Problem: The density of solid Cu is 8.96 g/cm3. How many atoms are present per cubic centimeter of Cu? If a solid, Cu adopts a face-centered cubic unit cell. How many unit cells are present per cubic centimeter of Cu? What is the volume of a unit cell of this metal? What is the edge length of a unit cell of Cu?

Face-centered cubic lattice contains an atom in each of the face of the cube and an atom in each of the corners:

a) Cu atoms per cm³

$\frac{\mathbf{8}\mathbf{.}\mathbf{96}\mathbf{ }\mathbf{ }\cancel{\mathbf{g}\mathbf{ }}}{{\mathbf{cm}}^{\mathbf{3}}}\mathbf{\times }\frac{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }\mathbf{Cu}}}{\mathbf{63}\mathbf{.}\mathbf{55}\cancel{\mathbf{ }\mathbf{g}\mathbf{ }\mathbf{Cu}}}\mathbf{\times }\frac{\mathbf{6}\mathbf{.}\mathbf{022}\mathbf{ }\mathbf{\times }\mathbf{ }{\mathbf{10}}^{\mathbf{23}}\mathbf{ }\mathbf{Cu}\mathbf{ }\mathbf{atoms}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }\mathbf{Cu}}}$

= 8.49 x 10²² Cu atoms/cm³

There are 8.49 x 10²² Cu atoms per cubic centimeter of Cu

b) Unit cells per 1 cm³ Cu

Cu atoms per unit cell:

• corner atoms = 1/8  → 8 corners
• face atoms = 1/2 → 6 faces 

$\frac{\mathbf{atoms}}{\mathbf{unit}\mathbf{ }\mathbf{cell}}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{8}\left(\frac{1}{8}\right)\mathbf{+}\mathbf{ }\mathbf{6}\left(\frac{1}{2}\right)\mathbf{ }\mathbf{=}\mathbf{ }$4 Cu atoms/ unit cell