Question

A face centred cubic arrangement of A and B atoms is given, where A atoms are at the corners of the unit cell, B atoms are at the face centres, and one of A atoms is missing from one corner in the unit cell. Find the simplest formula of the compound.

• A. $A_7{B}_3$
• B. $A{B}_3$
• C. $A_7{B}_{24}$
• D. $A_2{B}_3$

Answer 1

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

In FCC unit cell there are 8 corner atoms out of which one is missing.
$\text{Number of A atoms}=7\times \frac{1}{8}=\frac{7}{8}$
There are six face centre atoms and each has contribution of half in the unit cell. Thus,
$\text{Number of B atoms}=\frac{6}{2}=3$
Thus the formula of the compound is given as:
$A_{\frac{7}{8}}{B}_3$
On simplification, formula = $A_7{B}_{24}$