Question

MgO crystallizes in a cubic unit cell with O²⁻ ions on each corner and each face. How many Mg²⁺ and O²⁻ ions are in each unit cell of MgO?

A. 2 Mg²⁺ ions and 2 O²⁻ ions
B. 8 Mg²⁺ ions and 8 O²⁻ ions
C. 1 Mg²⁺ ion and 1 O²⁻ ion
D. 4 Mg²⁺ ions and 4 O²⁻ ions

Answer 1

MgO crystallizes in a cubic unit cell with O²⁻ ions on each corner and each face. There are 14 O²⁻ ions and 14 Mg²⁺ ions in each unit cell.

Step-by-step explanation:

MgO crystallizes in a cubic unit cell with O²⁻ ions on each corner and each face. This means that there are O²⁻ ions at each of the 8 corners and O²⁻ ions at each of the 6 faces of the unit cell. In total, there are 8 O²⁻ ions at the corners and 6 O²⁻ ions at the faces, making a total of 14 O²⁻ ions in each unit cell.

Since each O²⁻ ion has a charge of -2, the total charge of the O²⁻ ions in the unit cell is -2 * 14 = -28.

To balance the charges, there must be an equal number of Mg²⁺ ions in the unit cell, with a total charge of +28. Since the charge of each Mg²⁺ ion is +2, there must be a total of 28 / 2 = 14 Mg²⁺ ions in the unit cell.

Therefore, the correct answer is D. 4 Mg²⁺ ions and 4 O²⁻ ions.