Question

A substance $A_x{B}_y$ crystallizes in a face centred cubic (FCC) lattice in which atoms $A$ occupy each corner of the cube and atoms $B$ occupy the centre of each face of the cube.

The correct composition of the substance $A_x{B}_y$ is:

• A. $A{B}_3$
• B. $A_4{B}_3$
• C. $A_{3}B$
• D. None of the above

Answer 1

Answer: (A)

$A{B}_3$

$A_x{B}_y$ crystallizes in a face-centered cubic (FCC) lattice.

$A$ atoms occupy each corner of the cube. So, the number of atoms of $A$ is $8\times \frac{1}{8}=1$.

$B$ atoms occupy the center of each face of the cube. So, the number of atoms of $B$ is $6\times \frac{1}{2}=3$.

Hence, the formula becomes $A{B}_3$.