The first ionization enthalpy of sodium is lower than that of magnesium primarily because sodium has a lower effective nuclear charge and a larger atomic size, which means its outermost electron (in the 3s orbital) is less tightly held. In sodium (Na: 1s² 2s² 2p⁶ 3s¹), the single 3s electron experiences less attraction from the nucleus compared to the two 3s electrons in magnesium (Mg: 1s² 2s² 2p⁶ 3s²), where the effective nuclear charge is higher. After the removal of the first electron, sodium achieves the stable noble gas configuration of neon (1s² 2s² 2p⁶), making its second ionization enthalpy much higher because removing an electron from a stable, filled shell requires considerably more energy. In contrast, magnesium still has one electron in the 3s orbital after its first ionization, so its second ionization requires less energy compared to sodium's second ionization. Thus, sodium's first ionization enthalpy is lower than magnesium's, but its second ionization enthalpy is higher due to the stable electronic configuration it attains after losing one electron.
