Question

# The coordination number of zinc in zinc blende $\left( {ZnS} \right)$ is _________A: $6$ B: $4$ C: $8$ D: $12$

Hint: Coordination number is the number of atoms or ions surrounding a central atom in a complex or crystal structure. Zinc blende has face centered cubic close packing(FCC). This packing has $4$ atoms per unit cell.
We know coordination number is the number of atoms surrounding the central metal atom zinc blende has face centered cubic close packing. Since the number of atoms in a single unit cell of zinc and sulphur is the same it is consistent with the formula $ZnS$. Ionic radius of $Z{n^{2 + }}$ is $74pm$ and for ${S^{2 - }}$ is $190pm$ therefore the ratio between cationic and anionic radii in zinc blende is $0.39$ . This means zinc blends will possess a tetrahedral ion arrangement and there will be four nearest neighbors for both zinc and sulphur, this means coordination number of zinc and sulphur is$4$. So the answer to this question is B that is$4$ .
Additional information: Coordination number is also called ligancy. For molecules and polyatomic ions coordination number of an atom can be simply calculated by counting the number of atoms which are bound to that atom, it doesn’t matter if they are connected with single bond, double bond or triple bond. $ZnS$ Has unique structure as compared to other molecules. Zinc blende possess diamond type network but at different temperatures $ZnS$ can become the wurtzite structure type which has hexagonal symmetry but structure wise zinc blende is thermodynamically stable.
Wurtzite has (HCP) hexagonal close packing which is characterized by $12$ ions in the corners of each unit that create a hexagonal prism due to thermodynamic stability zinc blende slowly transforms to wurtzite.
Note: In these types of questions remember which compound possesses which type of crystal lattice. After knowing crystal lattice you will be able to find nearest neighbors of atoms which will be the coordination number of that atom. Zinc blende is also known as sphalerite which has cubic structure with $1:1$ zinc sulphur ratio. By this ratio we mean the number of zinc atoms is equal to the number of sulphur atoms. Sphalerite is a mineral which is the chief ore of zinc.