Question

If fcc unit cell is converted into an end centred unit cell, then its packing efficiency will decrease by:

• A. 25%
• B. 50%
• C. 40%
• D. 60%

Answer 1

The correct option is B 50%

A fcc unit cell contains eight atoms on the corners and six atoms on the six face centres.
$\text{Number of atoms in fcc}=Z_{fcc}=\frac{1}{8}\times 8+6\times \frac{1}{2}=4$
An end centred cubic has eight atoms on corners but only two atoms on opposite faces of cube.

$\text{Number of atoms in end centred cube}=Z_{endcentred}=\frac{1}{8}\times 8+2\times \frac{1}{2}=2$

We know,
$\text{Packing efficiency}=\frac{\text{Volume occupied by spheres}}{\text{Volume of the cell}}\times 100$

As the volume of the cell is same in both fcc and end centred

$\text{Packing fraction}\propto \text{volume occupied by sphere}\propto Z$
$\therefore$
$\%\text{decrease in packing efficiency}=\frac{4-2}{4}\times 100=50\%$
Thus, option (b) is correct.