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Question

The potential energy between two atoms in a molecule is given by U=ax3bx2 where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when x is equal to

A
0
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B
2b3a
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C
3a2b
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D
3b2a
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Solution

The correct option is B 2b3a
Given: U=ax3bx2
Force, F=dUdx=(3ax22bx)
=2bx3ax2

Now, for equilibrium,
F=0
2bx3ax2=0
x=0,2b3a

For stable equilibrium, U should be minimum
i.e d2Udx2=6ax2b
For x=2b3a,
d2Udx2=6a×2b3a2b=2b>0
at x=2b3a, P.E is minimum
i.e a condition of stable equilibrium.

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