2. The ground-state wave function of the Hydrogen atom has the form h} are2 wk} 2 A camring). as = {1) (to be derived later) where :1 is the normalization constant. 3" is the position vector of the electron relative to the nucleus, r=|r|_. and a}; is Bohris radius. Compute (a) The normalization constant A; (b) the mean (average) potential energy of interaction between the electron and the nucleus: (\".2 02 Q I\" (c) Assuming the relationship between the mean potential energy of interaction and the total energy of the electron is the same as that between their classical counterparts employed in Problem 1 of Assignment 1_. determine the ground-state energy of the Hydrogen atom. (d) Employing the fact that the average electron charge density is given by Mr) = lunar 3) compute the electric field in the Hydrogen atom in its ground state. As a reminder, the electric field inside spherically-synunetric charge distribution is radial and given by EU) = E\"? (4) 1'" where of?) is the total charge inside the sphere of radius r (Gaussis theorem in disguise). Leave your answer in terms of Bohris radius (and electron charge a} and explain the behavior of the electric field as a function of distance r from the nucleus in the r sir: a3 and r :3} :13 limits