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Calculate the density of Na metal.

  1. Aug 30, 2009 #1
    1. Calculate the density of Na metal. The length of the body-centered cubic unit cell is 4.24 Å.


    2. Attempted solution:

    [4 Na Atoms/unit cell] * [1 mol Na atoms/(6.022*10^23 atoms)] * [22.99g Na/1 mol Na] = 1.527 * 10-22 g/unit cell

    (4.24 Å)3 = 7.6225 * 10-23 cm3/unit cell


    [1.527 * 10-22 g/unit cell] / [7.6225 * 10-23 cm3/unit cell] = 2.00 g/cm3


    The correct answer is 1.00 g/cm3... What went wrong in my calculations?
     
  2. jcsd
  3. Aug 30, 2009 #2

    tiny-tim

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    Hi daviddee305! :smile:

    There are 9 atoms in a body-centered cubic cell (1 in the centre, and one at each vertex), but how many cells is each atom in (and why)? :wink:
     
  4. Aug 30, 2009 #3
    Each corner atom is shared by 8 unit cells, so only (1/8)th of each atom belongs to the body-centered cubic. Plus the one in the middle. Thank you.

    That was a great follow-up question, exactly what I needed to see through these confusing diagrams in my text.
     
  5. Aug 30, 2009 #4

    tiny-tim

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    Yup … always go back to the definition. :biggrin:

    (And now have a look at http://en.wikipedia.org/wiki/Body-centred_cubic. :wink:)
     
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