The potential energy between two atoms in a molecule is given by U=ax3−bx2 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 B2b3a Given: U=ax3−bx2 ∴ Force, F=−dUdx=−(3ax2−2bx) =2bx−3ax2
Now, for equilibrium, F=0 ⇒2bx−3ax2=0 ⇒x=0,2b3a
For stable equilibrium, U should be minimum
i.e d2Udx2=6ax−2b
For x=2b3a, d2Udx2=6a×2b3a−2b=2b>0 ∴ at x=2b3a, P.E is minimum
i.e a condition of stable equilibrium.