What the potential energy curve for $H_2$ should look like

For a diatomic molecule like $H_2$, the potential energy $U$ varies with internuclear distance $r$ as follows:

• For very large $r$, the two H atoms are essentially separate, so $U \to 0$ if we take the zero of energy at infinite separation.

• As the two atoms come closer, attractive interactions dominate, so the energy decreases.

• At some distance $r=r_e$, the energy becomes minimum. This is the equilibrium bond length.

• If the atoms are pushed even closer than $r_e$, strong nucleus-nucleus and electron-electron repulsions dominate, so the energy rises very steeply.

Hence the correct shape must have

• a minimum at a finite internuclear distance,
• approach zero from below as $r \to \infty$,
• rise sharply upward as $r \to 0$.

Identify the matching option

Among the given choices, the correct graph is the one with the above shape. That corresponds to Option C.

Conclusion

Therefore, the potential energy curve for $H_2$ is represented by: $\boxed{\text{C}}$