How would you explain the fact that the first ionization enthalpy of sodium is lower than that of magnesium but its second ionization enthalpy is higher than that of magnesium ?

Hint: As we are aware, ionization requires energy and the amount of energy which is required to separate one electron from its atom will depend on how tightly the electron is held. This energy will depend upon the number of protons and the orbitals in which the electron occupies.

Complete Solution :
- The amount of energy which is needed to remove electrons from an atom can be termed as Ionization enthalpy. The enthalpy to go from neutral atoms to cations with a +1 charge is the first ionization enthalpy.
-Also, the atoms with more than one electron can have them successively removed and it will have successive ionization enthalpy such as second ionization enthalpy , third ionization enthalpy and so on.
- The electronic configuration of sodium is $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{1}}$ and of magnesium is $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}$ Thus, the first electron in case of both the elements has to be removed from 3s-orbital. But the nuclear charge of Sodium has +11 charge and Magnesium has +12 charge, which causes the electrons to held more tightly in case of magnesium.Hence, the first ionization enthalpy of sodium is lower than that of magnesium.
- Similarly , after the first ionization occurs, the second electron has to be removed from the s-orbital in case of magnesium and from the p-orbital in case of sodium which has already attained its stable noble gas configuration.Consequently, the second ionization enthalpy of sodium is higher than that of magnesium.

Note: The difference between the terms ionization enthalpy and ionization potential should be noted. ionization energy or ionization enthalpy is the energy required to eject an electron from an atom which is usually expressed in Kilojoule per mole whereas ionization potential is the potential required to eject an electron from an atom and is generally expressed in electron volt.