d and f Block ElementshardNUMERICAL

Given the following targeted pairs of transition elements: , , , , . What is the exact total integerd and f Block Elements Chemistry Question

Question

Given the following targeted pairs of transition elements: $(Ti, Zr)$, $(Zr, Hf)$, $(Nb, Ta)$, $(Y, La)$, $(Mo, W)$. What is the exact total integer count of the pairs that exhibit chemically indistinguishable atomic radii strictly as a direct result of the Lanthanoid contraction?

Answer: 3

💡 Solution & Explanation

The lanthanoid contraction severely affects the $5d$ elements immediately following the lanthanide series ($Lu$, $Z=71$). It forces the $5d$ transition metals to shrink to the size of their $4d$ counterparts positioned directly above them. Therefore, $(Zr, Hf)$, $(Nb, Ta)$, and $(Mo, W)$ are all valid pairs showing this identical size anomaly. $(Ti, Zr)$ is a regular $3d/4d$ pair and shows an expected increase. $(Y, La)$ are Group 3 elements positioned before the $4f$ block fills, so $La$ is notably larger than $Y$. Thus, only $3$ pairs fit the criteria.

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