Explanation:

The atomic size of an element refers to the size of its atoms. It is determined by the distance between the nucleus and the outermost electron shell. The atomic size generally decreases across a period (from left to right) and increases down a group (from top to bottom) in the periodic table.

a) Zr and Hf:
Zirconium (Zr) and hafnium (Hf) are both transition metals and are located in the same period (period 5) of the periodic table. They have similar electronic configurations and therefore have similar atomic sizes. Thus, Zr and Hf have the same atomic size.

b) Nb and Ta:
Niobium (Nb) and tantalum (Ta) are also transition metals and are located in the same period (period 6) of the periodic table. They have similar electronic configurations and therefore have similar atomic sizes. Thus, Nb and Ta have the same atomic size.

c) Mo and W:
Molybdenum (Mo) and tungsten (W) are transition metals and are located in the same period (period 6) of the periodic table. They have similar electronic configurations and therefore have similar atomic sizes. Thus, Mo and W have the same atomic size.

d) Y and La:
Yttrium (Y) and lanthanum (La) are both transition metals, but they are not located in the same period of the periodic table. Yttrium is in period 5, while lanthanum is in period 6. Therefore, they have different electronic configurations and different atomic sizes. Thus, Y and La do not have the same atomic size.

In summary, the pairs Zr and Hf, Nb and Ta, and Mo and W have the same atomic size because they are located in the same period of the periodic table and have similar electronic configurations. Y and La do not have the same atomic size because they are located in different periods of the periodic table.