Feynman Lectures exercises problem 1.9

[CalebB-M]

Homework Statement

The density of air is given as .001g/cm^-3 and the density of liquid air 1g/cm^-3
A.) Estimate the number of air molecules per cm^3
B.) Estimate the Mass of a single molecule.
C.) Estimate the average distance L an air molecule should travel between collisions at normal temperature and pressure (20c and 1atm) "mean free path"
D.) Estimate at what pressure P in normal atmosphere a vacuum system should be operated under so that L = 1 meter.
That is all given data.

Homework Equations

None were given at all in the book or referenced in the Feynman lectures themselves. This is what caused most of my confusion as I simply don't know some of what is asked.

The Attempt at a Solution

A.) I used the average molar mass of air and 15*1avagadros number to estimate the number of molecules in the 1cm^3. But my answer was 2*10^19 wheras the book gives the answer as 10^19, I am not sure where I could have gotten my answer off by a factor of two. .001g/cm^-3 * (6.022*10^23)/(28g/mole) = aprox 2.15*10^19

B.) This one confused me as i used it to calculate the first one, but still that lead to me getting 4*10^-23 g simply dividing the .001g/cm^3 by #of atoms from a per cm^3 the cm^3 cancel leaving .001g/(#of atoms)
C.) This one I'm confused on how to even start. I literally have lost it I tried thinking about how I could get a unit of length from the values I had been given, but I haven't remotely begun to understand it. I tried imagining that i had a 1cm^3 box and there are #number of atoms whirling around randomly in the box. But i still have hit a road block and could use some pointers.
D.) Havent gotten to this problem yet.

Notes:
The book exercises for the Feynman lectures has really challenging problems, but studying all by myself and not within a classroom environment makes it impossible to ask questions or get clarification. I am alone in this endeavor, maybe someone on the forum could do them with me?

 

[TSny]

It could be that you are meant to estimate the answers only to the nearest power of 10. This is called an "order of magnitude estimate". So, you wouldn't worry about a factor of 2.

In lecture 1 Feynman does give you the approximate size of an atom. From that and the densities of liquid air and gaseous air, you can estimate the number of molecules per cm³ in gaseous air.

Likewise you can estimate (B) based on the density of liquid air and the approximate size of an atom.

I do think that (C) is a challenging question. There is an elementary way to estimate the answer, but I bet very few beginning students would be able to come up with it on their own based solely on the information in the first lecture (unless I overlooked something in skimming the lecture).

Spoiler

http://hyperphysics.phy-astr.gsu.edu/hbase/Kinetic/menfre.html

(D) can be answered from (C) and information given in the lecture concerning the relation between pressure and density of a gas.

 

[CalebB-M]

I'm finding it very difficult haha. But at the same time I'm heavily enjoying the challenge. I intend on going through all of the Feynman problems, but in all honesty I'm not the best student. I plan on working more on the problems in a few days with a fresh mind and some helpful hints from your reply.

I will probably start posting regularly asking questions.

 

[TSny]

OK. Sounds good.