The potential energy, E, per Cs+-Cl- ion pair within the CsCl crystal depends on

Question

The potential energy, E, per Cs+-Cl- ion pair within the CsCl crystal depends on the interionic separation, r, expressed mathematically thus: E(r) = -e2M/(40r) + B/rm, where, e = 1.6 x 10-19 C, M = 1.763, 0 = 8.85x10-12 Fm-1, B = 1.192 x 10-104 Jm9, or 7.442 x 10-5 eV(mm)9, and m = 9, . Find the equilibrium separation (requ), of the ions in the crystal and the ionic bonding energy that is the ionic cohesive energy. Next, generate the corresponding Energy-Separation plot for the cesium chloride solid.

Explanation / Answer

The equilibrium expression is when the Force = 0

Force = dE/dr =E(r) / dr = ( -e2M/(4pi0r) + B/rm) / dr = ( -e2M/(40r^2) + B/r (m+1)) = 0

e2M/(4pi0r^2) = B/r^(m+1)

So we can solve value of r from this expression.

e2M/(4pi0r2) = B/r10

(1.6X 10-19)2 X 1.763 / 4 X 3.14 X 8.85x10-12 = 1.192 x 10-104 / r^8

However the value of B is very high

So we can not calculate the value of r here

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