(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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 E_{0}in terms of A, B, and n by the following procedure:

1. find dE_{N}/dr

2. set this expression equal to zero and solve for r=r_{o}

3. substitute r_{o}back into the original equation

3. 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

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# Homework Help: Net Potential Energy between two Adjacent Ions

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