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Relativistic Calculations for De-Broglie Wavelength

  1. Nov 12, 2015 #1
    1. The problem statement, all variables and given/known data
    At what energy will a non-relativistic calculation of the De Broglie wavelength of an electron be in error by 5%? What is this energy for a proton? Comment on your results.

    2. Relevant equations
    I have two (seemed to be) logical answers for this question, but with different values

    how to resolve this, there must be at least one wrong answer

    i need a resolution



    3. The attempt at a solution
    Solution 1
    Untitled.png
    Solution 2
    Untitled2.png
     
  2. jcsd
  3. Nov 12, 2015 #2

    mfb

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    Staff: Mentor

    The second approach has the right relativistic de-Broglie wavelength. It depends on the momentum, not on "the energy above the rest energy plugged into the nonrelativistic expression".
     
  4. Nov 12, 2015 #3
    As far as i understand, there is nothing in the first approach states that the De-Broglie wavelength depend in anything but the momentum
    in the first approach i replaced the momentum by the kinetic energy, and this is a valid replacement

    please explain your point
     
  5. Nov 13, 2015 #4

    mfb

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    Staff: Mentor

    You replaced momentum by the kinetic energy in nonrelativistic mechanics. It won't give the right result for relativistic speeds.
     
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