bluejay27 20161222 22:12:03  Air is obviously less dense than the atomic radius 10^{10}?? What does this mean?  
Bacon 20120927 18:18:32  Number density = # atoms per volume (or N/V). From ideal gas law PV=NkT we get N/V = P/kT.
The cross section is pi*r^2. One should know the radius of an atom is on the order of one angstrom, so say r = 10^10. Therefore, the cross section (call it A) is A = pi*10^20, or just 10^20.
As for the number density N/V = P/kT, plug in standard pressure/temp values (10^5 Pa and 300 K), combine it with the above area, and you'll get very close to the answer.  
wittensdog 20091016 16:34:27  I think the best strategy, if you want to do the numbers, having looked at all of the comments below, is to use two facts:
1.) an ideal gas takes up about 22.4 liters at normal room conditions
2.) a cubic meter is 1,000 liters
and then use a radius on the order of the Bohr radius. The first two pieces of information, when combined, say the number density should be about 3*10^25 for every cubic meter. Taking the Bohr radius as the radius of our molecules (which is kind of close), we get a cross sectional area of about 2.5 * pi * 10 ^ 21. Multiplying this and inverting gives on the order of (1/2) * 10^8 , so we should choose B.
Having said that, I think it would be better to consider two things:
1.) the mean free path cannot be on the order of the Bohr radius or lower, because then the spacing between atoms would be on the order of their size, and we would be starting to end up with a quantum gas, far removed from how air behaves at normal room conditions
2.) the mean free path of air molecules should not start approaching the macroscopic range
This rules out everything except for B, and is pretty much what the original solution says.
I think the most important moral here to remember is that the characteristic spacing between air molecules is about 1,000 times larger than their characteristic size.  
gotfork 20080712 15:28:34  Again, just pointing out that the ohio state site cites this one as a source...  
bkardon 20070930 09:19:42  Here's how one might solve the problem:
Assuming air is an ideal gas,
since represents the molar density of the gas,
represents the number density, with being Avogadro's number:
using room conditions,
as given on the equation sheet
Once you approximate your way through the math, you arrive at
We can approximate the cross section of air molecules as , or , so the mean free path is found to be
This answer is closest to , so we can choose answer B.  
Richard 20070926 12:59:02  The diameter of an air molecule is ~
The number density of air is ~
So I guess you choose (B).  
Richard 20070926 12:31:26  Has anyone heard the Fermi atomic bomb story?
...these problems are appropriately called "Fermi Problems."  
warisit 20070724 19:27:20  What about this?
The density of air is
(6.02 * 10^23 # ) / (22.4 * 10^(3) m^2 )
and,
assuming the size of 1 molecule is about 1nm,
the collision cross section is 1nm^2
Putting this value into the equation gives the answer
~10^(7) m
 
RootMeanSquare 20061119 02:15:33  Common sense might require some time that we don\'t have in the exam, so...:
If you remember and the mol volume 22.4 litres, you end up with a number density of rougly . With a guessed molecule radius of a little more than twice the atomic radius of (hint: guessing helps here:)) you end up with , which gets you right to solution (B)  
RootMeanSquare 20061119 02:06:51   
scottopoly 20061103 15:44:48  I was going to recommend this site:
http://www.physics.ohiostate.edu/undergrad/ugs_gre.php />
but apparently Yosun has been copying solutions from there....
gotfork 20080712 15:21:15 
Wrong. The solutions there cite her site as the source.

sirius 20081106 22:25:49 
I'm pretty sure it's the other way around.

athithi 20091209 23:16:57 
its other way...they are copying from this website...just check properly..

Crandor 20100409 19:27:22 
Other way around.

dinoco 20101101 07:46:38 
I think that it was a joke.

 
radicaltyro 20061102 17:31:06  Apparently I don't have any common sense. Anyone with a real solution?
ali8 20110718 05:25:19 
Neither do I.

 