Calculating Vrms of a neutron

[johns123]

Homework Statement

The equation for the "average" velocity of a gas molecule
in a closed container is:

Vrms = ( 3 x k x T / m )^ 1/2 where

k = 1.38 x 10 ^ 23 Joules/K

T is temp in Kelvin

m = mass per ion in kg = Atomic Mass M / Avagadro's Number Na

so for N2, I can calculate m = (28 grams/mole) / 6.02 x 10^23 ions/mole

and get m = 4.65 x 10^-23 grams/ ION , which I change to 4.65 x 10^-26 kg/ION

Homework Equations

Vrms = ( 3kT/m)^1/2

I read the 28 grams/mole from the Atomic Table. ( 14 + 14 for N2 ).

And I realize that m must be in kg because of the units of k.

The Attempt at a Solution

( trying to edit out some errors here )

Now, I'm given the problem of calculating Vrms of a neutron
in the core of a reactor at 400K. I looked up the mass of
the neutron on-line and got 1.675 x 10^-27 kg .. OK, fine!

But I can't use that for Atomic Mass M. Instead the proper M = 1.0 x 10^-3 kg/mole

And the lab book uses the formual Vrms = ( 3k Na T )/ M )^1/2 where

m = M / Na .. atomic weight / Avagadro's number

This must be an elementary question, but why is M = 10^-3 kg/mole
for the neutron ? .. as used in the book ? What is a mole
of neutrons ??

 

[DrClaude]

Now, I'm given the problem of calculating Vrms of a neutron
in the core of a reactor at 400K. I looked up the mass of
the neutron on-line and got 1.675 x 10^-27 kg .. OK, fine!

But I can't use that for m. Instead the proper m = 1.0 x 10^-3 kg/mole

This must be an elementary question, but why is m = 10^-3 kg/mole
for the neutron ? .. as used in the book ? What is a mole
of neutrons ??

A mole of anything is Avogadro's number $N_\mathrm{A} = 6.022141 \times 10^{23}$ units of that thing. Therefore, 1 mole of neutrons is $6.022141 \times 10^{23}$ neutrons. I'll let you figure out the mass of that

 

[DrClaude]

Reading more carefully, I don't understand why you need to know the molar mass of neutrons. Your units are not consistent, as in

so for N2, I can calculate m = (28 grams/mole) / 6.02 x 10^23 ions/mole

and get m = 4.65 x 10^-23 grams/ mole , which I change to 4.65 x 10^-26 kg/mole

m should be in units of mass, kg, not in kg/mol.

 

[johns123]

I just reedited the problem above. Hope the errors are gone!

My mistake. I meant m = 4.65 x 10^-23 grams/ion which I have to change to kg/ion. Also, I'm reading online at Yahoo that the problem should have specified a gas like Li where I could calculate Kg/mole of Li; go to kg/ion of Li, and then realize that Li has a few neutrons per atom .. and THAT would give kg/mole of neutrons which I could reduce to m = M/Na for that number of neutrons in 1 mole of Li.. That is really chasing me in circles trying to completely understand it.. And the problems coming after are the same, but for electrons and protons. I think I better get a grasp on the neutrons first. Thanks

 

[Nickie]

I understand your confusion about the value of M for a neutron. The reason for this discrepancy is due to the fact that the concept of a "mole" is not applicable to individual particles like neutrons. The mole is a unit used to quantify the amount of a substance, typically in terms of the number of particles. For example, one mole of a substance contains Avogadro's number (6.02 x 10^23) of particles. However, since a neutron is an individual particle, it does not make sense to talk about a mole of neutrons.

In this case, the value of M that is used in the equation is the atomic mass of the neutron, which is 1.0 x 10^-3 kg/mole. This value is used to convert the temperature (in Kelvin) to a unit that is appropriate for the calculation of Vrms. This is because the units for k (Joules/K) and T (Kelvin) must match in order for the equation to be valid.

I hope this explanation helps clarify the use of M in the equation. Keep up the good work in your studies!