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

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?

(300) nlm) n'l'm') | 100).