It is difficult to separate the ores of Zr and Hf because:

Their radii are almost same

The correct answer is Option (1) → Their radii are almost same

The difficulty in separating the ores of zirconium (Zr) and hafnium (Hf) primarily arises from:

Their Radii Are Almost the Same

Zirconium and hafnium have very similar ionic radii and similar chemical properties because they are both d-block elements in the periodic table. Specifically:

Ionic Radii: Zr^4+ has an ionic radius of about 0.72 Å, while Hf^4+ has a radius of about 0.70 Å. The close similarity in their sizes makes it challenging to separate them using methods like selective precipitation or ion exchange.

Explanation of Other Options

They Do Not Experience Lanthanoid Contraction: This is not correct; both Zr and Hf are affected by the lanthanoid contraction, which influences their properties but does not contribute directly to the difficulty of their separation.

Zr Has Half-Filled Orbital But Hf Does Not: This is misleading. While Zr does have a half-filled 4d subshell, hafnium (Hf) has a filled 5d subshell. However, this factor does not significantly influence their separability.

They Belong to Different Groups: Both Zr and Hf are in group 4 of the periodic table, so this statement is incorrect.

Conclusion

The primary reason for the difficulty in separating Zr and Hf is indeed their similar ionic radii and chemical properties.

Thus, the correct answer is: Their radii are almost the same.