Question

In a face centred cubic arrangement of A and B atoms, 'A' atoms are at the corners of the unit cell and 'B' atoms are at the face centers. One of the 'A' atoms is missing from one corner in the unit cell. The simplest formula of compound is:

• A. $A_7{B}_{24}$
• B. $A_7{B}_8$
• C. $A{B}_3$
• D. $A_7{B}_3$

Answer 1

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

Each corner atom contributes to $\frac{1}{8}$ of an atom since each corner is shared by 8 cubes. On removing one atom, the remaining atoms of A and B would be:
Atoms of A = $7\times \frac{1}{8}=\frac{7}{8}$
Atoms of B = $6\times \frac{1}{2}=3$
Emeprical formula of the compounds is $A_7{B}_{24}$