Question

A mineral consists of a cubic close-packed structure formed by $O^{2–}$ ions where half the octahedral voids are occupied by $A{l}^{3+}$ and one eighth of the tetrahedral voids are occupied by $M{n}^{2+}$. The chemical formula of the mineral is:

• A. $M{n}_{2}A{l}_2{O}_3$
• B. $MnA{l}_2{O}_4$
• C. $MnA{l}_4{O}_7$
• D. $M{n}_{2}A{l}_2{O}_3$

Answer 1

The correct option is B $MnA{l}_2{O}_4$

$\text{No. of}{O}^{2-}\text{per unit cell}=8\times \frac{1}{8}+6\times \frac{1}{2}=4$

$\text{No. of}A{l}^{3+}\text{per unit cell}=4\times \frac{1}{2}=2$

$\text{No. of}M{n}^{2+}\text{per unit cell}=8\times \frac{1}{8}=1$