Sodium ions are smaller than neutrally charged sodium atoms.
An ion is a charged atom. Ions are charged because they gain or lose electrons. Electrons are negative subatomic particles that move around the small, dense central nucleus of an atom. Because electrons are negative, the charge of an atom changes when electrons are gained or lost. Cations are positively charged ions that have lost electrons. Anions are negatively charged ions that have gained additional electrons.
Atoms gain or lose electrons in order to obtain the octet rule. The octet rule states that, in order to feel stable, all main-group elements want to have eight valence electrons. Valence electrons are the electrons found in the outermost orbital of an atom.
Neutrally charged sodium atoms have one valence electron. In order to fulfill the octet rule, this single valence electron is lost. In this way, sodium drops to the next lower orbital that is full.
Because a sodium atom loses an energy level (orbital) when becoming an ion, sodium ions are smaller than neutrally charged sodium atoms.