A compound forms hexagonal close packed structure. What is the number of octaheral voids in 0.5 mole of it?

Question : A compound forms hexagonal close packed structure.  What is the number of voids in 0.5 mole of it ? how many of these are tetrahedral voids ?

key points to answer this question : When asked to calculate the number of voids in hexagonal close packed structure , we have to calculate octahedral and tetrahedral voids , and these voids depends on the number of atoms present in 0.5 mole , that is represent by N , tetrahedral voids are equal to 2N and total voids.

Solution : The total numbers of atoms (N) in a closed packed structure in 0.5 mole

One mole contain 6.022 × 10²³  particles

so the total numbers of atoms (N) in 0.5 moles = 0.5 × 6.022 × 10²³ = 3.011 × 10²³

as we know or we have discussed here that the octahedral voids = numbers of atoms (N)

hence number of octahedral voids = 3.011 × 10²³

we also know that the tetrahedral voids are equal to 2N

means tetrahedral voids = 2 x numbers of atoms (N)

hence number of tetrahedral voids = 2 × 3.011 × 10²³ = 6.022 ×10²³

Total voids = octahedral voids + tetrahedral voids

so The total number of voids are = 3.011 × 10²³ + 6.022 × 10²³ = 9.033 × 10²³