Explanation:

Gadolinium is a chemical element with atomic number 64 and symbol Gd. It is a member of the lanthanide series of elements. The third ionization enthalpy refers to the energy required to remove the third electron from an atom in its gaseous state.

High exchange enthalpy:
The exchange enthalpy is the energy required to remove an electron from an atom and put it onto another atom. In the case of gadolinium, the third ionization enthalpy is low because of the high exchange enthalpy. This means that it is relatively easy to remove the third electron from a gadolinium atom and transfer it to another atom.

Small size:
The size of an atom plays a role in determining its ionization enthalpy. Smaller atoms have higher ionization enthalpies because the electrons are closer to the nucleus and are held more tightly. However, in the case of gadolinium, its small size does not have a significant effect on its third ionization enthalpy.

High electronegativity:
Electronegativity is the tendency of an atom to attract electrons towards itself. Gadolinium has a relatively high electronegativity, which means that it has a strong attraction for electrons. However, this does not directly affect its third ionization enthalpy.

High basic character:
Basic character refers to the tendency of an atom to lose electrons and form positive ions. Gadolinium does not have a high basic character, as its ionization enthalpy is relatively low compared to other elements.

Conclusion:
The low value of third ionization enthalpy in gadolinium is primarily due to its high exchange enthalpy. This means that it is relatively easy to remove the third electron from a gadolinium atom and transfer it to another atom. The small size, high electronegativity, and high basic character of gadolinium do not have significant effects on its third ionization enthalpy.

Electronic configuration of Gadolinium