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Q.

In a molecule, the potential energy between two atoms is given by : U(x)=ax12−bx6  where a and b are positive constants and x is the distance between atoms. For stable equilibrium of atom, the value of x is.

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a

Zero

b

[a2b]16

c

[2ab]16

d

[11a5b]16

answer is C.

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Detailed Solution

For stable equilibrium of atom, dUdx=0 a(−12x)x−12−1−b(−6)x−7=0⇒          −12ax13+6bx7=0⇒          −12ax6=−6bx6=12a6b=2ab⇒x=(2ab)1/6
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