The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x)=\frac{a}{x^{12}}-\frac{b}{x^6}$, where a and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D=\left[U(x=\infty)-U_{ ext…

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The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U(x)=\frac{a}{x^{12}}-\frac{b}{x^6}$, where a and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D=\left[U(x=\infty)-U_{	ext {at equilbrium }}ight], D$ is

Aicharya · Accepted Answer

$ \begin{aligned} & U(x)=\frac{a}{x^{12}}-\frac{b}{x^6} \ & U(x=\infty)=0 \end{aligned} $ as, $\quad \mathrm{F}=-\frac{\mathrm{dU}}{\mathrm{dx}}=-\left[\frac{12 \mathrm{a}}{\mathrm{x}^{13}}+\frac{6 \mathrm{~b}}{\mathrm{x}^7}ight]$ at equilibrium, $\quad F=0$ $\begin{array}{ll}	herefore & x^6=\frac{2 a}{b} \ 	herefore & U_{	ext {at equiltrium }}=\frac{a}{\left(\frac{2 a}{b}ight)^2}-\frac{b}{\left(\frac{2 a}{b}ight)}=\frac{-b^2}{4 a} \ 	herefore & D=\left[U(x=\infty)-U_{	ext {at equilibium }}ight]=\frac{b^2}{4 a}\end{array}$

The potential energy function for the force between two atoms in a diatomic molecule is approximately given…

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