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 $D=[U(x=\infty )-U_{atequilibrium}]$, $D$ is:

1. A
   $\frac{b^2}{2a}$
2. B
   $\frac{b^2}{12a}$
3. C
   $\frac{b^2}{4a}$
4. D
   $\frac{b^2}{6a}$