Given below are two statements:

Statement I: The second ionisation enthalpy of Na is larger than the corresponding ionisation enthalpy of Mg.

Statement II: The ionic radius of $$O^{2-}$$ is larger than that of $$F^{-}$$.

In the light of the above statements, choose the correct answer from the options given below

We need to evaluate two statements about ionization enthalpy and ionic radius.

Statement I: The second ionisation enthalpy of Na is larger than the corresponding ionisation enthalpy of Mg.

The second ionization involves removing an electron from:

- Na$$^+$$: configuration $$[Ne]$$ ($$1s^2 2s^2 2p^6$$) -- removing an electron from the stable noble gas core requires enormous energy (IE$$_2$$ of Na $$\approx$$ 4562 kJ/mol).

- Mg$$^+$$: configuration $$[Ne] 3s^1$$ -- removing the lone $$3s$$ electron is much easier (IE$$_2$$ of Mg $$\approx$$ 1451 kJ/mol).

Since removing a core electron from Na$$^+$$ requires far more energy than removing a valence electron from Mg$$^+$$, Statement I is TRUE.

Statement II: The ionic radius of $$O^{2-}$$ is larger than that of $$F^-$$.

Both $$O^{2-}$$ and $$F^-$$ are isoelectronic with 10 electrons each. For isoelectronic species, the ion with fewer protons (lower nuclear charge) has a larger radius because the electrons are less tightly held.

- $$O^{2-}$$: 8 protons, 10 electrons

- $$F^-$$: 9 protons, 10 electrons

Since oxygen has fewer protons, $$O^{2-}$$ has a larger ionic radius ($$O^{2-} \approx 1.40$$ angstroms vs $$F^- \approx 1.33$$ angstroms). Statement II is TRUE.

The correct answer is Option 3: Both Statement I and Statement II are true.