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Question 56

Ga (atomic mass 70 u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is ________ $$\times 10^{21}$$. (Round off to the Nearest Integer).


Correct Answer: 15

Gallium (atomic mass 70 u) crystallizes in a hexagonal close-packed (HCP) structure. We need to find the total number of voids in 0.581 g of Ga.

Moles of Ga = $$\frac{0.581}{70} = 8.30 \times 10^{-3}$$ mol.

Number of Ga atoms = $$8.30 \times 10^{-3} \times 6.022 \times 10^{23} = 4.998 \times 10^{21} \approx 5.0 \times 10^{21}$$ atoms.

In a close-packed structure (HCP or CCP), for every atom in the structure, there is 1 octahedral void and 2 tetrahedral voids. Therefore, the total number of voids per atom = $$1 + 2 = 3$$.

Total number of voids = $$3 \times 5.0 \times 10^{21} = 15 \times 10^{21}$$.

The answer is $$15$$.

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