Solid State Question 261
Question: $ MgAl_2O_4 $ , is found in the spinel structure in which $ {{O}^{2-}} $ ions constitute CCP lattice, $ M{{g}^{2+}} $ ions occupy l/8th of the tetrahedral voids and $ A{{l}^{3+}} $ ions occupy 1/2 of the octahedral voids. Find the total +ve charge contained in one unit cell.
Options:
A) +7/4 electronic charge
B) +6 electronic charge
C) +2 electronic charge
D) +8 electronic charge
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Answer:
Correct Answer: D
Solution:
[d] In ccp lattice, $ Z _{eff}=4 $ No. of TVs=8, No. of OVs=4 Total positive charge = Charge on $ M{{g}^{2+}} $ + Charge on $ A{{l}^{3+}} $
$ =\frac{1}{8}\times 8\times 2+\frac{1}{2}\times 4\times 3=8 $ electronic charge.
BETA
