Discussion
The spinel structure of MgAl2O4 has cubic close packed arrangement of oxide ions. The fractions of the octahedral and tetrahedral sites occupied by cations, respectively, are
Answer: D
The cations occupy ½ of the octahedral sites and ⅛ of the tetrahedral sites.
A cubic close-packed array of n anions has n octahedral holes and 2n tetrahedral holes. Per formula unit MgAl2O4 there are four oxide ions, so 4 octahedral and 8 tetrahedral holes.
MgAl2O4 is a normal spinel: the one Mg2+ sits in a tetrahedral hole and the two Al3+ in octahedral holes. So
\[ \begin{aligned} \text{octahedral} &= 2/4 = 1/2 \\ \text{tetrahedral} &= 1/8 \end{aligned} \]
The other options swap the two fractions or use the wrong number of sites: ¼ would mean one cation per four holes, which is neither the Mg nor the Al count.
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