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A mineral consists of a cubic close-packed structure formed by $\mathrm{O}^{2-}$ ions where half the octahedral voids are occupied by $\mathrm{Al}^{3+}$ and oneeighth of the tetrahedral voids are occupied by $\mathrm{Mn}^{2+}$. The chemical formula of the mineral is
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$\mathrm{MnAl}_{2} \mathrm{O}_{4}$
No of $\mathrm{O}^{-2}$ per unit cell $=8 \times \frac{1}{8}+6 \times \frac{1}{2}=4$
No of $\mathrm{Al}^{+3}$ per unit cell $=4 \times \frac{1}{2}=2$
No of $\mathrm{Mn}^{+2}$ per unit cell $=8 \times \frac{1}{8}=1$
$\mathbf{M n A l}_{2} \mathbf{O}_{4}$
No of $\mathrm{Al}^{+3}$ per unit cell $=4 \times \frac{1}{2}=2$
No of $\mathrm{Mn}^{+2}$ per unit cell $=8 \times \frac{1}{8}=1$
$\mathbf{M n A l}_{2} \mathbf{O}_{4}$
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