The question asks about the maximum difference in electron gain enthalpy between the given pairs of elements. To solve this, we need to understand the concept of electron gain enthalpy and how it varies across the periodic table.
Electron gain enthalpy is the enthalpy change when an electron is added to a neutral atom in the gaseous state to form a negative ion. It generally becomes more negative across a period (from left to right) and less negative down a group (from top to bottom).
After analyzing the characteristics and trends of electron gain enthalpy, we conclude that the maximum difference will be observed between Ne and Cl.