An electron in the n — 3, l = 0, m = 0 state of hydrogen decays by a sequence of (electric...

An electron in the n — 3, l = 0, m = 0 state of hydrogen decays by a sequence of (electric dipole) transitions to the ground state.

(a) What decay routes are open to it? Specify them in the following way:

(b) If you had a bottle full of atoms in this state, what fraction of them would decay via each route?

(c) What is the lifetime of this state? Hint: Once it's made the first transition, it's no longer in the state |300), so only the first step in each sequence is relevant in computing the lifetime. When there is more than one decay route open, the transition rates add.