The lanthanoid contraction is responsible for the fact that:

The correct answer is Option (3) → Zr and Hf have about the same atomic radius

• Across the lanthanoids (La to Lu) the 4f orbitals fill, and one 4f electron shields another poorly, so the radii fall steadily: the lanthanoid contraction.

• The 5d series comes after these 14 elements, so the expected increase in size from the 4d to the 5d series is cancelled, and Zr (4d) and Hf (5d) have almost the same radius.

Why the other options are incorrect

Option (1) Zr and Y have about the same atomic radius — Incorrect. Y and Zr are neighbours in the same (4d) series; their sizes are governed by the usual decrease of radius along a series, not by the lanthanoid contraction.

Option (2) Ti and Zr have about the same atomic radius — Incorrect. Radii increase from the 3d to the 4d series, so Zr is larger than Ti; no f orbitals are filled between them.

Option (4) La and Lu have about the same atomic radius — Incorrect. The radius decreases from La to Lu; that decrease is the lanthanoid contraction itself, not a result of it.

NCERT (2026-27 edition):
4.5.2 Atomic and Ionic Sizes – “… The cumulative effect of the contraction of the lanthanoid series, known as lanthanoid contraction, causes the radii of the members of the third transition series to be very similar to those of the corresponding members of the second series. The almost identical radii of Zr (160 pm) and Hf (159 pm), a consequence of the lanthanoid contraction, account for their occurrence together in nature and for the difficulty faced in their separation.”