The lanthanide contraction is responsible for the fact that:

Zr and Hf have about the same atomic radius

The answer is (3) Zr and Hf have about the same atomic radius.

The lanthanide contraction is the decrease in the atomic radius of the lanthanide elements from lanthanum to lutetium. This is caused by the filling of the 4f orbitals, which are not very effective at shielding the outer electrons from the nuclear charge.

The elements Zr and Hf are located in the same period, but they are in different groups. Zr is in group 4, while Hf is in group 5. However, because of the lanthanide contraction, the atomic radius of Zr is very similar to the atomic radius of Hf.

The other options are incorrect.

(1) Zr and Y have about the same radius:  This is not true. Zr has a larger atomic radius than Y.

(2) Zr and Zn have the same oxidation state:  This is not true. Zr has an oxidation state of +4, while Zn has an oxidation state of +2.

(4) Zr and Nb have similar oxidation states:  This is not true. Zr has an oxidation state of +4, while Nb has an oxidation state of +5.