Cohesive energy of ionic solid
F=Fatt+Frep
F=rmA−rnB
Fatt=4πϵr2Ae2
Frep=rnB
Work done by system of atom equal to negative of potential energy
W=−P.E,P.E=−W
PE=−4πϵrAe2+rnB
Equilibriumr=r0
PE=-W=U(r)=min
Differenciate U(r) at r=r0 W.r.t. to r is zero
drdU(r)∣r=r0=0
drd(−4πϵr2Ae2)+drd(r0nB)=0
4πϵAe2(−r021)−nBr0n−1=0
4πϵr0Ae2αn1=r0nB
Now potential energy
−4πϵr0Ae2+4πϵr0Ae2×n1=PE
P.E=−4πϵr0Ae2(1−n1)
Unit are ev and Jules
Cohesive energy ionic solid per molecule per ion
PE=−4πϵr0Ae2(1−n1)×21
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