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## Homework Statement

The force between an ion pair is given by [itex]F=-k\alpha\frac{e^{2}}{r^{2}}[1-\left(\frac{r_{\circ}}{r}\right)^{m-1}] [/itex]

Find the value of [tex]r[/tex] where the equilibrium position is.

Determine the effective spring constant for small oscillations from the equilibrium.

Using [itex]m=8~\text{and}~\alpha=1.7476[/itex] estimate the frequency of vibration of a Na+ ion in NaCl

## Homework Equations

Binomial expansion theorem

## The Attempt at a Solution

The first question is easy as you set the force equal to 0 and it is no surprise that the answer is [itex]r=r_{\circ}.[/itex] When I try using the binomial expansion theorem, I always end up with a dependence on [itex]r_{\circ}[/itex]. But in the next portion, I have to find the frequency of vibration for Na+ ion and am only given alpha and m. Thanks for any help.

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