Statement I examines second ionization enthalpy:
Na (1s2 2s2 2p6 3s1) loses its first electron to achieve a stable noble gas configuration. The second ionization would break into the 2p core, requiring enormous energy.
Mg (1s2 2s2 2p6 3s2) loses its second electron from the 3s orbital, which is less stable.
Thus, IE2 of Na is much larger than IE2 of Mg.
Statement I is TRUE.
Statement II compares O2− and F−:
both are isoelectronic with 10 electrons.
O2− has 8 protons while F− has 9 protons.
The lower nuclear charge in O2− results in weaker electrostatic attraction, making the ionic radius of O2− larger than F−.
Statement II is TRUE.