Starting with the result of Problem 28, approximate r r0 + δ r (where δ r << r0)...

Starting with the result of Problem 28, approximate r r₀ + δ r (where δ r << r₀) and show that

Perform a Taylor series expansion about r = r₀, keeping terms up to and including order (δ r)². Show that

where

and

Problem 28

Use Equation (10.19) to evaluate the net force (F =-dV/dr) on an atom in a sodium chloride lattice. Then show that the force can be expressed as