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Homework Help: Finding atomic diameter from molecular diffusion proportionality

  1. Apr 9, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the diameter of one atom of argon given that Dp = 2 where D is diffusion and p is pressure.

    3. The attempt at a solution

    molar mass of argon is 40g/mol
    using that for one atom can find mass in kgs.
    but thats its!

    im not given V, T or p. can put V in terms of d so that gives me one. need 2 so i can solve for the last one.

    the relevant equation seems to be
    $$Dp=\frac{1}{\pi d^3\sqrt{m}}(\frac{2kT}{\pi})^\frac{3}{2}$$

    good luck finding d.
  2. jcsd
  3. Apr 9, 2013 #2


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    Staff: Mentor

    The diffusion constant has units m^2/s, pressure has units N/m^2 = kg /(m s^2). The product of both cannot be a dimensionless number ("2").
    I think there is something missing here.

    Unrelated: if you just need T, room temperature is a good value.
  4. Apr 9, 2013 #3
    It's not a constant. Diffusion D and pressure p are inversely proportional. The info I'm given is as pressure increases the product of diffusion and pressure is 2. So the 2 is the x in D=x/p hence dimensionless. I'm fairly sure that this means T is constant.
    Sorry probably a poor worded question.
    Given a figure of a graph of Dp vs p for argon and it's a line parallel to x-axis with the value 2.
    Question says find diameter of argon. So I don't have particular values for p and D either...
  5. Apr 9, 2013 #4
    Hmm but I see what you mean... It still needs units... But even then with units it won't make a difference.

    And I think there's something missing too.

    And I actually have the answer as d=3.1*10^-10m out of the book but that corresponds to a T of about 330K
    but there's no way to find T with the info given..
  6. Apr 10, 2013 #5


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    Staff: Mentor

    Is that the full, exact problem statement?
    If yes, I think you really have to assume that it happens at room temperature, and I still doubt that the units match.
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