According to quantum mechanics, the electron cloud for a hydrogen atom in the ground state has a charge density
ρ(r)=πa3qe−2r/a,
where q is the charge of the electron and a is the Bohr radius. Find the atomic polarizability of such an atom. [Hint: First calculate the electric field of the electron cloud, Ee(r); then expand the exponential, assuming r≪a.]