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A compound is formed by elements A, B and O. Atoms of oxygen form ccp lattice. Atoms of A (cation) occupy $\frac{1}{8}^{\text {th }}$ of tetrahedral voids and atoms of B (cation) occupy half of octahedral voids. What is the molecular formula of the compound?
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The correct answer is:
$\mathrm{AB}_2 \mathrm{O}_4$
No. of tetrahedral voids is twice the no. of atoms. No. of octahedral voids is same as the no. of atoms. Oxygen at $\mathrm{CCP}=1$
A occupy $\frac{1}{8}$ of tetrahedral voids i.e. $\frac{1}{8} \times 2=\frac{1}{4}$
B occupy half of octahedral void i.e. $\frac{1}{2} \times 1=\frac{1}{2}$ $\therefore \mathrm{A}_{\frac{1}{4}} \mathrm{~B}_{\frac{1}{2}} \mathrm{O}_1$
A occupy $\frac{1}{8}$ of tetrahedral voids i.e. $\frac{1}{8} \times 2=\frac{1}{4}$
B occupy half of octahedral void i.e. $\frac{1}{2} \times 1=\frac{1}{2}$ $\therefore \mathrm{A}_{\frac{1}{4}} \mathrm{~B}_{\frac{1}{2}} \mathrm{O}_1$
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