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They are not the same thing but they do share the same pattern. For both cases, the radius of an element increases as you move down the periodic table and also as you move from the right to the left. However, the reasoning behind it is a bit different. For the atomic radius, it increases as you move down because you are adding an additional shell. And it decreases as you move from left to right because you are adding more protons without adding additional energy levels so the protons are pulling on the electrons with a greater force. As you move across to the right, the ionic radius decreases for metals forming cations, because the metals lose their outer electron orbitals (less electrons, smaller atom. example. Na^+, Mg^2+). The ionic radius increases for nonmetals as the effective nuclear charge decreases due to the number of electrons exceeding the number of protons. (Non-metals are anions and they tend to gain electrons rather than lose it. for example, O^2-, F^1-).
Ionic radius follows the same pattern of atomic radius on the periodic table (increases down a group and decreases across a period). However they are different in that in ionic radius, the periodic table is separated into anions and cations. Cations are going to be smaller than anions since they lost an electron and have increased effective nuclear charge, or the pull of the nucleus on the electrons. Anions are considerably larger than cations since they gained an electron and have created decreased effective nuclear charge with electron-electron repulsion.
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