Q. The potential energy as a function of the force between two atoms in a diatomic molecules 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 position of stable equilibrium for the system of the two atoms is given
A) $x = \frac{a}{b}$
B) $x = \sqrt{\frac{a}{b}}$
C) $x = \frac{\sqrt{3a}}{b}$
D) $x = \sqrt[6]{\left( \frac{2a}{b} \right)}$
Explanation
(d) $U(x) = \frac{a}{x^{12}} - \frac{b}{x^{6}}$ at the stable equilibrium $\frac{du}{dx} = 0$
$\therefore\ \ - \frac{12}{x^{13}} + \frac{6b}{x^{7}} = 0 \Rightarrow x = \left( \frac{2a}{b} \right)^{1/6}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.