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Although, $Zr$ belongs to $4d$ and $Hf$ belongs to $5d$ transition series but it is quite difficult to separate them, why?

Answer
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Hint: Two elements are difficult to separate if they either have a same chemical reactivity or have the same size which actually affects the chemical reactivity. The possible reason for the difficulty in the separation of two elements of two separate groups can be lanthanide contraction, which causes two elements of different periods to have similar sizes.

Complete step by step answer:
The element zirconium ($Zr$ ) belongs to the $4d$ transition series and the atomic size of zirconium is $160pm$ . On the other hand, the element hafnium ($Hf$ ) belongs to the $5d$ transition series with an atomic size of $159pm$ . Due to the similar atomic size, both the elements are difficult to separate as both of them show similar chemical reactivity. The ionic radii of $Z{r^{ + 4}}$ is about $9\% $ more than $T{i^{ + 4}}$ . Similarly the trend is not mentioned on passing from the second to third transition series. The ionic radius of $H{f^{ + 4}}$, instead of increasing (because of the addition of one or more electronic shell), it decreases and becomes almost equal to the size of the $Z{r^{ + 4}}$. This is due to the lanthanoid contraction. Thence, this explains the close similarities between the members of the second and the third transition series than between the elements of the first and second series.

Note:
Besides the above one, the other applications of lanthanide contraction are:

Basic nature of hydroxide: The effect of lanthanide contraction is that the basic nature of hydroxide regularly decreases.

Similarity in properties of the lanthanoid: Due to small differences in the size of the atoms of the elements, the chemical properties of the lanthanides are similar and the separation is difficult.