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

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${(\frac{A}{B})}^{\frac{1}{5}}$

${(\frac{B}{A})}^{\frac{1}{5}}$

${(\frac{2 A}{B})}^{\frac{1}{5}}$

${(\frac{B}{2 A})}^{\frac{1}{5}}$

answer is C.

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Detailed Solution

For Equilibrium, Force acting on the body must be zero.

$\Rightarrow - \frac{dU}{dr} = 0$

$\Rightarrow \frac{- 10 A}{r^{11}} + \frac{5 B}{r^{6}} = 0$
$\Rightarrow r^{5} = \frac{10 A}{5 B} = \frac{2 A}{B}$

$∴ r = {(\frac{2 A}{B})}^{\frac{1}{5}}$

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