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Number of atoms per unit cell from molar mass, density and the value of a^3 x NA

The same question, asked 3 times: 10 May 2023 S1*, 10 May 2024 S2*, 13 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2023 S1

    92
    Calculate number of atoms per unit cell of an element having molar mass 92.0 g mol−192.0\,\text{g mol}^{-1} and density 8.6 g cm−38.6\,\text{g cm}^{-3} forming cubic unit cell structure. a3×NA=21.5 cm3mol−1a^3\times N_A=21.5\,\text{cm}^3\text{mol}^{-1}

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  2. Question 2

    10 May 2024 S2

    100
    Calculate the number of atoms present in unit cell of an element having molar mass 190 g mol−1190\,g\,mol^{-1} and density 20 g cm−320\,g\,cm^{-3}, a3NA=38 cm3 mol−1a^3 N_A = 38\,cm^3\,mol^{-1}

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  3. Question 3

    13 Apr 2026 S1

    17
    An element with a molar mass 27g mol−1\mathrm{mol^{-1}} forms a cubic unit cell. Calculate the number of atoms present in a unit cell if the density of metal is 2.7g cm−3\mathrm{cm^{-3}}. [a3×NA=40 cm3 mol−1][a^3 \times N_A = 40\ \mathrm{cm^3\,mol^{-1}}]

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