•• We saw in Example 13.1 that the PE of any one ion in NaCl has the form U = −α ke2/r0, w...

•• We saw in Example 13.1 that the PE of any one ion in NaCl has the form U = −α ke2/r0, where α = 1.75 is called the Madelung constant. The calculation of this constant in three dimensions is much more trouble than it is worth here, but the one-dimensional Madelung constant is fairly easy to calculate, as follows: Consider a long one-dimensional “crystal” of alternating Na+ and Cl− ions spaced a distance r0 apart. Prove that the PE of any one ion is U = −a ke2/r0, where α = 1.39. [Hint: The series for ln(l + z) in Appendix B (with z = 1) is useful in this calculation.]