3. The molecular bonding in a diatomic molecule such as the nitrogen $(\mathbf{N}_2)$ molecule can be modeled by the Lennard-Jones potential, which has the form $U(x) = 4U_0\left(\left(\frac{x_0}{x}\right)^{1/2} - \left(\frac{x_0}{x}\right)^6\right)$, where $x$ is the separation distance between the two nuclei and $x_0$, and $U_0$ are constants. The equilibrium separation $x_0$, which is the value of $x$ for which the two atoms experience zero force from each other, is equal to
(A)$2^{-1/6}x_0$
(B)$3^{1/6}x_0$
(C)$3^{1/3}x_0$
(D)$3^{-1/6}x_0$

(E)$2^{1/6}x_0$

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