$A$ compound forms a hexagonal close-packed $(HCP)$ structure. What is the total number of voids in $0.5 \ mol$ of it? How many of these are tetrahedral voids?

Let the number of close-packed particles be $N$.
Given,$N = 0.5 \ mol = 0.5 \times 6.022 \times 10^{23} = 3.011 \times 10^{23}$ particles.
In a close-packed structure:
Number of octahedral voids $= N = 3.011 \times 10^{23}$.
Number of tetrahedral voids $= 2N = 2 \times 3.011 \times 10^{23} = 6.022 \times 10^{23}$.
Total number of voids $= N + 2N = 3N = 3 \times 3.011 \times 10^{23} = 9.033 \times 10^{23}$.
Thus,the total number of voids is $9.033 \times 10^{23}$ and the number of tetrahedral voids is $6.022 \times 10^{23}$.