How Do You Calculate Work Done in Lattice Compression?

[RAD17]

I'm given the energy for a crystal lattice is

U(Ro) = (-2Nq^2 ln(2) (1-1/n))/Ro for equilibrium separation (Ro).
I need to show that the work to compress the crystal from Ro --> Ro(1-x) is 1/2Cx^2

where C = (n-1)q^2 ln(2)/ Ro.

Any hints about where to start? I thought it would just be taking the differences of the two energies but my value for C is not matching the one given.

 

[Gokul43201]

Please write down the original question EXACTLY as it was given to you (and include the source, if you know it). There is no way you can determine the work done in compressing the crystal simply from knowing the energy at one particular separation.

All you've done is calculate what the equilibrium energy would be for a different crystal whose lattice spacing is not Ro. That's not what the question is asking for.

If you have a general expression for the lattice energy, think about what the Taylor expansion about the equilibrium spacing tells you.