Question

Nickel, Ni, has a face-centered cubic structure(Figure 1) with an edge length of 352 pm. What is the density of this metal? Use the periodic table as needed.

Answer 1

The structure of face centered cubic unit cell is shown as below:

Now from this we can easily count the no of Ni atoms per unit cell:
The atoms at the corner contributes 1/8 and the atoms centered at the face contributes 1/2
The no. of Ni atoms per unit cell = (8 x 1/8) + (6 x 1/2)
   = 4 atoms per unit cell
Now molar mass of Ni = 58.693 g/mol
In 1 mol we have = 6.023 x 10²³ atoms/ mol.
Mass of 1 atom of Ni = (58.693 g/ mol)/ 6.023 x 10²³ atoms/ mol
   = 58.693/ 6.023 x 10²³ g/ atom
Mass of 4 atoms of Ni = 4 x (58.693/ 6.023 x 10²³ g/ atom)
Now volume of 1 unit cell = (352 pm)³ = (3.52 x 10^-8 cm)³.
Density = mass/ volume
   = [4 x (58.693/ 6.023 x 10²³ g/ atom)​]/ (3.52 x 10^-8 cm)³
  = 8.94 g/cm³