chemistry~radius of elements

Radius: Mg^2+ < Na^+ < O2- < Cl^-

For Mg^2+, Na^+ and O^2-, they same number of electrons and also have the same electronic configuration of 2, 8. Among them, the higher the nuclear charge (equal to number of protons), the smaller the radius of the species is. This is because electrons of the same number are attracted by a stronger nuclear attraction as the increase in nuclear charge. The nuclear charges (numbers of protons) of Mg^2+, Na^+ and O^2- are 12, 11 and 8 respectively.
Nuclear charges (Numbers of protons): Mg^2+ > Na^+ > O^2-
Hence, radius: Mg^2+ < Na^+ < O2-

Cl^- has the greatest radius among the four species. This is because Cl^- has 3 shells of electrons (2, 8, 8) while each of the other species has only 2 shells of electrons (2, 8).