Why do the atomic radii of the elements decrease across a period on the periodic table.

It may seem counterintuative that as the elemets' atomic numbers increase their atomic radii decrease. This is due to the increased electrostatic attraction (coulombic interaction) between nucleus and valence electrons. As long as elements are all in the same period then all thier valence electrons are in the same energy level, so there is no increase in the atomic radius due to fillig a new outer shell. This means the dominant effect is simple the electrostatic interaction. As the atomic number increases so does the interaction force, hence the atomic radius decreases.