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 are constants whose values depend on the specific material (a) Derive an expression for the bonding energy E 0 in terms of the equilibrium interionic separation r 0 and the constants D and using the following procedure 1 Differentiate E N with respect to r and set the resulting expression equal to zero 2 Solve for C in terms of D, , and r 0 3 Determine the expression for E 0 by substitution for C in Equation 2 12 (b) Derive another expression for E 0 in terms of r 0 , C, and using a procedure analogous to the one outlined in part (a) EN (2 12) P

Question: 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,

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

EN (2.12) + P.

in which r is the interionic separation and C, D, and ? 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 ? using the following procedure:

1. Differentiate E_N with respect to r and set the resulting expression equal to zero.

2. Solve for C in terms of D, ?, 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 ? using a procedure analogous to the one outlined in part (a).

EN (2.12) + P.

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