The second ionization energy refers to the energy required to remove the second electron from a singly charged cation. In the case of magnesium (Mg) and calcium (Ca), magnesium has a lower second ionization energy compared to calcium.
The difference in second ionization energy can be attributed to the electronic configuration and the effective nuclear charge experienced by the outermost electron in each element.
Magnesium (Mg) has an electronic configuration of 1s² 2s² 2p⁶ 3s². When the first electron is removed from Mg, it forms a Mg⁺ cation with the electron configuration of 1s² 2s² 2p⁶, leaving behind a stable, full valence shell of 2s² 2p⁶. The second ionization energy corresponds to removing an electron from this stable, full valence shell. Since the second electron being removed is closer to the nucleus, it experiences a greater effective nuclear charge (attraction from the positively charged nucleus). As a result, the second electron requires more energy to be removed, and the second ionization energy is higher than the first ionization energy.
Calcium (Ca), on the other hand, has an electronic configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 4s². When the first electron is removed from Ca, it forms a Ca⁺ cation with the electron configuration of 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹. Although the second ionization energy involves removing an electron from a partially filled 4s orbital, the effective nuclear charge experienced by this electron is less than that experienced by the outermost electron in magnesium. This is because the additional shielding effect from the inner electrons in calcium reduces the attractive force of the nucleus on the outermost electron. Consequently, the second ionization energy of calcium is higher than that of magnesium.
In summary, the lower second ionization energy of magnesium compared to calcium can be attributed to the greater effective nuclear charge experienced by the outermost electron in magnesium, making it more tightly held and harder to remove.