- #1
Saladsamurai
- 3,020
- 7
Homework Statement
The net energy is given by:
[tex]E_N=-\frac{A}{r}+\frac{B}{r^n}[/tex]
where A, B , and n are constants and r is the interionic separation. Calculate E0 in terms of A, B, and n by the following procedure:
1. find dEN/dr
2. set this expression equal to zero and solve for r=ro
3. substitute ro back into the original equation
The Attempt at a Solution
Okay, this is more or less an algebra problem that I am stuck on:
[tex]E_N=-\frac{A}{r}+\frac{B}{r^n}[/tex]
[tex]=-Ar^{-1}+Br^{-n}[/tex]
[tex]\Rightarrow \frac{dE_N}{dr}=Ar^{-2}-nBr^{-n-1}[/tex]
[tex]0=Ar^{-2}-nBr^{-n-1}[/tex]
[tex]\Rightarrow 0=\frac{A}{r^2}-\frac{nB}{r^{n+1}}[/tex]
[tex]\Rightarrow 0=\frac{Ar^{n+1}-nBr^2}{r^2*r^{n+1}}[/tex]
[tex]\Rightarrow 0=Ar^{n+1}-nBr^2[/tex]
Here is where my brain melted. Any blatant errors and/or hints?
Hmmm delicious hints