Materials Science - Derivation of Kapustinskii equation

10-D King

[b]1. The equilibrium bond length r₀ in ion components (or salts) can always be obtained from the tabulated values of cationic, r₊, and anionic radii, r_-, respectively as
r₀=r₊ + r_-

Show how on this basis, and that above (refering to the first part of the problem where i was to verify that the magdelung constants divided by the number of ions in one formula unit is constant(A/v)), the Born-Lande and Borne-Mayer equations become the Kapustinskii equations.

[b]2. Borne-Lande equation


Borne-Mayer Equation




[b]3. When carrying out the first part of the equation i obtained an average (A/v) value of 0.839 and i can easily derive the actual Borne equations but no matter what i try i cant get a decent answer for the derivation of the Kapustinskii equation

Any assistance would be of great appreciation.