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Question

The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x)=ax12bx6, where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D=[Ux=Uat equilibrium], D is

A
b22a
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B
b212a
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C
b24a
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D
b26a
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Solution

The correct option is C b24a
U(x)=ax12bx6
At x;U()=0

At equilibrium: dUdx=0
12ax13+6bx7=0
12ax13=6bx7
x6=2ab

At equilibrium, U=ax6.x6bx6
=ab(2ab)(2ab)2
=b24a

D=[UUat equilibrium]
=[0+b24a]=b24a

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