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The density of an unknown metal is 1.55 and its atomic radius is 0.197 . It has a face-centered cubic lattice. What is the atomic weight of this metal?

  • Chemistry - ,

    I could work this problem if it had units. No units on density, none on radius (that could be pm, nm, what?).

  • Chemistry - ,

    Sorry about that - the density is 1.55 g/cm3 and the radius is 0.197 nm.

  • Chemistry - ,

    There are 4 atoms to the unit cell in a fcc.
    (4*atomic mass /6.02 x 10^23) = mass of unit cell. You need the mass.

    4*radius atom = a*21/2
    Solve the last equation for a

    volume of unit cell = a3

    Then plug into mass = volume x density to calculate mass of unit cell. Plug mass into the top equation to calculate atomic mass.

  • Chemistry - ,

    By the way, I would not use the radius in pm. I would change that to cm first thing out of the cage; otherwise you must convert volume in pm3 to cc and that's a little more difficult and one more step to make an error. Same thing for your next post.

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