Q 11-05-120JEE MainJEE Main 2022 (24 Jun, Shift 2)Easy
Potential energy as a function of $r$ is given by $U = \dfrac{A}{r^{10}} - \dfrac{B}{r^5}$, where $r$ is the interatomic distance, $A$ and $B$ are positive constants. The equilibrium distance between the two atoms will be:
Answer: (C) $\left(\dfrac{2A}{B}\right)^{1/5}$
At equilibrium $F = -\dfrac{dU}{dr} = 0$:
$$-\frac{10A}{r^{11}} + \frac{5B}{r^6} = 0\ \Rightarrow\ r^5 = \frac{2A}{B}\ \Rightarrow\ r = \left(\frac{2A}{B}\right)^{1/5}$$
Solution by Sreeraj P, M.Sc Physics