The net potential energy EN between two adjacent ions, is sometimes represented by the expression EN = -(C/r) + D exp(-r/rho)

in which r is the interionic separation and C, D, and rho are constants whose values depend on the specific material.

Required:
a. Derive an expression for the bonding energy E0 in terms of the equilibrium interionic separation r0 and the constants D and rho using the following procedure:

1. Differentiate EN with the respect to r and set the resulting expression equal to zero.
2. Solve for C in terms of D, rho, and ro.
3. Determine the expression for Eo by substitution for C in the equation EN = -(C/r) + D exp(-r/rho)

b. Derive another expression for Eo in terms of ro, C, and rho using a procedure analogous to the one outlined in part (a).