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

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 r 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 r using the following procedure:

(i) Differentiate EN with respect to r, and set the resulting expression equal to zero.

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(ii) Solve for C in terms of D, r, and r0.

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(iii) Determine the expression for E0 by substitution for C in Equation 2.18.

(b) Derive another expression for E0 in terms of r0, C, and r using a procedure analogous to the one outlined in part (a).

 (2.18)