Chemistry - Solid State Question with Solution | TestHub

In an fcc unit cell, there are $8$ corners and $6$ face centers.

Since one 'A' atom is missing from a corner, the number of 'A' atoms at the corners is $7$.

Contribution of each corner atom to the unit cell is $\frac{1}{8}$.

Effective number of 'A' atoms per unit cell = $7\times \frac{1}{8}=\frac{7}{8}$

The 'B' atoms are at the $6$ face centers.

Contribution of each face center atom to the unit cell is $\frac{1}{2}$.

Effective number of 'B' atoms per unit cell = $6\times \frac{1}{2}=3$

Ratio of atoms A to B = $\frac{7}{8}:3=7:24$

The simplest formula of the compound is ${\text{A}}_7{\text{B}}_{24}$.

Answer: ${\text{A}}_7{\text{B}}_{24}$