**NaCl → face-centered cubic (FCC) l**

- 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:**

$\overline{){\mathbf{density}}{\mathbf{}}{\mathbf{=}}\frac{\mathbf{mass}}{\mathbf{volume}}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{volume}\mathbf{=}\frac{\mathbf{mass}}{\mathbf{density}}$

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

**volume = 7.477 x 10 ^{-23} cm^{3}/1 unit cell**

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/cm^{3}, estimate the radius (in centimeters) of the O^{2-} anions and the Mg^{2+} cations.

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