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  4. In a cubic close packed structure of mixed oxides, the lattice is made up of oxide ions, one fifth of tetrahedral voids one occupied by X ions while one half of the octahedral voids are occupied by Y ions. Then formula of the oxide will be

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Q. In a cubic close packed structure of mixed oxides, the lattice is made up of oxide ions, one fifth of tetrahedral voids one occupied by $X$ ions while one half of the octahedral voids are occupied by $Y$ ions. Then formula of the oxide will be

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Solution:

Number of $O^{2 -}$ ions $= n$
Number of tetrahedral voids $= 2n$
Number of octahedral voids $= n$
Number of $X$ ions $=\frac{2 n}{5}$
Number of $Y$ ions $=\frac{n}{2}$
$\begin{matrix} X:Y:O \\ \frac{2 n}{5}:\frac{n}{2}:n \\ 4:5:10 \end{matrix}$
Simplest formula $=X_{4}Y_{5}O_{10}$ .