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Relativistic De Broglie wavelength

  1. Mar 16, 2009 #1
    1. The problem statement, all variables and given/known data
    De Broglie wavelength

    What is the De Broglie wavelength of the 1.0-TeV (1TeV=1012eV)
    protons (mpc2=938.3MeV) accelerated at the Fermilab Tevatron
    accelerator? These high-energy protons are needed to probe
    elementary particles [Hint: You need to use relativistic formula, but
    consider potential simplification].

    2. Relevant equations

    λ = h / p
    λ = h /(mv*gamma)
    hc = 1240 eV

    3. The attempt at a solution

    Using the relativistic form i then squared both sides to get λ2 = (h2 /(mv)2)(1-v2/c2)

    From there i multiplied the two and multiplied by c2/c2 to get λ2 = (hc)2 /((mv2)(mc2)) - (hc)2 /((mc2)2)

    I got stuck after that and not sure if i am doing it right i was thinking the mv2 could be the kinetic energy after multiplying by 1/2. λ2 = (hc)2 /2(((1/2)mv2)(mc2)) - (hc)2 /((mc2)2)and that the 1TeV is Kinetic Energy but that gives a negative number
    Last edited: Mar 16, 2009
  2. jcsd
  3. Mar 16, 2009 #2
    The easy equations to use here are

    p = h / lambda

    and E^2 = ( p * c )^2 + ( m c^2 )^2

    you're pretty much done at that point
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