Consider a hypothetical X+—Y− ion pair for which the equilibrium interionic spacing and bo...

Consider a hypothetical X+—Y− ion pair for which the equilibrium interionic spacing and bonding energy values are 0.35 nm and –6.13 eV, respectively. If it is known that n in Equation 2.11 has a value of 10, using the results of Problem 2.14, determine explicit expressions for attractive and repulsive energies EA and ER of Equations 2.8 and 2.9.

Problem 2.14

The net potential energy between two adjacent ions, EN, may be represented by the sum of Equations 2.8 and 2.9; that is,

Calculate the bonding energy E0 in terms of the parameters A, B, and n using the following procedure:

1. Differentiate EN with respect to r, and then set the resulting expression equal to zero, because the curve of EN versus r is a minimum at E0.

2. Solve for r in terms of A, B, and n, which yields r0, the equilibrium interionic spacing.

3. Determine the expression for E0 by substituting r0 into Equation.

 (2.8)

 (2.9)

 (2.11)