Atomic radii of 3^rd transition series elements are same as that of corresponding 2^nd transition series elements due to which of the following reason?

Lanthanoid contraction

The correct answer is option 3. Lanthanoid contraction.

The atomic radii of the third transition series elements are the same as those of the corresponding second transition series elements due to the lanthanide contraction.

The lanthanide contraction is a phenomenon that occurs when the atomic radii of the lanthanide elements decrease as the atomic number increases. This is because the lanthanide elements have a filled 4f subshell, which does not shield the 5d electrons very well from the nuclear charge. This causes the 5d electrons to be pulled closer to the nucleus, which results in a decrease in the atomic radius.

The contraction of the lanthanide elements affects the atomic radii of the third transition series elements because the 5d electrons of the third transition series elements are shielded by the 4f electrons of the lanthanide elements. This means that the 5d electrons of the third transition series elements are not as strongly pulled towards the nucleus as they would be if the lanthanide elements did not exist. This results in atomic radii that are similar to those of the corresponding second transition series elements.

Here is a table of the atomic radii of some of the third transition series elements:

As you can see, the atomic radii of these elements are all very similar. This is due to the lanthanide contraction.