A) 249pm
B) 220pm
C) 608pm
D) 176pm
Correct Answer: B
Solution :
\[\sqrt{2}a=660\sqrt{2}\,pm\] |
So \[a=660\,pm\] |
Now if tetrahedral void is occupied by cations than |
\[\frac{\sqrt{3}}{4}a=({{r}_{+}}+{{r}_{-}})\,;{{r}_{-}}=\left( \frac{\sqrt{3}+600}{4}-110 \right)\]\[=110\left[ \frac{3}{2}\sqrt{3}-1 \right]=1.598\times 110\] |
So \[\frac{{{r}_{+}}}{{{r}_{-}}}=\frac{1}{1.598}=\frac{1}{1.6}=\frac{10}{16}=0.625\] |
But \[\frac{{{r}_{+}}}{{{r}_{-}}}>0.414\]so it must not be occupying tetrahedral void then |
\[a=2({{r}_{+}}+{{r}_{-}})\] \[\Rightarrow \] \[330={{r}_{+}}+{{r}_{-}}\] |
\[{{r}_{-}}=220\,pm\] |
{\[\frac{{{r}_{+}}}{{{r}_{-}}}=0.5\]it can occupy octahedral void} |
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