Explain the variations in atomic radii of transition elements in group.

Down the group, with the increase in atomic number, the atomic radii increases because of addition of new shells. Hence, the atomic radii of elements of second transition series are greater than corresponding elements of first transition series.

The atomic radii of elements of second and third transition series are almost same because of intervention of the $4 f$-orbitals which must be filled before the $5 d$ series of elements begin. The filling of $4 f$ before $5 d$ orbital results in regular decrease in atomic radii called lanthanoid contraction. The lanthanoid contraction counter balances the increase in atomic size with the increasing atomic number.

Ex. : $\mathrm{Zr}$ and $Hf$ have very similar chemical and properties and have nearly same atomic radii because of lanthanoid contraction.

The lanthanoid contraction is because of the imperfect sheilding of one electron by another in the same set of orbitals. However, the sheilding of one $4 f$ electron by another is less than one $d$ electron by other, and as the nuclear charge increases along the series, there is fairly regular decrease in the size of entire $4 f^{\mathrm{n}}$ orbitals.