(a) (i) $5 f$ orbital electrons have poor shielding effect than $4 f$ orbital electrons.(ii) Due to $d$ - $d$ transition or the energy of excitation of an electron from lower $d$ orbital to higher $d$-orbital lies in the visible region and presence of unpaired electrons in the $d$-orbital.(b) $2 \mathrm{MnO}_4^{-}+6 \mathrm{H}^{+}+5 \mathrm{NO}_2^{-} \rightarrow 2 \mathrm{Mn}^{2+}$ $+3 \mathrm{H}_2\mathrm{O}+5 \mathrm{NO}_3^{-}$