Calculating Ion Distance in a 1D Lattice: A Simple Solution

[sinna]

Homework Statement

Calculate the distance between the nearest ions at which the two forms of the repulsive potential give equal lattice energies.

Relevant Equations

On the image

 

[DaveE]

You'll need to show us your attempted solution for us to help you.

Also, check out the homework forum guidelines here:
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

 

[kuruman]

Also, the image has no equations.

 

[haruspex]

"nearest ions" suggests there are more than two in the scenario. Is there more intro to this question?

 

[nasu]

In the simplest models of lattice, the repulsive potential is considered to drop much faster than the attractive one so the repulsive effects are considered only between the nearest neighbors in the calculations of the total energy. This is how it is done is some introductory solid-state books, like Kittel's.

 

[hutchphd]

Also are we to assume a 1 dimensional lattice? 2D? 3D? Choose the simplest case and attempt a solution.....