Highly excited atoms have electrons with large principal quantum numbers. Such Rydberg atoms have unique properties and are of interest to astrophysicists.

(a) For hydrogen atoms with large n, derive a relation for the separation of energy levels.

(b) Calculate this separation for n = 100; also calculate the average radius, the geometric cross section, and the ionization energy.

(c) Could a thermal collision with another hydrogen atom ionize this Rydberg atom?

(d) What minimum velocity of the second atom is required? 

(e) Could a normal sized neutral H atom simply pass through the Rydberg atom leaving it undisturbed?

(f) What might the radial wavefunction for a 100s orbital be like?