Why does atomic size increase down a group?

As we go across a Period, a row, of the Periodic Table, from left to right as we FACE the Table, we add another positive charge (a proton, a fundamental, positively charged nuclear particle) to the nucleus. This results in a DECREASE in atomic radii across the Period, due to the increased nuclear charge which draws in the valence electrons.

On the other hand, going down a Group, we go to another so-called shell of electrons, that build on the preceding shell. Atomic radii thus INCREASE down the Group. This contest between nuclear charge, i.e. #Z#, and shielding by other electrons, underlies the structure of the Periodic Table. And note that incomplete valence electronic shells, shield the nuclear charge VERY ineffectively.

AS a scientist, however, you should seek data that inform your argument. And I leave this up to you. You want details of #"atomic radii"# only, not #"ionic radii"#! If you can remember #"Atomic size INCREASES down a Group, but DECREASES"# #"across a Period,"# where a Group is a column and Period is a row of the Periodic Table, you have mastered a fundamental principle of chemistry.