# Potential energy between two oppositely charged ions in a crystal

Hi, I am having trouble with the following:

All I have really done is differentiate the function to give an expression for F(r), but I am a bit clueless about the rest. How can there be equilibrium if the two ions are attracted to each other?

Cheers,
GeoffreyThelm

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## Answers and Replies

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kuruman
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Your potential has two terms, are they both attractive?

I see.. So one (the first term?) is due to the attractive force from one ion, and vice versa for the other? So c is gonna end up being something which looks like electric potential should. So is the point of equilibrium the point between the ions where the first term= the second term?

kuruman
Science Advisor
Homework Helper
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The point of equilibrium is where the sum of the forces is zero. When you have a potential, it is where dU/dx = 0, i.e. where the potential has an extremum (maximum or minimum). In this case it had better be a minimum. Consider plotting this potential to see what it looks like.