Similar sizes of zirconium (Zr) and hafnium (Hf) of transition series elements can be explained on the basis of:

The similar sizes of Zirconium (Zr) and Hafnium (Hf) can be explained on the basis of the Lanthanide contraction. Here are the steps to understand this:

1. Zirconium (Zr) and Hafnium (Hf) are both part of the transition series of the periodic table. Zirconium is in the 4th period, and Hafnium is in the 6th period.

2. Normally, we would expect the atomic radius to decrease as we move down a group in the periodic table. This is because the number of electron shells increases, which would typically result in a larger atomic radius.

3. However, Zirconium and Hafnium have nearly the same atomic radii. This is due to the phenomenon known as the Lanthanide contraction.

4. The Lanthanide contraction refers to the fact that the 5f orbitals, which are being filled in the lanthanide series of elements, do not shield the increasing nuclear charge very well. This results in a greater effective nuclear charge, which pulls the electron cloud closer to the nucleus.

5. Therefore, despite Hafnium having more electron shells than Zirconium, its atomic radius is not significantly larger. This is because the increased nuclear charge due to the Lanthanide contraction effectively 'contracts' the size of the atom.

6. Hence, the similar sizes of Zirconium and Hafnium can be explained on the basis of the Lanthanide contraction.