Question

The potential energy between two 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 stable equilibrium, when

• A. $x=\bigg(\frac{2a}{b}\bigg)^{1/6}$
• B. $x=\bigg(\frac{11 a}{5b}\bigg)^{1/6}$
• C. $x=0$
• D. $x=\bigg(\frac{a}{2b}\bigg)^{1/6}$

Answer 1

Answer: (A)

$U(x)=\frac{a}{x^{12}}-\frac{b}{x^{6}}$
or $-\frac{12 a}{x^{13}}-\frac{-6 b}{x^{7}}=0$
or $x^{6}=\frac{2 a}{b}$.
Therefore $x=\left(\frac{2 a}{b}\right)^{1 / 6}$.