The potential energy between two atoms in a m | vedclass

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(D) The condition for stable equilibrium is that the net force $F$ acting on the system must be zero,where $F = -\frac{dU}{dx} = 0$.Given $U(x) = ax^{

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$x = \sqrt[6]{\frac{2a}{b}}$

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(D) The condition for stable equilibrium is that the net force $F$ acting on the system must be zero,where $F = -\frac{dU}{dx} = 0$.Given $U(x) = ax^{-12} - bx^{-6}$.Differentiating with respect to $x$:$\frac{dU}{dx} = -12ax^{-13} - (-6bx^{-7}) = -12ax^{-13} + 6bx^{-7}$.Setting the force to zero:$F = -(-12ax^{-13} + 6bx^{-7}) = 0$$12ax^{-13} - 6bx^{-7} = 0$$\frac{12a}{x^{13}} = \frac{6b}{x^7}$$\frac{12a}{6b} = \frac{x^{13}}{x^7}$$\frac{2a}{b} = x^6$$x = \sqrt[6]{\frac{2a}{b}}$.

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:

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