[UPSC CSE 2004] Atomic Physics (Q106, 20M)

(i) Calculate the Zeeman shift observed in the normal Zeeman effect when a spectral line of wavelength 5000\text{ \AA} is subjected to the magnetic field of 0.4\text{ Wb m}^{-2}. (ii) Show that for the ground state of hydrogen atom the mean value of r is 3/2\text{ a}_0, where \text{a}_0 being Bohr radius constant.