 #1
Jaccobtw
 162
 31
 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:
$$\frac{A}{r^2} \frac{Bn}{r^{n1}} = 0$$
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:
$$r^{n3} = \frac{Bn}{A}$$
Would it be:
$$r = \sqrt[n3]{\frac{Bn}{A}}$$
?
Am I doing this problem correctly?
Thank you
$$\frac{A}{r^2} \frac{Bn}{r^{n1}} = 0$$
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:
$$r^{n3} = \frac{Bn}{A}$$
Would it be:
$$r = \sqrt[n3]{\frac{Bn}{A}}$$
?
Am I doing this problem correctly?
Thank you