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The potential energy function for the fo...

The potential energy function for the force between two in a diatomic molecule can approximately be expressed as `U(x)=(a)/(x^(12))-(b)/(x^(4))`, where `a` and `b` are positive constants, and `x` is the distance between the atoms. Answer the following question by selecting most appropriate alternative.
The graph between potential energy vs `x` will be

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
B
`U(x)=(a)/(x^(12))-(b)/(x^(6))`
`(delta u)/(delta x)=-(12a)/(x^(13))+(6b)/(x^(7))`
For `(delta u)/(delta x)=0 rArr (2a)/(b)=x^(6)`
For `x rArr 0 " " U rarr + oo`
For `x rarr oo " " U rarr 0` from negative side
`U=0 rArr x = root(6)(a/b)`
Hence (B) is correct.
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Knowledge Check

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    B
    `x = 6sqrt((a)/(2b))`
    C
    `x =0`
    D
    `x = 6sqrt((2a)/(b))`

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    A
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