Quantum wavefunction (Question 2 (20 Marks)) — UPSC Physics Optional CSE 2011 Paper II

The normalized wave function for the electron in the ground state of the hydrogen atom is given by \psi(r)=\frac{1}{(\pi a_0^3)^{1/2}}e^{-r/a_0} where a_0 is the radius of the first Bohr orbit. Calculate \langle r\rangle and \left\langle\frac{1}{r}\right\rangle.