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Calculating Spacing Using Ideal Gas Law

  1. Apr 26, 2005 #1
    Here's the question:

    For what temperatures are the atoms in an ideal gas at pressure [itex] P [/itex] quantum mechanical?

    Hint: Use the idea gas law
    [tex]
    PV = N k_B T
    [/tex]
    to deduce the interatomic spacing.

    Answer:
    [tex]
    T < \left( \frac{1}_{k_B} \right) \left( \frac{h^2}_{3m} \right)^{\left( \frac{3}_{5} \right)} \left( P^\frac{2}_{5} \right)
    [/tex]

    -------------

    Now, I have been given the formula for the typical de Broglie wavelength:

    [tex]
    \lambda = \frac{h}_{\sqrt{3 m k_B T}}
    [/tex]

    Further, I know I am trying to determine when
    [tex]
    \lambda > d
    [/tex]
    where d is the interatomic spacing.

    However, what I don't understand is how I can calculate a value for d given the idea gas law in the question. Any ideas?
     
  2. jcsd
  3. Apr 27, 2005 #2
    More generally, is there some approach that can be used to calculate the interatomic spacing using the ideal gas law outside of the quantum mechanics context?
     
  4. Apr 27, 2005 #3

    krab

    User Avatar
    Science Advisor

    Just use [itex]d=V^{1/3}[/itex]. Doesn't that make sense to you?
     
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