Chapter 7.8, Problem 88E

Adding a proton to a nucleus The nucleus of an atom is positively charged because it consists of positively charged protons and uncharged neutrons. To bring a free proton toward a nucleus, a repulsive force F(r) = kqQ/r² must be overcome, where q = 1.6 × 10⁻¹⁹ C (coulombs) is the charge on the proton, k = 9 × 10⁹ N-m²/C², Q is the charge on the nucleus, and r is the distance between the center of the nucleus and the proton. Find the work required to bring a free proton (assumed to be a point mass) from a large distance (r → ∞) to the edge of a nucleus that has a charge Q = 50q and a radius of 6 × 10⁻¹¹ m.