The unit cell in a crystal of diamond belongs to a crystal system different from any we have discussed. The volume of a unit cell of diamond is 0.0454 nm3 and the density of diamond is 3.52 g/cm3. Find the number of carbon atoms in a unit cell of diamond.

8.03 atoms of carbon

Given data;

Volume of unit cell diamond = 0.0454 nm³ (4.54*10⁻²³cm³)

Density = 3.52 g/cm³

Number of atoms = ?

Solution;

d = m/v

m = d * v

m = 3.52 g/cm³ * 4.54*10⁻²³cm³

m = 16 * 10⁻²³ g

Now we will determine the moles:

Number of moles of carbon = mass / molar mass

Number of moles of carbon = 16 * 10⁻²³ g / 12 g/mol

Number of moles of carbon = 1.3 * 10⁻²³ mol

one mole = 6.022 * 10²³ atoms

1.3 * 10⁻²³ mol * 6.022 * 10²³ atoms / 1mol

8.03 atoms of carbon