# Finding atomic diameter from molecular diffusion proportionality

1. Apr 9, 2013

### ProPatto16

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. Apr 9, 2013

### 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.

3. Apr 9, 2013

### ProPatto16

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...

4. Apr 9, 2013

### ProPatto16

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..

5. Apr 10, 2013

### 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.