Question

Fraction of empty space in ccp packing is :

• A. 0.74
• B. 0.26
• C. 0.68
• D. 0.32

Answer 1

The correct option is B 0.26

In ccp lattice:


Packing efficiency (P.F) of ccp:

$P.F=\frac{\text{No of spheres in one ccp unit cell}\times \text{Volume of each sphere}}{\text{Total Volume of the Unit cell}}$

ccp unit cell have FCC arrangement



Here,
$\sqrt{2}\times a=4Ra=2\sqrt{2}\times R$

$Z_{eff}\text{for FCC}=(8\times \frac{1}{8})+(6\times \frac{1}{2})=4$
So,

$\text{The total volume occupied by sphere}V=4\times \frac{4}{3}\times \pi r^3$
$\text{Volume of the cube}=a^3=(2\sqrt{2}R{)}^3$

$\text{Packing efficiency (P.F)}=\frac{4\times \frac{4}{3}\times \pi r^3}{(2\sqrt{2}R{)}^3}P.F=\frac{\pi }{3\sqrt{2}}\approx 0.74$
$\text{Fraction empty space}=1-0.74=0.26$