Potential energy of a diatomic molecule is given by U = frac{A}{r^{12}} - frac{B}{r^6} . A and

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11.Thermodynamics

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The potential energy of a diatomic molecule is given by $U$ = $\frac{A}{r^{12}} - \frac{B}{r^6}$.$A$ and $B$ are positive constants. The distance $r$ between them at equilibrium is

A

$(\frac{A}{B})^\frac{1}{6}$

B

$(\frac{2A}{B})^\frac{1}{6}$

C

$(\frac{A}{2B})^\frac{1}{6}$

D

None of these

Solution

At equilibrium $\frac{\mathrm{d} \mathrm{U}}{\mathrm{dr}}=0$

$\frac{-12 A}{r^{13}}+\frac{6 B}{r^{7}}=0$

$r=\left(\frac{2 A}{B}\right)^{1 / 6}$

Standard 11

Physics

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