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The potential energy between two atoms i...

The potential energy between two atoms in a molecule is given by `U(x)= (a)/(x^(12))-(b)/(x^(6))`, where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when

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Force is zero `rArr (dU)/(dx)=0`
i.e., `a(-12)x^(-13)-b(-6)x^(-7)=0`
`(-12a)/(x^(13))+(6b)/(x^(7))=0 rArr (12 a)/(x^(13))=(6b)/(x^(7))`
`rArr x^(6)=(2a)/(b) therefore x=[(2a)/(b)]^(1//6)`
`U_(min)=a((b)/(2a))^(12//6)-b((b)/(2a))^(6//6)`
`rArr U_(min)=(ab^(2))/(4a^(2))-(b^(2))/(2a)rArr U_(min)=(-b^(2))/(4a)`
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