Potential energy between two oppositely charged ions in a crystal

AI Thread Summary
The discussion centers on understanding the potential energy between two oppositely charged ions in a crystal. The user, Geoffrey, is confused about how equilibrium can exist despite the attractive forces between the ions. It is clarified that equilibrium occurs when the forces acting on the ions balance out, leading to a net force of zero. The equilibrium point is where the derivative of potential energy with respect to position equals zero, indicating a minimum potential. Visualizing the potential through a graph is recommended to better understand the relationship between the forces and equilibrium.
geoffreythelm
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Hi, I am having trouble with the following:

attachment.php?attachmentid=20081&stc=1&d=1250100045.jpg


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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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 going to 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?
 
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.
 

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