Question

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

• A. $A_7{B}_3$
• B. $A{B}_3$
• C. $A_7{B}_{24}$
• D. $A_4{B}_3$

Answer 1

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

If one atom (A) is missing from one corner, then number of atoms per unit cell $=7\times \frac{1}{8}=\frac{7}{8}$
Number of atoms (B) present at the face centres $=6\times \frac{1}{2}=3$
Thus, $A:B=\frac{7}{8}:3$

Hence, the simplest formula is $A_7{B}_{24}$.