Q71 / 90 · JEE Main 2022 (24 Jun Shift 2) · Physics

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 :

Solution

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

Now, for equilibrium, $\frac{d U}{d r} = 0$ .

So, differentiating the given equation,

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

$\Rightarrow \frac{10 A}{r^{11}} = \frac{5 B}{r^{6}} \Rightarrow r^{5} = \frac{2 A}{B} \Rightarrow r = {(\frac{2 A}{B})}^{\frac{1}{5}}$

Hence, the correct answer is option: 'C'.