To solve this problem, we need to understand why gadolinium has a low value of third ionisation enthalpy.$\newline$Gadolinium is a lanthanide element with the electronic configuration:$\newline [Xe] \, 4f^7 \, 5d^1 \, 6s^2 \newline$The third ionisation involves removing an electron from the 4f subshell, which is half-filled (4f^7).$\newline$A half-filled subshell is particularly stable due to the exchange energy, which is the energy released when electrons with parallel spins exchange positions.$\newline$This exchange energy is maximized in a half-filled subshell, making it more stable.$\newline$Therefore, the removal of an electron from a half-filled 4f subshell requires less energy, resulting in a lower third ionisation enthalpy.$\newline$This is due to the high exchange enthalpy associated with the half-filled 4f subshell.$\newline$Analyzing the options:$\newline$• Option 1: Small size - This is not the reason for low third ionisation enthalpy.$\newline$• Option 2: High exchange enthalpy - This is the correct reason.$\newline$• Option 3: High electronegativity - This is not relevant to ionisation enthalpy.$\newline$• Option 4: High basic character - This is not related to ionisation enthalpy.$\newline$Therefore, the correct option is Option 2.