Introduction:
In the case of halogens, energy is released when an electron is added to the atom, leading to the formation of a negatively charged ion. This process is known as electron gain enthalpy or electron affinity. The electron gain enthalpy is expressed as a negative value because it represents the energy released during the addition of an electron.

Explanation:
The electron gain enthalpy is defined as the energy change when an electron is added to a neutral gaseous atom to form a negatively charged ion. It is a measure of the tendency of an atom to accept an electron. The negative sign indicates that energy is released during this process.

Reason for Negative Value:
The negative value of the electron gain enthalpy can be understood based on the energy changes involved in the process. When an electron is added to an atom, two opposing energy changes occur simultaneously:

1. Energy Change due to Electron Affinity:
The first energy change is the release of energy due to the electron affinity of the atom. Electron affinity is the energy change that occurs when an electron is added to a neutral atom in the gas phase. Halogens have a high electron affinity because they have a strong attraction for an additional electron to complete their octet. This energy release is negative.

2. Energy Change due to Repulsion:
The second energy change is the energy required to overcome the electrostatic repulsion between the incoming electron and the existing electrons in the atom. As the negatively charged electron approaches the negatively charged electron cloud of the atom, repulsion occurs. This energy required is positive.

Combining Energy Changes:
The overall energy change is obtained by combining these two opposing energy changes. If the energy released due to electron affinity is greater than the energy required to overcome the repulsion, the overall energy change is negative. This indicates that energy is released during the addition of an electron.

Significance of Negative Value:
The negative value of the electron gain enthalpy indicates that the halogens have a high affinity for gaining an electron. It suggests that halogens readily accept an electron to achieve a stable electronic configuration with a complete octet. The higher the negative value of electron gain enthalpy, the more energy is released, indicating a greater tendency to gain an electron.

Conclusion:
In conclusion, the negative value of electron gain enthalpy for halogens represents the energy released during the addition of an electron. This negative value indicates the high electron affinity and the strong tendency of halogens to accept an electron to achieve a stable electronic configuration.