# Electrostatic Potential Energy of an ion

1. Mar 17, 2013

### mateomy

Working from Krane's Modern Physics 11.5

Calculate the first 3 contributions to the electrostatic potential energy of an ion in the CsCl lattice.

I believe the formula I'm supposed to use is
$$U_{c}\,=\,-\alpha\frac{e^{2}}{4\pi\epsilon_{0}R}$$

Just from looking in the chapter I can see this is a bcc type lattice with an $\alpha$ of 1.7627, but I'm not sure how they're getting the answer in the back of the book which is;
$$U_{c}\,=\,-\frac{e^{2}}{4\pi\epsilon_{0}R}\left(8-\frac{6}{2/\sqrt{3}} + \frac{24}{\sqrt{11/3}}\right)$$
There's an example in the book showing the same procedure for an fcc lattice (NaCl) and that converging term is,
$$6-\frac{12}{\sqrt{2}}+\frac{8}{\sqrt{3}}-\ldots$$
but it doesn't derive it, so I'm not really sure how they get it.

Just looking for a few pointers, thanks.

2. Mar 17, 2013

### mateomy

Figured it out.