The given statement about radii is false and the correct statement is only radii of cation are always smaller than radii of corresponding atoms of same elements.
Radii of anions are greater than its parent atoms due to the following reasons: 1. Size of anion is always greater than its parent atom because anions are formed due to gain of electrons. When electrons increases there are still same number of protons. The attractive force is thus reduced as there are same number of protons attraction increased number of electrons. This causes the electrons to not be bound as tightly to the nucleus resulting in an increase in size. 2. Size of cation is always smaller than its parent atom because as a particular atom looses electron, no of proton become more than no of electron and attraction forces increases. So radius decreases.
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