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6 October, 15:44

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.

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  1. 6 October, 16:10
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    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)
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