Isn't Born-Landé equation double the electrostatic energy?

Tags:
1. Aug 31, 2015

D O

I'm confused as to how the Born-Landé equation can be extrapolated to find the electrostatic potential for an ionic lattice without halving it, as each interaction is otherwise counted twice.

As I understand it, and according to Wikipedia, the electric potential energy in a charge configuration can be found by this equation:

This is half the sum of the products of the charge of each ion in the lattice with the electric potential at its location provided by each other ion - the Born-Landé equation, however, does not include this factor of 1/2.
I accept that

is the correct sum of the energy stored in the interactions of any one ion, but the final equation multiplies this by the Avogadro constant:

I would have thought that this would have counted every interaction twice, by following this equation for the energy stored in a charge configuration:

Last edited: Aug 31, 2015
2. Sep 5, 2015