The net potential energy EN between two adjacent ions is sometimes represented by the expression

in which r is the interionic separation and C, D, and ρ are constants whose values depend on the specific material.
(a) Derive an expression for the bonding energy E0 in terms of the equilibrium interionic separation r0 and the constants D and ρ using the following procedure:
1. Differentiate EN with respect to r and set the resulting expression equal to zero.
2. Solve for C in terms of D, ρ, and r0.
3. Determine the expression for E0 by substitution for C in Equation 2.12.
(b) Derive another expression for E0 in terms of r0, C, and ρ using a procedure analogous to the one outlined in part (a).

(2.12)