Question

In the face-centered cubic lattice, atom ${}^{\prime }{A}^{\prime }$ occupies the corner positions and atom ${}^{\prime }{B}^{\prime }$ occupies the face-centered positions. If one atom of ${}^{\prime }{B}^{\prime }$ is missing from one of the face-centred points, the formula of the compound is:

• A. $A_2{B}_5$
• B. $A_{2}B$
• C. $A{B}_2$
• D. $A_2{B}_3$

Answer 1

The correct option is A $A_2{B}_5$

Number of atoms of ${}^{\prime }{A}^{\prime }=8\times \frac{1}{8}=1$
Number of atoms of ${}^{\prime }{B}^{\prime }=5\times \frac{1}{2}=\frac{5}{2}$
$A:B=1:\frac{5}{2}=2:5$
Formula of the solid $=A_2{B}_5$