# Question #96797

Nov 20, 2016

There are four sodium ions in a unit cell of sodium chloride.

#### Explanation:

The unit cell

A unit cell is the smallest group of particles that constitutes the repeating pattern in a crystal.

Each unit cell is surrounded by other unit cells in all directions to make up a crystal lattice.

The $\text{NaCl}$ unit cell

Here is a diagram of the NaCl unit cell.

It is called a face centred cubic cell because the large chloride ions (green) are at the faces of a cube.

The smaller sodium ions (grey) fill in the holes around the edges of the cube.

Here is an expanded view of the unit cell.

You can see that there is also a sodium ion in the centre of the cube, and it does not belong to any other unit cell.

Number of ${\text{Na}}^{+}$ ions in unit cell

Four other cubes share each edge of the cube, so there is ¼ of a sodium ion at each edge.

There are four edges at the top, four at the bottom, and four at the sides.

$\text{Number of Na"^+ "ions" = 12 color(red)(cancel(color(black)("edges"))) × (1/4 color(white)(l)"ion")/(1 color(red)(cancel(color(black)("edge")))) + 1 color(red)(cancel(color(black)("centre")))× "1 ion"/(1 color(red)(cancel(color(black)("centre")))) = "3 ions + 1 ion" = "4 ions}$

There are four sodium ions in a unit cell of sodium chloride.