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It's said that atomic size/radius decreases across a period, in spite of addition of electrons. But how does this actually work?

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Atomic radius decreases across a period because electrons are being added to the same energy level and at the same time the nucleus is increasing in protons. The increase in nuclear charge $$Z_{eff}$$ attracts the electrons more strongly, (addition of one proton has a greater effect than addition of 1 electron) thus pulling electron closer to the nucleus and making atomic radius decrease.

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