Explain why cations are smaller and anions larger in radii than their parent atoms?

The nucleus of an atom consists of protons and hence possesses a positive charge and electrons rotate around the nucleus in fixed shells. Therefore, in the case of cations & anions are as follows:

Since a cation is formed by getting a rid of electron from the atom, the cation contains lesser electrons than the parent atom, resulting in an increment in the effective nuclear charge. Thus, the size of the cation is smaller as compared to that of its parent atom. For instance, the ionic radius of sodium ion is 95 pm, whereas the atomic radius of Na atom is 186 pm.

On the other hand, in case of anion the size of the anion is larger as compared to the size of the parent atom. This is because in case of the anion the nuclear charge remains the same but more electrons get added to the atom resulting in an increased repulsion between the electrons and a reduction in the effective nuclear charge. For instance, the ionic radius of the fluoride ion is 136 pm, whereas the atomic radius of fluorine atom is 64 pm.