Question

Calculate the number of unit cells in 0.3 g of a species having density of 8.5 g/cm3

and unit cell edge length

3.25×10-8

cm.​

Answer 1

The number of unit cells is 1.03 × 10^21 unit cells.

Given:

0.3 g of a species having a density of 8.5 g/cm3 and unit cell edge length of 3.25×10-8cm.

To Find:

The number of unit cells.

Solution:

To find the number of unit cells we will follow the following steps:

As we know,

$number \: of \: unit \: cell = \frac{given \: mass \: of species\: }{mass \: of \: 1 \: unit \: cell}$

$mass \: of \: 1 \: unit \: cell = volume \: \times density = 8.5 \times ({3.25 \times { 10}^{ - 8} )}^{ 3}$

As Volume is the cube of side =

$({3.25 \times { 10}^{ - 8} )}^{ 3}$

Putting values in the above formula for finding several unit cells we get,

$\frac{0.3}{8.5 \times ({3.25 \times { 10}^{ - 8} )}^{ 3} }$ = $\frac{0.3}{8.5 \times ({34.33 \times { 10}^{ - 24} )}^{ 1} }$ = $\frac{0.3× { 10}^{ +24}}{8.5 \times34.33}$ = $\frac{0.3 \times { 10}^{ +24}}{291.8}$ = 1.03 × 10^21 unit cells.

Henceforth, the number of unit cells is 1.03 × 10^21 unit cells.