The potential energy between two atoms in a molecule is given by U(x)=ax12−bx6 where a and b b are positive constants and x is the distance between the atoms. The atoms is in stable equilibrium when
x=6√11a5b
x=6√a2b
x=0
x=6√2ab
A
x=6√11a5b
B
x=6√a2b
C
x=6√2ab
D
x=0
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Solution
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The potential energy between two atoms in a molecule is given by
U(x)=ak12−bx6
The atom is in stable equilibrium. When,
condition for stable equilibrium
F=−dUdx=0
⇒−ddx[ax12−bx6]=0
or, −12ax−13+6bx−7=0
or, +12ax13=6bx7
or, 2ab=x6
x=6√2ab
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