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# In a crystalline solid, having formula $AB_2O_4$, oxide ions are arranged in cubic close packed lattice while cations A are present in tetrahedral voids and cations B are present in octahedral voids.(i) What percentage of the tetrahedral voids is occupied by A?

$\begin{array}{1 1}(A)\;12\%&(B)\;12.3\%\\(C)\;12.5\%&(D)\;13.5\%\end{array}$

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## 1 Answer

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In a cubic close packed lattice of oxide ions there would be two tetrahedral voids and one octahedral void for each oxide ion.
$\therefore$ For four oxide ions there would be 8 tetrahedral and four octahedral voids two are occupied by B.
Percentage of tetrahedral voids occupied by A =$\large\frac{1}{8}$$\times 100=12.5\%$
Hence (C) is the correct answer.
answered May 28, 2014

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