Related Formula
IE₂ requires breaking stable noble gas configurations if M^+ is isoelectronic with a noble gas.$$IE_2 \text{ requires breaking stable noble gas configurations if } M^+ \text{ is isoelectronic with a noble gas.}$$
Core Logic
Statement I: Let's analyze the electronic configurations.
Na$Na$ (Z=11$Z=11$): 1s² 2s² 2p⁶ 3s¹ Na^+$1s^2 2s^2 2p^6 3s^1 \implies Na^+$ is 1s² 2s² 2p⁶$1s^2 2s^2 2p^6$ (Stable Neon noble gas core).
Mg$Mg$ (Z=12$Z=12$): 1s² 2s² 2p⁶ 3s² Mg^+$1s^2 2s^2 2p^6 3s^2 \implies Mg^+$ is 1s² 2s² 2p⁶ 3s¹$1s^2 2s^2 2p^6 3s^1$.
Removing a second electron from Na^+$Na^+$ (IE₂$IE_2$) involves disrupting a highly stable, fully-filled 2p⁶$2p^6$ shell, requiring massive energy. Removing a second electron from Mg^+$Mg^+$ (IE₂$IE_2$) just removes the 3s¹$3s^1$ electron. Thus, IE₂$IE_2$ of Na > IE₂$IE_2$ of Mg. Statement I is true.
Statement II: Both O²⁻$O^{2-}$ and F⁻$F^{-}$ are isoelectronic species, possessing 10 electrons (1s² 2s² 2p⁶$1s^2 2s^2 2p^6$). However, the nuclear charge (number of protons, Z) is different.
O²⁻$O^{2-}$ has 8 protons pulling 10 electrons.
F⁻$F^{-}$ has 9 protons pulling 10 electrons.
Since F⁻$F^{-}$ has a higher effective nuclear charge (Zeff$Z_{\text{eff}}$), its electron cloud is pulled more tightly, making its radius smaller. Thus, the radius of O²⁻$O^{2-}$ > F⁻$F^{-}$. Statement II is true.
Pattern Recognition
For isoelectronic species, more negative charge always equals a larger ionic radius (lower Z/e$Z/e$ ratio implies less nuclear pull per electron).
Chapter Mix
Class 11 Chemistry: Classification of Elements and Periodicity