The Balmer series refers to the emission of photons corresponding to transitions in atomic hydrogen which give wavelengths in the visible region of the electromagnetic spectrum. The relevant transitions are given special names: the H-a transition corresponds to a 3p to 2s transition; H-b corresponds to 4p to 2s; H-g corresponds to 5p to 2s; and H-d corresponds to 6p to 2s. (a) Show that the selection rule for l is satisfied for each of these transitions. (b) Find the wavelengths for the given transitions.  (c) What is the ionization energy for the electron in the n = 4 state of atomic hydrogen?

Note:  The following values are the result of experimental measurements.

H_a = 656.3 nm        H_b = 486.1 nm        H_g = 434.0 nm        H_d = 410.2 nm