Final answer:
Barium forms the ion with the largest radius, and magnesium forms the one with the smallest radius, as size increases down a group on the periodic table.
Step-by-step explanation:
The element barium forms the ion with the largest radius, while magnesium forms the ion with the smallest radius among magnesium, calcium, and barium. This is explained by the periodic trend that states atomic and ionic size increases down a group on the periodic table, as each element has more electron shells.