The anions (A) of $\mathrm{C}_{\mathrm{p}} \mathrm{A}_{\mathrm{q}}$ molecule forms an fcc lattice. Cations…
The anions (A) of $\mathrm{C}_{\mathrm{p}} \mathrm{A}_{\mathrm{q}}$ molecule forms an fcc lattice. Cations (C) are positioned at the body center and half of the edge centers. The formula of the molecule is
$\mathrm{CA}$
$\mathrm{CA}_2$
$\mathrm{C}_3 \mathrm{~A}_4$
$\mathrm{C}_5 \mathrm{~A}_8$
Solution
In a unit cell of fcc lattice, $A$ is present at 8 corners and 6 faces.
$\therefore \quad$ Effective no. of ${ }^{\prime} \mathrm{A}^{\prime}=\frac{1}{8} \times 8+\frac{1}{2} \times 6=4$
$\mathrm{C}$ is present at body centre and 6 edges.
$\therefore \quad$ Effective no. of ' $\mathrm{C}^{\prime}=1+6 \times \frac{1}{4}=\frac{5}{2}$
$\therefore \quad \mathrm{C}_{\frac{5}{2}} \mathrm{~A}_4=\mathrm{C}_5 \mathrm{~A}_8$