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Homework Help: Dimensional analysis - quantum and classical lengthscale ratio

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data
    I was supposed to use dimensional analysis to approximate the length scale (in classical and quantum mechanics). The results I got(same as those in the answer sheet): classicaly[tex]l_c≈\frac{e^2}{4πm_ec^2ε_0}≈2.8*10^-15m[/tex] In quantum mechanics[tex]l_q≈\frac{h}{m_ec}≈2.4*10^-12m[/tex]

    2. Relevant equations
    The next question is: how would your analysis in case of [tex]l_q[/tex]have to change if [tex]l_q≈l_c?[/tex]

    3. The attempt at a solution
    I have the answer to question b), but I don't think I understand it. The answer they give is:
    'If[tex]l_q≈l_c[/tex] it would not be possible to estimate l_q without considering electromagnetic effects and write [tex]l_q=f(\frac{l_c}{l_q})[/tex] In fact ratio l_c/l_q is is small (apart from a factor of 2π it is just the fine structure constant).'

    Could anyone please explain or comment on the given answer?
  2. jcsd
  3. Apr 22, 2012 #2
    Could anyone explain why the electromagnetic effects need to be considered and how it influences the ratio?
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