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BE particle density

  1. Feb 2, 2016 #1
    1. The problem statement, all variables and given/known data
    For the observation of quantum mechanical Bose-Einstein condensation, the interparticle
    distance in a gas of noninteracting atoms must be comparable to the de Broglie
    wavelength, or less. How high a particle density is needed to achieve these conditions
    if the atoms have mass number A = 100 and are at a temperature of 100 nanokelvin?

    2. Relevant equations
    I found on the web that at the critical temp. for BEC, ##\lambda = \sqrt{ \frac{2\pi \hbar^2}{m k_b T}} ##

    I also found a formula for the critical density for BEC at that temp., ##n_c \approx 2.612 \frac{1}{\lambda_{T_c}^3}##

    3. The attempt at a solution
    I took m = particle mass ## \approx 100 \times m_p = 1.67 \times 10^{-25} kg##
    Mechanically plugging the numbers in I got ##\lambda_{T_c} = 3.46 \times 10^{-6} m ##, and ## n_c = 6.3 \times 10^{16} ## particles per ## m^3##

    I'd appreciate if someone could tell me if I am on the right track? The numbers seem OK although I think the ##\lambda## looks high?
     
  2. jcsd
  3. Feb 4, 2016 #2

    DrClaude

    User Avatar

    Staff: Mentor

    The approach is correct. I haven't checked the numbers, but they seem reasonable.
     
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