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Modify the Radius

  1. Nov 23, 2007 #1
    1. The problem statement, all variables and given/known data

    The atomic mass of iron (Fe) is approximately 56 grams per mole.

    (a) Assume each iron atom in a bar of iron takes up a volume equal to a sphere of radius 2.35×10-10 m. Calculate the density of iron based on this model.

    (b) The actual density of iron is 7870 kg/m^3. Modify the atomic radius in (a) such that the calculated density agrees with the actual value.

    2. Relevant equations

    Density = mass/(4/3)[tex]\pi[/tex]r^3 ( D=m/V )

    3. The attempt at a solution

    I figured out a) to be 1.71E3 kg/m^3. However, I can't figure out b).

    The new radius is 1.41E-9 from what I calculated , but it is not the right answer.
    Last edited: Nov 23, 2007
  2. jcsd
  3. Nov 24, 2007 #2
    Does anyone know??? Can anyone help???
  4. Nov 24, 2007 #3
    You just need to find how many atoms are in one mole.

    One mole weighs 56 grams,and density is

    [tex]\rho=\frac{56 g}{Nv_0}[/tex], where [tex]v_o[/tex] is a volume of one atom.
  5. Nov 24, 2007 #4
    Thanks azat for making me realize my mistake. I was calculating the actual mass to be in g and not kg (I had already converted N) while leaving the density in kg/m^3. Thank you, it turns out to be 1.41E-10 m.
    Last edited: Nov 24, 2007
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