Justify the following statements:
$(a)$ Cations are smaller in size than the corresponding neutral atom.
$(b)$ The size of the atom increases as we move down a group.
$(c)$ Atomic size decreases as we move across a period.

(N/A) Cations are formed by the loss of valence electrons. This results in a higher effective nuclear charge per electron,which pulls the remaining electrons closer to the nucleus,thereby decreasing the size of the cation compared to the parent atom.
$(b)$ As we move down a group,a new electron shell is added to each subsequent element. This increases the distance between the valence electrons and the nucleus,leading to an increase in atomic size.
$(c)$ As we move across a period,the number of protons in the nucleus increases,which increases the nuclear charge. Since the electrons are added to the same shell,the increased nuclear attraction pulls the electron cloud closer to the nucleus,resulting in a decrease in atomic size.