Of the elements magnesium, calcium, and barium, which forms the ion with the largest radius? the smallest? what periodic trend explains this?

Atom radius is made of the electron which was orbiting around the outer part of the atom. The radius of the ion should be influenced by the number of the electron. 
in the periodic table, the electron will be increased as the atoms move right and down. That means the highest radius ion should have the most right-down position in the periodic table. 
Barium will have the largest radius since it located in the most bottom and magnesium would be the smallest radius.

Because electrons have negligible mass, to account for the mass of the isotope, there must be 16 neutrons, 16 neutrally charged, massive, fundamental particles present in the sulfur nucleus. and thus finally, if we have the 32s2− ion, there are 18 electrons, 16 protons, and 16 neutrons.