Question

The number of tetrahedral voids in the hexagonal primitive unit cell is:

Answer 1

Hint: To answer this question recall the concept of close packing in a solid crystal. Voids refer to the gaps between the constituent particles. These voids in solid crystals mean the vacant space between the constituent particles

Complete step by step answer:
Crystalline solids show regular and repeating pattern arrangement of constituent particles resulting in two types of interstitial voids in a 3D structure:
Tetrahedral voids: In case of a cubic close-packed structure, a second layer of spheres is present over the triangular voids of the first layer. This results in each sphere touching the three spheres of the first layer. When we join the centre of these four spheres, we get a tetrahedron and the space left over by joining the centre of these spheres forms a tetrahedral void.
Octahedral voids: Adjacent to tetrahedral voids you can find octahedral voids. When the triangular voids of the first layer coincide with the triangular voids of the layer above or below it, we get a void that is formed by enclosing six spheres. This vacant space which is formed by a combination of the initial formed triangular voids of the first layer and that of the second layer is known as Octahedral Voids.
In a hexagonal unit cell there are 6 atoms, this means that the number of octahedral voids are 6. So, we can conclude that the number of tetrahedral voids in a hexagonal primitive unit cell is double the octahedral voids thus, it is 12.

Note:
A crystal is a solid where a periodic arrangement of atoms is formed. Not all crystals are solids. One example of this phenomenon is that when liquid water starts to freeze, the transition in the process begins with tiny ice crystals rising until they merge, creating a polycrystalline structure.