(a) The magnitude of the electric field of an ionic species i of valence zi and radius ri located a radial distance r from the centre of the ion in a medium of dielectric constant medium is; Ei(r)=4r2mediumrelativeoqozi where qo(1.6021019C) is the magnitude of the electronic charge, and o(8.851012Fm1) is the dielectric permittivity of free space. Derive an expression for the Born energy of such an ion assuming that it is located solely in the bulk of a medium remote from any other media. (6 marks) (b) What are the changes in Born energy in units of kT, when a sodium ion (of radius rNa+=0.095nm), an hydrated sodium ion (rNa+H2O=0.24nm), a chloride ion solution of dielectric constant 78.9 to the bulk of a fully cross-linked polymer of dielectric constant 10 , where k(1.381023JK1) is the Boltzmann constant and T(298K)? (c) In what states are Na+and Clions most likely to permeate the polymer? Explain why in one or more sentences. Shown on the next page are spatial distributions of Born energies for hydrated Na+and Clions through a planar 100A(10nm) thick membrane referenced to energies for those ions remote from the membrane in the bulk feed and filtrate solutions of respectively concentrations, Cfeed and Cfiltrate. Dot-dashed lines indicate where the dielectric constant changes from that for the membrane to that for the solutions. Dashed lines indicate where ions span both the membrane and solutions. (d) Explain in one or more sentences why Born energy difference estimated in part (b) may not compare favourably with the Born energy distributions shown above