Exercise 29 notes that more energy is required to ionize sodium than is retrieved by addin...

Exercise 29 notes that more energy is required to ionize sodium than is retrieved by adding that electron to an isolated chlorine atom, but the NaCl bond represents a lower energy because the attracting ions draw close together. Quantifying the energy-lowering effect of having alternating plus and minus charges can be rather involved for a 3D lattice, but a one-dimensional calculation is instructive. Consider an infinite line of point charges alternating between +e and -e, with a uniform spacing between adjacent (opposite) charges of a. (a) The electrostatic potential energy per ion is the same for a given positive ion as for a given negative ion. Why? (b) Calculate the electrostatic potential energy per ion. For simplicity, assume that a positive charge is at the origin. The following power series expansion will

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