Question

why cations are smaller and anions largest in radii with their parents atom

Answer 1

Cations are always smaller than their parent atoms this is because they have lesser electrons, while their nuclear charge remains the same. The remaining electrons are, therefore held more tightly by the protons in the nucleus and thus their radii are smaller than the parent atoms. This is opposite in case of anions. Anions are always larger than their parent atoms because the addition of 1 or more electrons would result in increased repulsion among the electrons and a decrease in the effective nuclear charge.

Answer 2

anion has more electron then cation so there is possibility to increase in the number of Orbital in the anion therefore radius increases