Atmospheric gas problem

(a) What would the temperature of the Earth's atmosphere have to be such thet the average speed of a hydrogen molecule(H2) is Equal to the Earth's escape velocity?  What about an oxygen molecule(O2)?

(b) It is thought that our atmosphere initially contained hydrogen molecules.  Assuming the temperature of our atmosphere is 300K, and assuming the velocity distribution of the molecules in our atmosphere is a Maxwell distribution, estimate the fraction of hydrogen molecules that had a velocity greater than the escape velocity, and use this fraction to estimate the rate of hydrogen molecules escaping from Earth (assume the initial density of hydrogen equal to the current density of our atmosphere at sea level).  Finally estimate the amount of time it would have taken for 50% of the original hydrogen gas in our atmosphere to escape.