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

(N/A) Down the group,with the increase in atomic number,the atomic radii increase because of the addition of new shells. Hence,the atomic radii of elements of the second transition series are greater than the corresponding elements of the first transition series.
The atomic radii of elements of the second and third transition series are almost the same because of the intervention of the $4f$-orbitals,which must be filled before the $5d$ series of elements begins. The filling of $4f$ before the $5d$ orbital results in a regular decrease in atomic radii,called lanthanoid contraction. The lanthanoid contraction counterbalances the increase in atomic size with the increasing atomic number.
Example: $Zr$ and $Hf$ have very similar chemical properties and have nearly the same atomic radii because of lanthanoid contraction.
The lanthanoid contraction is due to the imperfect shielding of one electron by another in the same set of orbitals. However,the shielding of one $4f$ electron by another is less than that of one $d$ electron by another,and as the nuclear charge increases along the series,there is a fairly regular decrease in the size of the entire $4f^n$ orbitals.