Why do the atomic radii of the elements decrease across Period 3 from sodium to chlorine?

The atomic radius of an atom is the distance from the atom's nucleus to its outermost electron. Moving across Period 3, the number of protons in the nucleus increases - for example sodium has 11 protons, and chlorine has 17 protons. Nuclear charge increases across the period, therefore the attraction between the positively charged nucleus and negatively charged electrons increases, so the atomic radii decreases. The number of electrons also increases across a period, but as each extra electron enters the same principal energy level, there is relatively little extra shielding.