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 $\mathrm{O}^{2-}$ is larger than that of $\mathrm{F}^{-}$.
In the light of the above statements, choose the correct answer from the options given below

Statement I examines second ionization enthalpy:
Na (1s$^2$ 2s$^2$ 2p$^6$ 3s$^1$) loses its first electron to achieve a stable noble gas configuration. The second ionization would break into the 2p core, requiring enormous energy.
Mg (1s$^2$ 2s$^2$ 2p$^6$ 3s$^2$) loses its second electron from the 3s orbital, which is less stable.
Thus, IE$_2$ of Na is much larger than IE$_2$ of Mg.
Statement I is TRUE.
Statement II compares O$^{2-}$ and F$^-$:
both are isoelectronic with 10 electrons.
O$^{2-}$ has 8 protons while F$^-$ has 9 protons.
The lower nuclear charge in O$^{2-}$ results in weaker electrostatic attraction, making the ionic radius of O$^{2-}$ larger than F$^-$.
Statement II is TRUE.