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De Broglie wavelength question

  1. Jun 8, 2006 #1
    I have been instructed to calculate the de Broglie wavelength of a proton moving at 1) 2 x 10^4 m/s and 2) 2 x 10^7 m/s

    For the first velocity, the particle is not relativistic, but for the second velocity the particle is.

    can someone explain to me what makes velocity 2 relativistic?
  2. jcsd
  3. Jun 8, 2006 #2


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    Staff Emeritus
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    Its a significant fraction of the speed of light basically. velocity 2 is approx. 7% the speed of light while the first is 0.007%.
  4. Jun 8, 2006 #3
    ah I see, is there a set percentage that makes a velocity relativistic?
  5. Jun 8, 2006 #4


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    To be Truthful, ANY nonzero velocity is relativistic ...
    but the factor gamma (1/sqrt(1-beta^2)) is CLOSE to 1
    for small beta ...
    if beta = v/c = 50 %, for example, then gamma = 1.15 ...
    you might be off by 15% if you calculated non-relativistically.
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