What happens to the radius of atoms as they become cations? anions? What are isoelectronic ions, and how can you tell which ones are largest and smallest?

When an atom becomes a cation, the radius becomes smaller, and when it becomes an anion the radius  becomes larger.

Isoelectronic ions are elements that have the same electronic configurations as a different element or ion on the periodic table.

http://www.mikeblaber.org/oldwine/chm1045/notes/Bonding/IonSize/Bond03.htm

As the nuclear charge in the atoms increases, their radius decreases (as shown above), so to be able to determine which isoeletronic atom's radius is either smallest or largest, one must look at the nuclear charge of the specific atom.