Question

In closest packed lattice, the number of octahedral sites as compared to tetrahedral ones will be:
(A) equal
(B) half
(C) double
(D) none of the above

Answer 1

For this problem, we have to study about the types of voids that are octahedral void and tetrahedral void and also how they are dependent on each other. After which we can choose the correct answer easily.

Complete step by step solution:
- In the given question, we have to choose the correct relationship between the tetrahedral void and octahedral void among the given options.
- As we know that when the spheres in the crystal lattice touch each other there is a formation of space between the spheres which is known as void.
- Now, we also know that there are two types of voids in the structure of crystal lattice that are octahedral and tetrahedral void.
- These voids can either be present in intramolecular spheres or in the intermolecular sphere.
- The tetrahedral void is formed when one sphere of the second is situated above the void of the first layer due to which it forms a tetrahedral void and that's why it is known as tetrahedral void.
- Whereas the octahedral void is formed when the tetrahedron void of the second layer is placed above the tetrahedron void of the first layer, it forms the octahedral void.
- That's why it is known as an octahedral void.
- Now, according to the characteristics of the tetrahedral void, if the crystal lattice N spheres then the number of tetrahedral voids will be 2N.
- Whereas the number of octahedral voids will be the same that is N.

Therefore, option (B) is the correct answer.

Note: The coordination number of octahedral and tetrahedral voids is also different that is 6 and 4 respectively. Because in the tetrahedral void, the void is surrounded by 4 spheres and in the octahedral void, the void is surrounded by 6 spheres.