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11 January, 02:22

The unit cell in a crystal of diamond belongs to a crystal system different from any we have discussed. The volume of a unit cell of diamond is 0.0454 nm3 and the density of diamond is 3.52 g/cm3. Find the number of carbon atoms in a unit cell of diamond.

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  1. 11 January, 03:45
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    8.03 atoms of carbon

    Given data;

    Volume of unit cell diamond = 0.0454 nm³ (4.54*10⁻²³cm³)

    Density = 3.52 g/cm³

    Number of atoms = ?

    Solution;

    d = m/v

    m = d * v

    m = 3.52 g/cm³ * 4.54*10⁻²³cm³

    m = 16 * 10⁻²³ g

    Now we will determine the moles:

    Number of moles of carbon = mass / molar mass

    Number of moles of carbon = 16 * 10⁻²³ g / 12 g/mol

    Number of moles of carbon = 1.3 * 10⁻²³ mol

    one mole = 6.022 * 10²³ atoms

    1.3 * 10⁻²³ mol * 6.022 * 10²³ atoms / 1mol

    8.03 atoms of carbon
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