Why Zr and Hf have identical sizes?

The answer is due to lanthanide contration the size for Zr and Hf is same. Lanthanide contraction can be explained on the basis of shielding effect.In multi-electron atoms the electrons are added in outer shells. The electrons already present in inner shells, shield the outer electrons from nuclear charge, making them experience a lower effective charge of the nucleus. The shielding effect exerted by the inner electrons decreases in the order s > p > d > f. This f subshell poorly shields the outer electron from nuclear attraction which results in more attractive pull of nucleus on outer electron and smaller size.In case of post lanthenide elements like Hf,  4f subshell is filled and it is not very effective at shielding the outer shell (n=5 and n=6) electrons. it is similar to Zr.

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Because of thelanthanide contractionof the elements in thefifth period, zirconium and hafnium have nearly identicalionic radii. Lanthanide contraction repesentsgreater than expected decrease inionic radiiof theelementsin thelanthanideseries fromatomic number58,cerium, to 71,lutetium, which results in smaller than otherwise expected ionic radii for the subsequent elements starting with 72,hf.

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