A solid metal oxide crystallizes in a cubic unit cell. Metal (M) ions are located at every corner and at the center of each face. Oxide ions (O) occupy half of the tetrahedral holes. What is the empirical formula of this metal oxide?

To determine the empirical formula of the metal oxide, we need to figure out the ratio of metal ions to oxide ions in the unit cell.

- Each corner atom is shared among eight unit cells, so each contributes 1/8 to the unit cell. Since there are eight corners in a cubic unit cell, this adds up to 8 * 1/8 = 1 metal ion from the corners. - Each face-centered atom is shared between two unit cells, so each contributes 1/2 to the unit cell. There are six faces on a cube, so this adds up to 6 * 1/2 = 3 metal ions from the face centers. - Together, this gives us a total of 1 + 3 = 4 metal ions (M) per unit cell.

Now we look at the oxide ions.

- The oxide ions fill half of the tetrahedral holes. In a face-centered cubic (FCC) unit cell, there are 8 tetrahedral holes, so if only half of them are filled, there are 8 * 1/2 = 4 oxide ions (O) per unit cell.

So, in one unit cell, there are 4 metal ions and 4 oxide ions, giving a metal-to-oxide ratio of 1:1. The empirical formula of the metal oxide is therefore MO.