- #1

Jaccobtw

- 163

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- Homework Statement
- $$E_N = \frac{-A}{r} + \frac{B}{r^{n}}$$

Calculate the bonding energy ##E_0## in terms of the parameters A, B, and n using

the following procedure:

1. Differentiate ##E_N## with respect to r, and then set the resulting expression equal

to zero, because the curve of ##E_N## versus r is a minimum at ##E_0##.

2. Solve for r in terms of A, B, and n, which yields ##r_0##, the equilibrium interionic

spacing.

3. Determine the expression for ##E_0## by substituting ##r_0## for r

- Relevant Equations
- $$E_N = \frac{-A}{r} + \frac{B}{r^{n}}$$

1.) So first I differentiate and set it equal to 0 and get:

$$\frac{A}{r^2} -\frac{Bn}{r^{n-1}} = 0$$

2.) When solving for r, I'm not quite sure how to take away the exponent so I get up to the second to last step:

$$r^{n-3} = \frac{Bn}{A}$$

Would it be:

$$r = \sqrt[n-3]{\frac{Bn}{A}}$$

?

Am I doing this problem correctly?

Thank you

$$\frac{A}{r^2} -\frac{Bn}{r^{n-1}} = 0$$

2.) When solving for r, I'm not quite sure how to take away the exponent so I get up to the second to last step:

$$r^{n-3} = \frac{Bn}{A}$$

Would it be:

$$r = \sqrt[n-3]{\frac{Bn}{A}}$$

?

Am I doing this problem correctly?

Thank you