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${MgAl}_{2} O_{4}$ is found in the Spinal structure in which $O^{2 -}$ ions constitute CCP lattice, ${Mg}^{2 +}$ ions occupy $\frac{1}{8} th$ of the Tetrahedral voids and ${Al}^{3 +}$ ions occupy $\frac{1}{2}$ of the Octahedral voids.
Find the total positive charge contained in one unit cell.

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$+ \frac{7}{4}$ electronic charge

+ 6 electronic charge

+ 2 electronic charge

+ 8 electronic charge

answer is D.

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Detailed Solution

In ccp lattice, $Z_{eff} = 4$

No. of $T V s = 8, No. of O V s = 4$

Total positive charge = Charge on ${Mg}^{2 +}$ +Charge on ${Al}^{3 +}$

$= \frac{1}{8} \times 8 \times 2 + \frac{1}{2} \times 4 \times 3 = 8$ electronic charge.

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