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Confused (supposedly easy chem question: volume, density)

  1. Aug 11, 2008 #1
    This doesn't seem like it should be too hard, but i'm stuck... Am i making a stupid mistake somewhere?

    1. The density of potassium metal is 0.89 g/cm3. Potassium's atomic radius is 231 pm. Assuming that r nuc = 10^-4 x r atom, estimate the density of an essentially spherical 39K nucleus.


    2. Relevant equations
    Volume of a sphere


    3. The attempt at a solution
    Convert pm to cm: 231 pm = 2.31E-8 cm

    Find number of grams in the whole atom by finding the volume of the atom and mulitplying it by the density: (4/3)(pi)(2.31E-8)^3 * .89 = 4.5953E-23 g

    Radius of nucleus = 1E-4 * 2.31E-8 cm = 2.31E-12 cm

    Volume of nucleus = (4/3)(pi)((2.31E-12)^3) = 5.1632666E-35

    Find density by: 4.5953E-23/5.1632666E-35 = 8.899E11 g/cm^3

    Unfortunately, that doesn't match with the answer given: The answer given is 1.26E12 g/cm^3
    Thanks for any help.
     
    Last edited: Aug 11, 2008
  2. jcsd
  3. Aug 12, 2008 #2
    there is something wrong.

    the "answer" * the volume of nucleus is larger than the total mass of the atom. this can't be.
     
  4. Aug 12, 2008 #3

    HallsofIvy

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    That makes no sense! "Volume" and "mass" are not comparable. It makes no sense to say one is larger than the other!
     
  5. Aug 12, 2008 #4
    I'm sorry, let me clarify. the supposed answer (which is a density) multiplied by the volume of nucleus is larger than the total mass of the atom.

    density times volume gives mass.
     
  6. Aug 12, 2008 #5

    Ygggdrasil

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    2015 Award

    Spheres cannot be packed together w/o leaving empty space, so it's wrong to assume the density of potassium metal is equal to the density of a potassium atom. To get the mass of a 39K atom, just convert 39 amu to grams.
     
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