Question

The unit cell for nickel arsenide is shown below. What isthe formula of this compound?

Short answer

The above structural compound formula is NiAs.

Step-by-step solution

Given data

The unit cell of nickel arsenide is shown in figure.

Step 2: The contribution of As to the given structure

Two atoms of As completely lie in the cell. They do not lie on the corners or the faces of the unit cell. The formula units of NiAs per unit cell is two.

Step 3: The formula of the given structure

Each Nickel atom per unit cell contributes $\frac{1}{8}$from each of the eight corner nickel atoms. One Nickel atom per unit cell gives the $\frac{1}{4}$contributions from each of the four edge-centered Nickel atoms.

The number of Ni ions in the unit cell =$\frac{1}{8}\times 8=1$

The number of As ions in the unit cell = $\frac{1}{4}\times 4=1$

Thus, the empirical formula of the compound is NiAs.