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Homework Help: Calculating Vrms of a neutron

  1. Apr 25, 2013 #1
    1. The problem statement, all variables and given/known data

    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

    2. Relevant 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.

    3. 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 ??
    Last edited: Apr 25, 2013
  2. jcsd
  3. Apr 25, 2013 #2


    User Avatar

    Staff: Mentor

    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 :smile:
  4. Apr 25, 2013 #3


    User Avatar

    Staff: Mentor

    Reading more carefully, I don't understand why you need to know the molar mass of neutrons. Your units are not consistent, as in
    m should be in units of mass, kg, not in kg/mol.
  5. Apr 25, 2013 #4
    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
    Last edited: Apr 25, 2013
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