Question

In a face-centered cubic of $A$ and $B-atoms$ in which $A$ atoms are at the corners of the unit cell and $B-atoms$ at the face-centers, one of the $A-atoms$ is missing from one corner in the unit cell. The simplest formula of the compound is:

• A. $A_7{B}_3$
• B. $A{B}_3$
• C. $A_7{B}_{24}$
• D. $A_8{B}_{21}$

Answer 1

The correct option is C $A_7{B}_{24}$

Number of $A$ atoms $=\frac{1}{8}\times 7=\frac{7}{8}$
Number of $B$ atoms $=6\times \frac{1}{2}=3$
$A:B=\frac{7}{8}:3=7:24$
Molecular formula $=A_7{B}_{24}$.