Question

In a face centred cubic arrangement of A and B atoms in which 'A' atoms are at the corners of the unit cell and 'B' atoms are 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. $A_7{B}_8$
• C. $A{B}_3$
• D. $A_7{B}_{24}$

Answer 1

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

In a face centred cubic arrangement of A and B atoms in which 'A' atoms are at the corners of the unit cell.
There are total 8 corners and each contributes one eight to the unit cell.
One of the 'A' atom is missing from one corner in unit cell.
So there are 7 'A' atoms with total contribution $7\times \frac{1}{8}=\frac{7}{8}$.
'B' atoms are at the face centres. There are six face centres. Each contributes one half to the unit cell.
Total contribution $=6\times \frac{1}{2}=3$
$A:B=\frac{7}{8}:3=7:24$
The simplest formula of compound is $A_7{B}_{24}$

Hence, the correct option is D.