The mineral ZnAl_2O_4 has a spinel structure. | vedclass

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(A) In a normal spinel structure,the oxide ions $(O^{2-})$ form a cubic close-packed $(ccp)$ lattice. For $N$ oxide ions,there are $N$ octahedral void

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$50$

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(A) In a normal spinel structure,the oxide ions $(O^{2-})$ form a cubic close-packed $(ccp)$ lattice. For $N$ oxide ions,there are $N$ octahedral voids and $2N$ tetrahedral voids. In $ZnAl_2O_4$,there are $4$ oxide ions per unit cell. Total octahedral voids = $4$. Total tetrahedral voids = $8$. In a normal spinel,$Zn^{2+}$ ions occupy $1/8$ of the tetrahedral voids,and $Al^{3+}$ ions occupy $1/2$ of the octahedral voids. Number of occupied octahedral voids = $(1/2) 	imes 4 = 2$. Percentage of occupied octahedral voids = $(2 / 4) 	imes 100 = 50 \%$.

The mineral $ZnAl_2O_4$ has a spinel structure. The percentage of occupied octahedral voids is ........... $\%$.

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