Problems 1-3, which ask you to explore expressions for the interatomic bonding e

Question

Problems 1-3, which ask you to explore expressions for the interatomic bonding energy, are confusing as you need the answer to problem 3 to answer problem 2 - they are a bit inverted. Please work you way through problems 1 and 2, and the answer to problem 3 is already contained in the earlier problems. Sorry for the confusion!
For the first 3 questions, refer to the following information: The net potential energy between two adjacent A B ions, EN, may be represented by as: EN where A and B are constants r is a radial distance. Question 1 Calculate the bonding energy (minimum energy) Eo in terms of A, B and n by calculating the minimum value for EMr) Question 2. Solve forrin terms of A, B and n, which provides the minimum interatomic spacing no. Question 3. Use the calculated no value to determine the expression for the minimum energy Eo.

Explanation / Answer

Given EN= -A/r + B/rn

Hence d(EN/dr) =A/r2 – nB/r(n+1) = 0 for minimum energy, r becomes r0 ( the minium interatomic spacing

A/ro2 = nB/ro(n+1)

ro (n+1)/ro2= nB/A

ro(n+1-2)= (nB/A )

ro= (nB/A )1/(n-1)

EN( Minimum)= -A/(nB/A)1/(n-1) +B/(nB/A)n/(n-1)

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