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Question

The potential energy between two atoms in a molecule is given by U(x)=ax12bx6 where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when

A
x=(2ab)16
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B
x=(11a5b)16
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C
x=0
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D
x=(a2b)16
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Solution

The correct option is A x=(2ab)16
Using Lennard jones potential graph,

Atoms will be in stable equilibrium when potential energy between them will be minimum.
Finding the minima for stable points
dUdx=0 (for minima)
dUdx=(ax12bx6)dx=12ax13+6bx7
On solving further,
2ab=x6
x=(2ab)1/6


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