Which of the following represents the correct order of increasing electron gain enthalpy with negative sing for the elements O, S, F and Cl?

Electron gain enthalpy (ΔH_eg) is the enthalpy change when a gaseous atom gains an electron. It is usually expressed with a negative sign, because energy is released. A more negative ΔH_eg means the atom releases more energy when the electron is added.

To rank the elements O, S, F and Cl in order of **increasing** electron‑gain enthalpy (i.e., from the least negative value to the most negative value), we must consider two main factors:

1. Periodic trend across a period: As we move from left to right, nuclear charge increases while the atomic radius decreases. The added electron feels a stronger attraction, so ΔH_eg becomes more negative.

2. Group trend down a group: As we move down a group, the atomic size increases and the added electron is farther from the nucleus, making ΔH_eg less negative.

However, there are important **anomalies** caused by electron‑electron repulsion in small, compact p‑orbitals:

• Oxygen (O) has the configuration 2p⁴. Adding an electron would pair it with an existing electron in a 2p orbital, creating significant repulsion. This reduces the magnitude of ΔH_eg compared with what would be expected from the periodic trend alone.

• Fluorine (F) also has a compact 2p⁵ configuration. Although it is the most electronegative element, the added electron would have to pair in a very small orbital, again creating repulsion. Still, the very high effective nuclear charge outweighs this repulsion, giving fluorine a very negative ΔH_eg, even more so than chlorine.

Putting these effects together, the qualitative order is:

Explanation of each step:

1. S vs O: Sulfur (3p⁴) is larger than oxygen (2p⁴). The added electron in sulfur experiences less repulsion and the atom has a larger radius, so ΔH_eg is **more negative** for sulfur than for oxygen. Therefore, O has a less negative value than S, giving S < O.

2. O vs Cl: Chlorine is in the same period as sulfur but one group to the right, with a higher nuclear charge and a smaller radius than oxygen. The increased attraction makes ΔH_eg more negative for chlorine, so O < Cl.

3. Cl vs F: Fluorine, despite the repulsion in its 2p orbital, has the highest effective nuclear charge of the four elements. This outweighs the repulsion, resulting in the most negative ΔH_eg among them. Hence, Cl < F.

Thus the complete order of increasing electron‑gain enthalpy (from least negative to most negative) is S < O < Cl < F, exactly matching the provided correct option.