Question

In a cubic unit cell, seven of the eight corners are occupied by atoms $A$ and centres of faces are occupied by atoms $B$. Total number of atoms in the general formula of the compound is:

Answer 1

The atoms in the corner contribute $\frac{1}{8}$ to the unit cell.
seven of the corners are occupied by A atoms
Hence number of atoms per unit cell = $7\times \frac{1}{8}=\frac{7}{8}$

The atoms in the faces contribute $\frac{1}{2}$ to the unit cell. There are six faces.
Hence number of B atoms per unit cell = $6\times \frac{1}{2}=3$

Hence the formula is
$A_{\frac{7}{8}}{B}_3$ or general formula is $A_7{B}_{24}$
The total number of atoms = 31