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31 May, 02:12

Many metals pack in cubic unit cells. The density of a metal and length of the unit cell can be used to determine the type for packing. For example, polonium has a density of 9.19 g/cm3 and a unit cell side length a of 3.37 Å. (1 Å = 1 10-8 cm.) (a) How many polonium atoms are in exactly 1 cm3? atoms (b) How many unit cells are in exactly 1 cm3? unit cells (c) How many polonium atoms are there per unit cell?

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  1. 31 May, 05:27
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    A.) 34.866 x 10¯23 g/atom

    B.) 2.64 x 10^22 atoms in 1 cm3

    C.) 1 atoms per unit cell

    Explanation:

    A) Calculate the average mass of one atom of polonium:

    210g mol¯1 : 6.022 x 1023 atoms mol¯1 = 34.866 x 10¯23 g/atom

    B) Determine atoms in 1 cm3:

    9.19g / 34.866x 10¯23 g/atom = 2.64 x 10^22 atoms in 1 cm3

    Determine volume of the unit cell:

    (3.37 x 10¯8 cm) 3 = 3.827 x 10¯23 cm3

    Determine number of unit cells in 1 cm3:

    1 cm3 / 3.827 x 10¯23 cm3 = 2.61 x 1022 unit cells

    C) Determine atoms per unit cell:

    2.64 x 1022 atoms / 2.61 x 1022 unit cells = 1 atoms per unit cell
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