Question

When copper crystallizes, it forms face-centered cubic cells. The unit cell edge length is 361.5 pm. Calculate the density of copper in g/cm3?

Answer 1

Density of copper can be calculated using the following formula:

$d=\frac{m}{V}$

Here, m is mass and V is volume, thus, to calculate density first calculate mass and volume of copper.

In FCC, number of atoms in a unit cell are 4, atomic mass of Cu is 63.546 g/mol and number of atoms in 1 mole is $6.023\times 10^{23}$.

Mass of Cu will be:

$m=4 atoms\times \frac{1 mol}{6.023\times 10^{23}}\times \frac{63.546 g}{mol}=4.22\times 10^{-22}g$

Now, volume can be calculate as:

$V=a^{3}$

Here, a is edge length.

First convert edge length from pm to cm

$1pm=10^{-10}cm$

Thus,

$361.5 pm=3.615\times 10^{-8}cm$

Putting the value,

$V=(3.615\times 10^{-8} cm)^{3}=4.72\times 10^{-23} cm^{3}$

Now, from mass and volume density can be calculated as follows:

$d=\frac{m}{V}=\frac{4.22\times 10^{-22}g}{4.72\times 10^{-23} cm^{3}}=8.932 g/cm^{3}$

Therefore, density of copper will be $8.932 g/cm^{3}$.