[UPSC CSE 2003] Angular momentum, spin etc (Q332, 10+10M)

(i) Show that the radial probability density of the ground state of the hydrogen atom has a maximum at r = a. The ground state wave function of the hydrogen atom is given by \psi (r) = \frac{1}{\sqrt{\pi a^{3/2}}} e^{-r/a} where a is the Bohr radius. (ii) Calculate the Larmor frequency of a spin 1/2 particle in a magnetic field B.