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  • Potential energy as a function of  is given by <img alt="\mathrm{U=\frac{A}{r^{10}}-\frac{B}

Potential energy as a function of \mathrm{r} is given by \mathrm{U=\frac{A}{r^{10}}-\frac{B}{r^{5}}}  where \mathrm{r} is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be:

Option: 1

\mathrm{\left (\frac{A}{B} \right )^{\frac{1}{5}}}


Option: 2

\mathrm{\left (\frac{B}{A} \right )^{\frac{1}{5}}}


Option: 3

\mathrm{\left (\frac{2A}{B} \right )^{\frac{1}{5}}}


Option: 4

\mathrm{\left (\frac{B}{2A} \right )^{\frac{1}{5}}}


Answers (1)

best_answer

U=\frac{A}{r^{10}} -\frac{B}{r^{5}}

F= -\frac{dU}{dr}

F= -10Ar^{-11}+5Br^{-6}
At equilibrium, F=0

0= -10A\left ( r^{-11} \right ) + 5B \left ( r^{-6} \right )

0= -10Ar^{-5}+5B

\frac{10A}{5B}=r^{5}

\Rightarrow \left ( \frac{2A}{B} \right )^{\frac{1}{5}}=r
The corredt option is (3)

Posted by

sudhir.kumar

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