Consider a model of the atom by assuming that the electron cloud possess a spherical charge distribution where the charge density is dependent on the radial coordinater, as measured from the center of the electron cloud. Specifically, the electron cloud charge density is given by pe(r) = Ae-2r/a where A is a constant and a is a characteristic length. [You may find the following integral useful: ſuebudu = ebu (u?/6 - 2u/62 +2/3) + (a) (2 pts) Find A such that the total electron cloud charge is - (b) (5 pts) Find the magnitude of the electric field, E(d), produced by the electron cloud at a distance d away from the center of the electron cloud. (c) (5 pts) Show that, in the limit d