Question

what is the percentage efficiency of packing in case of simple cubic lattice

Answer 1

Answer:

In simple cubic unit cell, two atoms touch along the edge of the unit cell.

For simple cubic cell, the relationship between the edge length a and the radius r is a=2r

The volume of the unit cell V=a

3

=(2r)

3

=8r

3

Each simple cubic cell contains eight atoms present at eight corners. Each atom contributes one eight to the unit cell. Hence, number of atoms present in one unit cell =8×

8

1

=1

The volume occupied by one atom in unit cell =

3

4

πr

3

Packing efficiency=

volume of unit cell

Volume occupied by one atom

×100

Packing efficiency=

8r

3

3

4

πr

3

×100

Packing efficiency=52.4%.

Hence, the percentage efficiency of packing in case of simple cubic cell is 52.4 %.