Why does an atom of sodium have a larger atomic radius than an atom of chlorine?

Even though sodium and chlorine belong to the same period, Sodium has a larger atomic radius than chlorine. This is because of the difference in the number of electrons on the valence shell. Because chlorine has seven valence electrons then these electrons are more tightly held by the nucleus than in the case of Sodium which only has one electron on the last shell thus the valence shell is loosely held by the nucleus.