Why a sodium ion has a smaller radius than a sodium atom?
Let’s look closer at the sodium atom. Really close, so we could see. Atom is a neutral species, with 11 protons in the nucleus. We can find that information in the periodic table. 11 proton charge should be compensated with 11 electron floating around positively charged nucleus. That positive field created by nucleus is spread around 11 electrons. That force holds them together. Now, we strip one electron off creating sodium ion. 11 protons and 10 electrons. Positive charge wins, giving us sodium cation with charge +1. The electrostatic force created by nucleus has not change, we still have 11 protons, whereas 10 electrons oppose the same filed that 11 did. Every single electron will experience greater nuclear attraction, due to missing electron fellow. This leads to shrinkage of atom – electrons come closer to nucleus, and this is what we experimentally observe.