no atmosphere.