Question

The simplest formula for the unit cell given below is:

• A. $A{B}_2{C}_2$
• B. $A{B}_3{C}_3$
• C. $A{B}_2{C}_3$
• D. $A{B}_3{C}_2$

Answer 1

The correct option is D $A{B}_3{C}_2$

$\text{Contribution of a corner particle is}=\frac{1}{8}$
$\text{Contribution of a face centre particle is}=\frac{1}{2}$
$\text{Contribution of a edge centre particle is}=\frac{1}{4}$
$\text{Contribution of a body centre particle is}=1$

In the given unit cell,
Atom A is present only at the body centre
Thus,
$\text{No. of A atom per unit cell}=1$

Atom B occupies 8 edge centres and 2 face centres of the cube.
$\therefore$
$\text{No. of B atoms per unit cell}=\frac{1}{4}\times 8+\frac{1}{2}\times 2=3$
Atom C occupies 8 corners and 2 face centres of the unit cell.
$\therefore$
$\text{No. of C atoms per unit cell}=\frac{1}{8}\times 8+\frac{1}{2}\times 2=2$


Hence, the formula of unit cell is
$A{B}_3{C}_2$