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De Broglie wavelength of nitrogen molecules

  1. Apr 7, 2015 #1
    1. The problem statement, all variables and given/known data
    According to statistical mechanics, the average kinetic energy of a particle at temperature T is 3kT/2, where k is the Boltzmann constant. What is the average de Broglie wavelength of nitrogen molecules at room temperature?

    2. Relevant equations
    KE = 3kt/2 = p2/2m
    λ = h / p

    3. The attempt at a solution
    So p = (2KEm)1/2, and inserting KE = 3kt/2
    p = (3kTm)1/2

    And thus λ = h/p = h / (3kTm)1/2

    The only problem I have is that it seems like the units don't work out.
    Inserting the units only into h / (3kTm)1/2 :

    (kg m2 /s2)/((m2 kg/s2 K)(K)(kg))1/2 =
    (kg m2 /s2)/(m kg/s) =
    m/s, not m

    Am I simplifying the units wrong or is the equation wrong?
     
  2. jcsd
  3. Apr 7, 2015 #2

    TSny

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    Homework Helper
    Gold Member

    Your units for h are not quite correct.
     
  4. Apr 7, 2015 #3
    Ah I see its kg m2 / s. Thanks!
     
  5. Apr 7, 2015 #4
    I'm having another problem. When I plug the values in where h = 1.602177x10-11 kg m2/s, k = 1.3806488 x 10-23 m2 kg/s2 K, T = 293.15 K, and m = 4.651734 x 10-26 kg/molecule

    I get 6.741 x 1011 m when the answer in the book is 0.0276 nm. I'm obviously doing something very wrong.

    EDIT: Oop wrong value for h, that explains why several of my answers to different questions were wrong hehe nevermind
     
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