Suppose two hydrogen atoms, both initially in their ground state, are accelerated up to high speed and then collide head on. 

(a) Derive an expression for the speed necessary to raise both atoms to the same excited state, n. Assume all the initial kinetic energy goes into the energy of the electrons in the two atoms. Express your answer as a function of n. 

(b) Evaluate this expression for n = 2. 

(c) To what temperature would you need to heat hydrogen gas to make this collision likely?