The potential energy curve for the $$\text{H}_2$$ molecule as a function of internuclear distance is:

For a diatomic molecule such as $$\text{H}_2$$ we define the potential energy $$V(r)$$ as a function of the internuclear distance $$r$$, where $$r$$ is the separation between the two hydrogen nuclei. By convention, the energy of the two hydrogen atoms taken infinitely far apart is set equal to zero, that is

$$\displaystyle \lim_{r \to \infty} V(r)=0.$$

When the two atoms come closer than this “infinite” separation, two opposite effects operate simultaneously:

(i) The electrostatic attraction between the electron of one atom and the nucleus of the other atom lowers the energy. In the simplest qualitative form, this attractive part is proportional to $$-\dfrac{A}{r}$$, where $$A$$ is a positive constant.

(ii) At very small separations the two positively charged nuclei repel each other strongly, and Pauli‐exclusion‐driven electron repulsion also becomes important. The repulsive part is often written phenomenologically as $$\dfrac{B}{r^{n}}$$ or, more realistically, $$Be^{-cr}$$ with $$B,c>0$$, so that it rises steeply as $$r$$ decreases.

Adding the two contributions we obtain a qualitative expression

$$V(r)= -\dfrac{A}{r}+Be^{-cr},$$

which is negative for an intermediate range of $$r$$ (because the attractive term dominates) and becomes positive when $$r$$ is made very small (because the repulsion takes over). The curve therefore has a single minimum at a particular separation $$r=r_0$$, called the equilibrium bond length. Mathematically, at this point

$$\left.\dfrac{dV}{dr}\right|_{r=r_0}=0 \quad\text{and}\quad V(r_0)<0.$$

As $$r\to\infty$$ the curve approaches the zero line from below, representing the dissociation of the molecule into two separate hydrogen atoms with no interaction energy. Summarising the essential features:

1. $$V(r)$$ is negative for $$r$$ near $$r_0$$ and has its minimum there.
2. $$V(r)\to +\infty$$ as $$r\to 0$$ because of strong repulsion.
3. $$V(r)\to 0^{-}$$ as $$r\to\infty$$, approaching the horizontal axis asymptotically.

Among the four curves supplied in the options, only Option (2) displays exactly these three characteristics: it starts very high and positive at $$r=0$$, dips below the zero line to a distinct minimum, and then climbs gradually to reach zero from the negative side at large $$r$$. The other curves fail to satisfy one or more of these conditions (for example, some never become negative, some do not rise steeply at small $$r$$, and so on).

Hence, the correct answer is Option B (Option 2).