Question

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.

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!

Answer 1

Given E_N= -A/r + B/rⁿ

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

A/r_o² = nB/r_o⁽ⁿ⁺¹⁾

ro ^(n+1)/r_o²= nB/A

r_o^(n+1-2)= (nB/A )

r_o= (nB/A )^1/(n-1)

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