Question

A solid is formed and it has three types of atoms P, Q and R. P forms a fcc lattice with Q atoms occupying all tetrahedral voids and R atoms occupying half of octahedral voids. The formula of solid is

• A. $P_{4}QR_{2}$
• B. $P_{4}Q_{2}R$
• C. $PQ_{2}R_{4}$
• D. $P_{2}Q_{4}R$

Answer 1

Answer: (D)

P is in f.c.c. lattice
Number of atoms $=$ atom at corner $\times \frac{1}{8}+$ atoms at faces $\times \frac{1}{2}$
$P=8\times \frac{1}{8}+6\times \frac{1}{2}=4$
Total tetrahedral voids $=8$
As Q are at T.V.
So $Q=8$
Number of octahedral voids $=4$
$R=\frac{1}{2}\times 4=2$
So, $P=4,Q=8,R=2$
Hence the formula of solid is $P_{4}Q_{8}R_{2}$ or $P_{2}Q_{4}R$