Question

Which of the following shows maximum packing efficiency?
A) Hexagonal close-packed lattice
B) Body-centred cubic
C) Simple cubic

Answer 1

Hint : The packing efficiency is defined as the fraction of the crystal or unit cell that is occupied by atoms. It is always less than a hundred percent because we cannot pack atoms which are in spherical shape without having empty space between them.
${\text{Packing efficiency = }}\dfrac{{{\text{Number of atoms}} \times {\text{volume occupied by one share}}}}{{{\text{Total volume of the unit cell}}}} \times 100$

Complete Step By Step Answer:
Packing efficiency is the percentage of space that is occupied by the constituent particles packed inside the lattice. It is used to define the structure of solid. It tells us about the different properties of solids such as density, consistency and isotropy. Many other attributes of solids can be obtained using packing efficiency.
The packing efficiency in fcc and hcp structures is $74\%$ .
The packing efficiency of a body-centred unit cell is $68\%$ .
Packing efficiency of a simple unit cell is $52.4\%$ .
Therefore, maximum packing efficiency is shown by hexagonal close packed lattice.

Note :
The purpose of the packing efficiency is to find the amount of available space occupied by atoms. It is represented as a volume fraction or by a volume percentage. Packing fraction is the fraction of total space that is filled with constituent particles of a cell or structure. When this fraction is shown in percentage form, that is the percentage of total space occupied by the constituent particles is the packing efficiency of the unit cell. The coordination number of hexagonal close packing (hcp) is $12$ . In hexagonal close packing, the layers of spheres are packed in such a way that spheres in alternating layers overlie one another.