Periodic trends in atomic radius and ionization energy

Steps:

• Locate each element: Boron (group 13, period 2), sodium (group 1, period 3), magnesium (group 2, period 3), calcium (group 2, period 4).
• Atomic radius decreases up the group; second smallest means second lightest in group 2 (Be smallest, Mg next).
• First ionization energy (IE) in period 3 increases overall left to right with exceptions: Na (496 kJ/mol, lowest), Al (578, second), Mg (738, third lowest).
• Magnesium fits both: second smallest radius in group 2, third lowest IE in period 3.

Why C is correct:

• Magnesium is second in group 2 (after Be) for radius and third lowest IE in period 3 per experimental values.

Why the others are wrong:

• A. Boron: smallest radius in group 13, not second; second lowest IE in period 2.
• B. Calcium: third smallest radius in group 2; fourth lowest IE in period 4.
• D. Sodium: second smallest radius in group 1; lowest IE in period 3.

Final answer: C