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This is a very complicated question, but most of the time the ionic radius has the opposite periodic table trend than the atomic radius, since the atomic radius is the general radius of the atom, while the ionic radius would be the general radius of the ion. Since certain atoms lose or gain electrons when they become ions, this trend is harder to identify than the atomic radius trend. But if we were to look at just the s and p block atoms, it is a generally opposite trend than atomic radius. For example, Na has a larger radius than Cl, however, Na+ ion would be smaller than Cl- ion, as the Cl gains an electron and because Cl has a net negative charge, while Na+ loses and electron and draws the others closer because of its net positive charge. I understand that this might not be the answer you were looking for, but at least I hope this is helpful.
For the most part the ionic radius does follow the same trend as the atomic radius. Both the atomic radius and the ionic radius decrease across periods and increase as you go down the group. This is because across the period increased protons leads to an increased positive charge which pulls electrons closer together. In a group as you go down energy levels are added and there's a more positive charge but electrons are further from the nucleus due to shielding. In ionic radius the difference is that ions with an increased negative charge have a larger size that ions with a greater positive charge.
According to our textbook, ionic radius is the shared distance between neighboring ions in an ionic solid; atomic radius is half the distance between the centers of neighboring atoms. Generally, ionic radius and atomic radius do follow the same trends, in which as you go down a group and go from right to left on the periodic table, ionic radius and atomic radius increase.
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