Linear ionic crystal Consider a line of 2N ions of alternating charge q with a repulsive

Question:

Linear ionic crystal Consider a line of 2N ions of alternating charge ± q with a repulsive potential energy A/Rⁿ between nearest neighbors.

(a) Show that at the equilibrium separation (CGS) U (R₀) = – 2Nq²In2/R₀(1 – 1/n).

(b) Let the crystal be compressed so that R₀ → R₀(l – δ). Show that the work done in compressing a unit length of the crystal has the leading term 1/2Cδ², where (CGS) C = (n – 1) q² In2/R_0.To obtain the results in SI, replace q² by q²/4πε₀. Note: We should not expect to obtain this result from the expression for U (R₀), but we must use the complete expression for U(R).