Calculating atomic radius from weight + density

  1. 1. The problem statement, all variables and given/known data
    Calculate the radius of a palladium atom, given that Pd has an FCC crystal structure, a density of 12.0g/cm3, and an atomic weight of 106.4g/mol


    2. Relevant equations
    Pd contains 4 atoms per unit cell.
    unit cell edge lengh = 2*Radius*sqrt(2)


    3. The attempt at a solution

    calculate atom weight:
    106.4/6.0221418e23 = 1.7668133e-22

    calculate unit cell weight:
    1.7668133e-22*4 = 7.0672532e-22

    calculate unit cell volume in cm3:
    7.0672532e-22/12 = 5.8893777e-23

    convert to nm3:
    5.8893777e-23*(10^7)^3 = 0.0588938

    calculate edge length:
    0.0588938^(1/3) = 0.3890659

    calculate radius:
    0.3890659/2 = 0.194533

    my answer:
    0.194533nm

    correct answer:
    0.138nm

    I cant figure out what i've done wrong here.
     
  2. jcsd
  3. I figured it out. I got confused and thought 2*sqrt(2) was equal to 2. So silly!
     
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