The potential energy between two atoms, in a molecule, is given by $U(x)=\frac{a}{x^{12}}-\frac{b}{x

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\

Professor PC Thomas Classes · 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 $x=\left(\frac{2 a}{b}ight)^{1 / 6}$\