The molecular formula of a compound is AB_2O_ | vedclass

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(D) In a $ccp$ lattice, if the number of atoms is $N$, then the number of octahedral voids is $N$ and the number of tetrahedral voids is $2N$. Given t

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$\frac{1}{2}$

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(D) In a $ccp$ lattice, if the number of atoms is $N$, then the number of octahedral voids is $N$ and the number of tetrahedral voids is $2N$. Given the formula $AB_2O_4$, let the number of $O$ atoms be $4$. Since $O$ forms a $ccp$ lattice, $N = 4$. Number of tetrahedral voids $= 2 	imes 4 = 8$. Number of octahedral voids $= 4$. Atoms of $A$ occupy $\frac{1}{8}$ of tetrahedral voids, so number of $A$ atoms $= \frac{1}{8} 	imes 8 = 1$. Atoms of $B$ occupy octahedral voids. From the formula $AB_2O_4$, there are $2$ atoms of $B$. Fraction of occupied octahedral voids $= \frac{	ext{Number of } B 	ext{ atoms}}{	ext{Total octahedral voids}} = \frac{2}{4} = \frac{1}{2}$. Fraction of vacant octahedral voids $= 1 - \frac{1}{2} = \frac{1}{2}$.

The molecular formula of a compound is $AB_2O_4$. Atoms of $O$ form a $ccp$ lattice. Atoms of $A$ (cation) occupy $\frac{1}{8}$ of the tetrahedral voids. Atoms of $B$ (cation) occupy a fraction of the octahedral voids. What is the fraction of vacant octahedral voids?

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