How does the outer energy level(period)relate to the atomic radius?

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Well definately the more levels you have, the bigger the radius will be. However, also, the more electrons you have in that level, the smaller the radius will become. This is because the force of attraction will become greater between the electrons and the protons. Thus, if you have two atoms with three energy levels each, one has 2 electrons in the outer shell, and the other has 6, then the one with 6 will have a smaller radius. Sorry if this wasn't precise or what you were looking for, it's all I know.
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