Match the following columns.
 

	Column I (Packing efficiency)		Column II
A	52%	1
B	68%	2
C	74%	3

Which of the following is correct?

$\mathrm{A}\to 1;\mathrm{B}\to 3;\mathrm{C}\to 2$

$\mathrm{The} \mathrm{Packing} \mathrm{efficiency}=\frac{\mathrm{Total} \mathrm{volume} \mathrm{of} \mathrm{sphere}}{\mathrm{volume} \mathrm{of} \mathrm{cube}}\times 100$
 

(1) It represents simple cubic lattice

In simple cubic structures, each unit cell has only one atom,

Packing efficiency =$\frac{\left(\frac{4}{3}\right)\pi r^3\times 100}{(2r{)}^3}$ = 52.4% (since a=2r)
(2)  It represents hcp (or) ccp structure.

Volume of the cube = a³ = $(\sqrt{8}r{)}^3$

Volume of the sphere = (4/3) π r³

No. of Sphere present in one FCC (or) ccp unit cell =4

The volume of the sphere = 4 x (4/3) π r³  

The packing efficiency $=\frac{\frac{16}{3}\pi r^3}{8\sqrt{8}{r}^3}\times 100$= 74%

(3) It represents bcc structure

In body centered cubic structures, each unit cell has two atoms,

Packing efficiency = $\frac{2\times \left(\frac{4}{3}\right)\pi r^3\times 100}{(\frac{4}{\sqrt{3}}r{)}^3}$ = 68% (since a=$\frac{4\mathrm{r}}{\sqrt{3}}$)