First slide

Potential energy

Question

The potential energy between the atoms in a molecule is given by $U (x) = \frac{a}{x^{12}} - \frac{b}{x^{6}}$ where, a and b are positive constants and x is the distance between the atoms . The atom is in equilibrium when

Moderate

A

$x = 0$
B

$x = {(\frac{a}{2 b})}^{1 / 6}$
C

$x = {(\frac{2 a}{b})}^{1 / 6}$
D

$x = {(\frac{11 a}{5 b})}^{1 / 6}$

Solution

At equilibrium. $F = - \frac{d U}{d x} = 0 \Rightarrow (- 12) a x^{- 13} + (6 b x^{- 7}) = 0$
$∴$ $x = {(\frac{2 a}{b})}^{1 / 6}$

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