Questions & Answers

Question

Answers

A. 275.1pm

B. 322.5pm

C. 241.5pm

D. 165.7pm

Answer

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The compound $XY$ has a crystal structure like $NaCl$. Which implies that ${{X}^{+}}$ is equivalent to the ion $N{{a}^{+}}$, and ${{Y}^{-}}$ is equivalent to the ion $C{{l}^{-}}$. We have to find the radius for the anion that is equivalent to the $C{{l}^{-}}$ ion.

We know that $NaCl$, has a face centered cubic structure. This means the coordination number of the anions and cations is 6. The crystals that have a face centered structure with coordination number 6 have cations that fit into the octahedral voids of the anions.

We know that the radius ratio of cations to anions in structures with octahedral voids is 0.414. Thus, we can say that:

\[\dfrac{{{X}^{+}}_{r}}{{{Y}^{-}}_{r}}=0.414\]

Where,

\[{{X}^{+}}_{r}\]= radius of cation

\[{{Y}^{-}}_{r}\]= radius of anion

We know the value of the radius of the anion and we have to find the radius of the cation.

\[\dfrac{100pm}{{{Y}^{-}}_{r}}=0.414\]

\[{{Y}^{-}}_{r}=\dfrac{100pm}{0.414}\]

\[{{Y}^{-}}_{r}=241.54pm\]