JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Solid State

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Ga (atomic mass 70u) crystallizes in a hexagonal close packed structure. The total number of voids in 0.581 g of Ga is ______

\times 1 0^{21}

. (Round off to the nearest integer).
[Given :

N_{A} = 6.023 \times 1 0^{23}

]

Answer: 15

Solution

The sample holds

\frac{0.581}{70} = 8.3 \times 1 0^{- 3}

mol of gallium, that is

8.3 \times 1 0^{- 3} \times 6.023 \times 1 0^{23} = 5.0 \times 1 0^{21}

atoms. A hexagonal close packed arrangement offers one octahedral void and two tetrahedral voids for every atom of the packing, three voids in all per atom. The total number of voids is

3 \times 5.0 \times 1 0^{21} = 15 \times 1 0^{21}

JEE Main · 2021 · 16 Mar 2021 · Shift 2 · Integer answer

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