Problem: The unit cell of MgO is shown below.Does MgO have a structure like that of NaCl or ZnS? If the density of MgO is 3.58 g/cm3, estimate the radius (in centimeters) of the O2- anions and the Mg2+ cations.

NaCl → face-centered cubic (FCC)  lattice 

• contains an atom in each of the face of the cube and an atom in each of the corners. 

ZnS → body-centered cubic (BCC) unit cell 

•  composed of a cube with one atom at each of its corners and one atom at the center of the cube. 

MgO:

• Has one O^2- ion:
  • at each corner
  • at each face

MgO follows an FCC cubic lattice, similar to NaCl structure.

$\mathbf{\#}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{atoms}\mathbf{=}\left(\mathbf{8}\mathbf{\times }\frac{\mathbf{1}}{\mathbf{8}}\right)\mathbf{+}\mathbf{6}\left(\frac{1}{2}\right)$

# of atoms = 4 per 1 unit cell

Step 1: Solve for volume using density:

$$\begin{gathered} \boxed{\mathbf{density}\mathbf{ }\mathbf{=}\frac{\mathbf{mass}}{\mathbf{volume}}} \\ \mathbf{volume}\mathbf{=}\frac{\mathbf{mass}}{\mathbf{density}} \end{gathered}$$

$\mathbf{volume}\mathbf{=}\frac{\mathbf{4}\mathbf{ }\cancel{\mathbf{atoms}}}{\mathbf{1}\mathbf{ }\mathbf{unit}\mathbf{ }\mathbf{cell}}\mathbf{\times }\frac{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }\mathbf{MgO}}}{(6.022\times {10}^{23})\mathbf{ }\cancel{\mathbf{atoms}}}\mathbf{\times }\frac{\mathbf{40}\mathbf{.}\mathbf{3}\mathbf{ }\cancel{\mathbf{g}\mathbf{ }\mathbf{MgO}}}{\mathbf{1}\mathbf{ }\cancel{\mathbf{mol}\mathbf{ }\mathbf{MgO}}}\mathbf{ }\mathbf{\times }\frac{\mathbf{1}\mathbf{ }{\mathbf{cm}}^{\mathbf{3}}}{\mathbf{3}\mathbf{.}\mathbf{58}\mathbf{ }\cancel{\mathbf{g}\mathbf{ }\mathbf{MgO}}}$

volume = 7.477 x 10^-23 cm³/1 unit cell