To determine the incorrect statement regarding the electron gain enthalpies (\(\Delta_{eg}H\)) of the given elements, we need to understand the concept of electron gain enthalpy:
- Electron gain enthalpy is the energy change that occurs when an electron is added to a neutral atom in the gaseous state to form a negative ion.
- A more negative electron gain enthalpy indicates a greater tendency to gain electrons.
Let's analyze each option:
- \(\Delta_{eg}H (Cl) < \Delta_{eg}H (F)\): Chlorine generally has a more negative electron gain enthalpy than Fluorine. Fluorine has a small atomic size which leads to electron-electron repulsions and a less negative electron gain enthalpy compared to Chlorine. This option is correct.
- \(\Delta_{eg}H (I) < \Delta_{eg}H (At)\): Astatine is less known but expected to have similar properties to other halogens. Since elements down a group generally have less negative electron gain enthalpies, this is an unlikely statement but is plausible under some conditions.
- \(\Delta_{eg}H (Te) < \Delta_{eg}H (Po)\): Polonium is placed below Tellurium in the periodic table, so it is expected to have less negative electron gain enthalpy. This is consistent behavior yielding less tendency to gain electrons as we move down the group, thus this statement is likely correct.
- \(\Delta_{eg}H (Se) < \Delta_{eg}H (S)\): Sulfur, being above Selenium in the periodic table, should have a more negative electron gain enthalpy. Therefore, the given statement implies the wrong order as Selenium has less negative electron gain enthalpy than Sulfur due to added shell increasing shielding effect.
Conclusion: The incorrect option is \(\Delta_{eg}H (Se) < \Delta_{eg}H (S)\) because Sulfur has a more negative electron gain enthalpy than Selenium, contrary to the statement.