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

The ionic radius of a cation is always smaller than the parent atom because a cation is formed by loss of one or more electrons by the neutral atom. The loss of one or more electrons increases the effective nuclear charge. As a result, the force of attraction of nucleus for the electrons increases and hence their ionic radii decrease. In contrast, the ionic radius of anion is formed by the addition of one or more electrons to the anion is formed by the addition of one or more electrons to the neutral atom. The addition of one  or more electrons decreases the effective nuclear charge. As a result, the force of attraction of the nucleus for the electrons decreases and hence the ionic radii increases.