Why does atomic radius decrease as you go across a period?
Nuclear charge dominates whilst adding electrons to the same shell. The net result is atomic contraction across a period.
This is a very important periodic phenomenon: the contraction of atomic radii across the period. While as we add to Z (the number of protons in the nucleus), we also add another electron (and charge is therefore kept neutral), the increased nuclear charge acts disproportionately on the valence electrons, and contracts this shell.
What happens to atomic radii down a Group?
Atomic radius decreases across a period because valence electrons are being added to the same energy level at the same time the nucleus is increasing in protons. The increase in nuclear charge attracts the electrons more strongly, pulling them closer to the nucleus.
The following diagram shows the periodic trends of atomic radius of the representative elements (main group elements) for the first six periods.