2. ( /34 pts) Consider an electron in the hydrogen atom described by the wave function /42m. (a) (6 pts) Determine the radial wave function as a function of r Rul(r) = _p'tie-Pf(p), using the recursion formula 2(j + 1+1-n) C+1 = (j + 1) (3 + 21 + 2) ? where f (p) = >cipi. You may use the normalization constant co = V1/5a. (b) (4 pts) Show that /42-2 is orthogonal to /420.For reference: 15 Y2-2 ( 0, 0 ) = -2id . sin2 0 4 2 TT 15 Y2-' (0, $ ) = e -id . sin 0 . cos 0 2 2 TT Y2 (0, $ ) = 1 . (3 cos2 0 - 1) TT 15 Y2 (0, 0) = - . el9 . sin 0 . cos 0 2 V 2 TT 15 Y2 (0, 0) = e2id . sin2 0 4 2 TT