I\'m having a difficult time figuring out how to approach thefollowing Inorganic

Question

I'm having a difficult time figuring out how to approach thefollowing Inorganic problem in 2-dimentional crystal structure ofan unknow compound. Problem Question: Consider a line of alternating cations andanions as shown below. Estimate a value for the Madelung constantof this "lattice." - + - + - + - + - + - + - +- -->| r0 |<-- Does anyone has any idea what's going on here? I'm having a difficult time figuring out how to approach thefollowing Inorganic problem in 2-dimentional crystal structure ofan unknow compound. Problem Question: Consider a line of alternating cations andanions as shown below. Estimate a value for the Madelung constantof this "lattice." - + - + - + - + - + - + - +- -->| r0 |<-- Does anyone has any idea what's going on here?

Explanation / Answer

You first charge has a attractive interaction (-) interacts with(+) The (-) then interacts with the (-) 2 units away (repulsion) Then it interacts favorably with the (+) 3 units away. Coulomb's law: -1 + 1/2 - 1/3 + 1/4 - 1/5 + .... => -(1 - 1/2 + 1/3 - 1/4 + 1/5 - ...) The number in parantheses converges to ln(2) (this is analternating harmonic series)

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