Ionisation Enthalpy and Electron Gain Enthalpy Trends Across Period

To determine the correct trends across a period in the periodic table:

1. First Ionisation Enthalpy of the Extreme Left Element: Across a period from left to right, the effective nuclear charge ($Z_{\text{eff}}$) increases while the principal quantum shell remains the same, resulting in a decrease in atomic radius. As a result, the attractive force between the nucleus and the valence electron increases across the period. The element at the extreme left (Group 1, alkali metals) has the largest atomic size and lowest effective nuclear charge in its period, making it easiest to remove an electron. Therefore, the first ionisation enthalpy ($\Delta_i H_1$) for the extreme left element is the lowest.

2. Negative Electron Gain Enthalpy of the Extreme Right Element (excluding noble gases): The electron gain enthalpy ($\Delta_{\text{eg}} H$) measures the energy change when an electron is added to a neutral gaseous atom. As $Z_{\text{eff}}$ increases across a period, the atom's capability to pull in an added electron increases. The elements at the extreme right before noble gases (Group 17, halogens) have the highest effective nuclear charge and are just one electron short of achieving a stable noble gas configuration. Hence, adding an electron to a halogen releases a very large amount of energy, yielding the most exothermic (i.e., the most negative) electron gain enthalpy. Thus, the negative electron gain enthalpy for the extreme right element (excluding noble gases) is the highest.

Therefore, the correct pair is lowest and highest, corresponding to Option C.