Q 11-05-143JEE MainJEE Main 2021 (25 Feb, Shift 1)Easy
The potential energy $(U)$ of a diatomic molecule is a function dependent on $r$ (interatomic distance) as $U = \dfrac{\alpha}{r^{10}} - \dfrac{\beta}{r^5} - 3$ where, $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be $\left(\dfrac{2\alpha}{\beta}\right)^{\frac{a}{5}}$, where $a$ = ______.
Numerical value type. Enter your answer.
Answer: 1
At equilibrium $\dfrac{dU}{dr} = 0$:
$$-\frac{10\alpha}{r^{11}} + \frac{5\beta}{r^6} = 0 \Rightarrow r^5 = \frac{2\alpha}{\beta} \Rightarrow r = \left(\frac{2\alpha}{\beta}\right)^{1/5}$$
So $a = 1$.
Solution by Sreeraj P, M.Sc Physics