Question

Explain why cation is smaller and anions is larger in radii than their parent atoms.

Answer 1

Cations are positive ions, meaning they lose electrons, thus decreasing their atomic radii. Anions, on the other hand, gain electrons, thus increasing their atomic radii. That ought to answer your question.

Answer 2

cations are proton donors so when the donate electrons from outermost shells their effective nuclear charge increases therefore they get pulled towards so size decrease than parent atom.
while anions are proton acceptors and they go into the outermost shell and their effective nuclear charge decreases due to shielding effect and size increases
Hope it helps...