SHOW ALL WORK! 1. The net potential energy between two ions, EN, can be represen
ID: 884024 • Letter: S
Question
SHOW ALL WORK! 1. The net potential energy between two ions, EN, can be represented by the sum Using calculus, determine: a) an expression for the separation distance (r r corresponding to a minimum in EN in terms of A,B, and n. This is the equilibrium separation distance. b) an expression for the interatomic potential (EN) at the equilibrium separation distance (re) in terms of A B, and n. This is often termed the bond energy (Eb) for the ion 2. Using the equations from Problem 1 above, assume that A 1.436 ev nm: B 5.86 x 10 eV nm and n -9. Use a computer to plot EA, ER and EN (on the same graph) as a function ofr up to 1.5 nm. NOTE: be sure to include enough points in your plot to roduce a ooth curve! If you do roduce a smooth curve, ou have not atisfactori ONO connect your computed points using anything but a straight line!! a) Determine and label the equilibrium separation distance (r) and bond energy (E) for this interaction on your graph. b) Using your expressions from Problem la and lb, determine the equilibrium separation distance and bond energy and compare with the results you obtained graphically.Explanation / Answer
1. If r = ro and En = Ea + Eb; Ea = -A/r; Eb= -B/rn then:
En = -A/r + B/rn Now let's derivate the expression
dEn/dr = d (-A/r)/dr + d(B/rn)/dr -----> dEn/dr = 0
0 = A/r2 - nB/rn+1
nB/rn+1 = A/r2
nB/A = rn+1 / r2
nB/A = rn-1
r = ro = (nB/A)1/n-1
b) En = -A/r + B/rn
En = B/rn - A/r
En = B / (nB/A)1/n-1 - A / (nB/A)1/n-1
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