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Molecules escaping Earth's gravity

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Escape velocity near Earth's surface is 11 km/s which means that a particle near Earth's surface traveling faster than about 11 km/s will have enough kinetic energy to completely escape from Earth's gravitational pull. Molecules in the upper atmosphere that are moving faster than this will therefore escape if they do not suffer any collision on the way out.

a) The temperature of the upper atmosphere is actually quite high, around 1000 K. Calculate the probability of a nitrogen molecule escaping from earth's atmosphere.

b) Repeat the calculation for a hydrogen molecule and for a helium atom and discuss the implications.

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