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Calculating the Bose-Einstein Condensation Temperature

  1. Mar 6, 2012 #1
    1. The problem statement, all variables and given/known data
    Estimate the Bose-Einstein condensation temperature of Rb 87 atoms with density of 10^11 atoms per cm^3.


    2. Relevant equations
    [itex]T=\frac{n^{2/3}h^{2}}{3mK_{B}}[/itex]


    3. The attempt at a solution
    This should be just a standard plug and chug question, but my answers are not even close to reasonable! I would expect to get anywhere from 500nK to 50nK for an answer, but I am getting thousands of Kelvin! Are my units wrong? I am using Boltzman constant with units of [itex]eV\bullet K^{-1}[/itex] and Plank's with units of [itex]eV\bullet s[/itex].
    Then I am using the density in Atoms per m^3 and the mass of a single Rb 87 atom in Kg.
    Am I missing something here with units? That is the only thing I can think is wrong.
     
  2. jcsd
  3. Mar 6, 2012 #2
    At first glance I would use joules (Nxm) instead of eV since since other units are SI...
     
  4. Mar 6, 2012 #3
    But since the plank constant is on the top and Boltzman on the bottom, the converting factor of eV to joules (1.6x10^-19) would cancel out anyway, so whether it's in eV or Joules should not matter.
     
  5. Mar 6, 2012 #4
    Actually, that IS the problem! I think you are correct, Bloby. Because the Plank constant is squared on the top, so there is still another 1.6x10^-19 to factor in there! I will give it a shot and see what I get for an answer!

    ****
    It Worked! Thank you Bloby! Final answer was 16nK, which seems pretty reasonable to me for a Bose-Einstein Condensate.
     
    Last edited: Mar 6, 2012
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