Question

In a face centred cubic arrangement of $A$ and $B$ atoms when $A$ atoms are at the corner of the unit cell and $B$ atoms of 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. $A_7{B}_8$

Answer 1

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

For FCC arrangement, atoms are on corners and face centres of the cube.

There is a total of $8$ corners and each contributes one eight to the unit cell.

One of the 'A' atoms is missing from one corner in the unit cell.

Effective A atoms $=7\times \frac{1}{8}=\frac{7}{8}$

'B' atoms are at the face centres. There are $6$ face centres. Each contributes one half to the unit cell.

Effective B atoms $=6\times \frac{1}{2}=3$

Total contribution $=6\times \frac{1}{2}=3$

$A:B=\frac{7}{8}:3=7:24$

The simplest formula of the compound is $A_7{B}_{24}$

Hence, the correct option is C.