How Many Atomic Diameters Does a Neon Atom Move Between Collisions?

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Homework Statement


The pressure inside a tank of neon is 150 . The temperature is 25C.
how many atomic diameters does a neon atom move between collisions?


Homework Equations



I used the number density N/V=p/KbT and the mean free path equation, where pressure is in pasquals, and tried both that the atomic radius is 0.5 x 10^-10 m and then searched and found that the atomic radius of neon is 3.8 x 10-11 m and am wondering if this is my problem...not understanding the radius/diameter of neon.



The Attempt at a Solution

oops see above, the answer is 61 in the back of the book, but I have not gotten that answer at all. Any help would be super appreciated!
 

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Sure, sorry about that. It's 150 atm, so 1519000 pascals, and then 298 K.

I first determined N/V=P/KbT...the number density is ...3.69x10^27 m-3.

Then using the mean free path equation 1/(4* sqrt2*pi*3.69x10^27m-3*r^2) where r is the radius (from Knight's engineering physics book, but saw on the net that it often in diameter...I'm new at some of this physics so a bit naive about it) where in the book, monatomic gases are 0.5 x 10^-10 m and so I wonder if this is where I'm messing up ...I did try a value of neon's radius of 3.8 x 10^-11 but still didn't come up with the final correct answer?

I get the mean free path to be with knight's radius value as 6.0 x 10^9 m...then divided that by the diameter (2r) to get (okay this is embarrassing because I'm reworking this in my calculator as I type this up and guess what...) I get 60.9 or 61. This is the correct answer. I seriously worked an hour on this simple intro problem and could not get that answer.

Well, thank you for making me redo this!