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I'm reading on ionic crystal structures and am confused by this from my textbook:

Because the metallic elements give up electrons when ionized, cations are ordinarily smaller than anions

I understand that having a positive charge will pull the electrons closer, but shouldn't the atom from the larger period (row on periodic table), have more electron shells and be the larger atom?

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It isn't true that any cation will be smaller than any anion.

You intuition that atoms with larger electron counts from lower rows of the periodic table will be bigger is correct. Size for atoms is determined by the highest occupied electron shell or orbital as the interactions with other things that define size are, crudely, caused by interactions between the electrons in their outer orbitals.

So a Rb+ cation radius is about 166pM but an F- anion is smaller at about only 119pm. There is a good table of such values in the Wikipedia article on ionic radii which also explains some of the trends and some of the difficulties in actually defining size for ions.

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Generally we say that cation is smaller than anion in case of iso-electronic species (see the fig). If you consider ions which are not iso-electronic, the statement may not be true always. As you say, if you consider cations consisting of many shells (say 6) and if you compare them with anions consisting of less shells (say 2), in that case cations will be larger than anion.
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