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De Broglie wavelength of an electron

  1. Mar 4, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the de Broglie wavelength of an 8 MeV proton.


    2. Relevant equations
    y = h/p
    where y is the wavelength
    p = mv
    K = Eo/sqrt(1-v^2/c^2)
    where Eo is the rest mass and K is the kinetic energy


    3. The attempt at a solution
    I make the assumption that "an 8 MeV proton" is an proton with a kinetic energy of 8 MeV.

    I know K = 8 MeV and Eo = 938.3 MeV. So I solve for v, get

    v = sqrt(1 - (Eo/(K+Eo))^2)c = 0.1297554914c

    I know m = 938.3 MeV/c^2. So I plug into p = mv and get

    p = 121749577.6 eV/c

    I know h = 4.136*10^-15 eV*s. So I plug into y = h/p and get

    y = 3.397*10^-23 s*c

    But I want nanometers, so since I know that c has units of m/s, I divide by the numerical value of c and multiply by 10^9 so that

    y = 1.133*10^-22 nm

    But this much too small, isn't it? Where am I going wrong?
     
  2. jcsd
  3. Mar 4, 2010 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    "I know m = 938.3 MeV/c^2. So I plug into p = mv and get

    p = 121749577.6 eV/c"

    I think you left out a "c".

    ehild
     
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