Question is in the attachment.

1) The electron in a hydrogen atom is in a 2p orbital state. Its time-independent wave function is (r, 0, 0) = Arexp (- 2ao sin 0 els, where A is a real positive constant. Here the Bohr radius do is given by AnEgh- do = me2 where m is the electron's mass and e its electric charge. (a) Demonstrate by explicit calculation that, for this wave function, Vay = Aa (b) Hence show that this wave function is a solution of the time-independent Schrodinger equation, h2 ATED -th = Ev, 2m and determine the energy E in terms of m, e, co, and h. (A demonstration by substitu tion is quite sufficient: you are not expected to find any kind of general solution to the equation.) (c) Using the normalisation condition IP av =1, in which the integral is taken over all space, determine an expression for A in terms of