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De Broglie Wavelength

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data
    Show that the de Broglie wavelength of a particle of mass m and kinetic energy KE is given by

    [tex]\lambda = \frac{hc}{\sqrt{KE(KE + 2mc^2)}}[/tex]



    2. Relevant equations



    3. The attempt at a solution
    I know:

    [tex]KE = {\gamma}mc^2 - mc^2 = pc - mc^2[/tex]

    But from here I am lost. I have a hunch that I need to use the equation that equates Energy and Momentum, but I'm lost.
     
    Last edited: Sep 19, 2010
  2. jcsd
  3. Sep 19, 2010 #2
    The problem is that your equation only applies to the relativistic limit, in general
    [tex]
    E_k = \sqrt{(pc)^2 + (mc^2)^2} - mc^2
    [/tex]
    Try using that.
     
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