The net potential energy between two adjacent ions, EN, may be represented by the sum of Equations 2.9 and 2.11; that is, (2.17) EN = A/r+B/r^n 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 2.17.

Question

Engineering

Alanna Parker

20 July, 10:07

The net potential energy between two adjacent ions, EN, may be represented by the sum of Equations 2.9 and 2.11; that is, (2.17) EN = A/r+B/r^n 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 2.17.

+1

Answers (1)

Know the Answer?

Malaki Mitchell · Answer 1

Eo = A/[-nB/A]^ (1/n-1) + B/[-nB/A]^ (n/n-1)

Explanation:

Step 1.

Taking derivative of the equation with respect to 'r' we get:

d/dr (EN) = - A/r² - nB/r^ (n+1)

Setting this equation to zero:

Step 2.

Solving for r:

- A/r² - nB/r^ (n+1) = 0

A/r² + nB/r^ (n+1) = 0

Ar^ (n+1) + nBr² = 0

Ar^ (n+1) = - nBr²

[r^ (n+1) ]/r² = - nB/A

r^ (n+1-2) = - nB/A

r^ (n-1) = - nB/A

Taking power 1 / (n-1) on both sides:

r = [-nB/A]^ (1/n-1)

This is the value of ro:

ro = [-nB/A]^ (1/n-1)

Step 3.

Substituting value of ro in eqn we get value of Eo

Eo = A/[-nB/A]^ (1/n-1) + B/[-nB/A]^ (n/n-1)