# Exercises for the Feyman Lectures on Physics: How can I calculate diameter of a molecule ?

Homework Statement:
How can I calculate diameter of a molecule
Relevant Equations:
none
How can I calculate diameter of a molecule

BvU
Homework Helper
find a relationship between something with a known number of molecules and its volume

thanks, but the issue is that I dont have the number of molecules because I thats the answer of the problem

hutchphd
Homework Helper
perhaps you should state the entire problem rather than us playing "twenty questions".....?

DaveE and BvU
ok,sorry...

hutchphd
About 1860 Maxwell sowed that the viscosity of a gas is given by η=ρνι where ρ iπs density ν mean velocity and ι mean free path.The latter quantity he had earlier shown to be ι = 1/(square root of 2)(π)(Ng)(d2)where d is diameter of a molecule.Loshmidt(1865)used the measured value of η,p(gas) and p(solid) together with Joules calculation of ν to determine Ng the number of molecules per cm3 in a gas at STP(1atm 0°C).He assumed the molecules to be hard spheres tightly ppacked ina solid.Given η = 2*10^-4 cm^-1 s^-1 for air at STP ρ(liquid)≈ 1 g cm^-3 p(gas)≈1*10^-3 g cm-3 ,and ν≈ 500 m/s-1. Calculate Ng(number of molecules)

BvU
Homework Helper
So, what are you missing ?

the diameter of the molecule

BvU
Homework Helper
He assumed the molecules to be hard spheres tightly ppacked ina solid
How are you going to use this ?

DaveE
Gold Member
Why do you think they gave you two density values, one for liquid, and one for gas?

i know because it it tighly packed the density of liquid and solid are very similar

DaveE
Gold Member
yes, so how can you use that information?

in the problem has a sentence that said "Loshmidt(1865)used the measured value of η,p(gas) and p(solid) together with Joules calculation of ν to determine Ng the number of molecules per cm3 in a gas at STP(1atm 0°C)".

hello?

DaveE
Gold Member
So your problem is to find d, and clearly that has something to do with the densities given, which are for air. Would the answer be different for H2 instead of air?

Notice that the density given includes mass (g) in the dimensions, but mass doesn't appear anywhere else in the equations. This needs to be resolved somehow with external information.

Also note that there is a typo as presented you (or they) have mixed up the gas density and the liquid density in the problem. Easy to resolve though, use the larger one for liquids, the smaller one for gas.

new90
DaveE
Gold Member
Here's a related problem that may help:
A 1 cm x 1cm x 1cm cube of Aluminum has a density of 2.70 g/cm3. How many Al atoms are there in the cube? How far apart are they?

Here's a related problem that may help:
A 1 cm x 1cm x 1cm cube of Aluminum has a density of 2.70 g/cm3. How many Al atoms are there in the cube? How far apart are they?

I dont know how to get the Al atoms

DaveE
Gold Member
OK, a 1cm x 1cm x 1cm cube has a volume of 1 cm3. With a density of 2.70 g/cm3, this means there are 2.70 g of Al in the cube. So, how many Al atoms weight 2.70 g? What information do you need to get to solve this problem? Where/how will you get it?

Then, when you find out how many atoms there are. How far apart are they (center to center, since they will be touching each other)? Imagine carefully placing tennis balls inside a big box to get as many as possible inside.

Finally, for the original problem, you will need to know that air is composed of 80% N2 and 20% O2. A N2 molecule weighs twice as much as a N atom.

thnaks for the help we solve it

DaveE
Gold Member
Congratulations, good work!