# Why is ionic radius smaller?

$\text{Why is cationic radius smaller than atomic radius......??}$
Let's consider an extreme case. This site reports that the ionic radius (of $N {a}^{+}$) is $116 \times {10}^{-} 12 \cdot m$; the atomic radius of sodium is $154 \times {10}^{-} 12 \cdot m$. (I use these numbers, because as physical scientists we are OBLIGED to use numerical data!)
Now the atomic radius is by definition the distance from the nucleus to the radius described by its valence electron.....And of course for sodium, the valence electron is a $3 s$ electron, ($1 {s}^{2} 2 {s}^{2} 2 {p}^{6} 3 {s}^{1}$). Now of course $3 s$ electrons describe a greater radius than $2 s$ or $2 p$, and thus the ionic radius necessarily reduces upon oxidation.
On the other hand, chlorine has an atomic radius of $99 \times {10}^{-} 12 \cdot m$; but chloride anion has a radius of $167 \times {10}^{-} 12 \cdot m$. Here, reduction, addition of an electron to the valence shell GREATLY expands the ionic radius of the ANION with respect to the radius of the atom.