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Question about De Broglie's laws

  1. Nov 20, 2011 #1
    1. The problem statement, all variables and given/known data
    Find the wavelength of an electron which is travelling at 4.35*10^6 m/s.

    2. Relevant equations
    p = h/λ
    p = mv
    E = hf
    E = 1/2mv^2

    3. The attempt at a solution
    I know this can be easily solved using the momentum equation and De Broglie's law like this:
    mv = h/λ
    (9.109*10^-31)*(4.35*10^6)=(6.626*10^-34)*λ
    λ ≈ 0.167nm

    But here comes the actual question...
    Why can't I solve this with the second law E = hf and the classical 1/2mv^2?
    1/2mv^2 = hf, where f = (c/λ)
    This gives me an incorrect result. If I wanted to use kinetic energy, I would have to first convert it to momentum
    p = √(2Em), which I would use with p = h/λ.

    After all, for instance the photoelectric effect can be calculated using kinetic energy with hf-W.
    I think I've missed something relevant, and I can't seem to find the answer. Sorry if this is too obvious.
     
  2. jcsd
  3. Nov 20, 2011 #2
    It is giving the correct result : 1.6722e-010 = 0.16722 nm.
    What result are you getting?
     
  4. Nov 20, 2011 #3
    If you are using the following equation:

    "1/2mv^2 = hf, where f = (c/λ)"

    then it is incorrect because f ≠ c/λ, it is f = v/λ i.e.the velocity of the electron, not that of light.
     
  5. Nov 20, 2011 #4
    You are on the right tracks.
    In the early days of this work it was realised that the energy of a light photon was given
    by E = hf (from photoelectric effect).
    DeBroglies hypothesis was to equate Einstein's E = mc^2 with hf
    So his hypothesis was that mc^2 = hf
    which becomes mc = h/λ
    De Broglie (controversially) said that this was a general relationship and since m x c looks like
    'momentum' he produced his equation momentum =h/λ
    ie mv = h/λ

    Simple algebra but remarkable that it is true.
     
  6. Nov 20, 2011 #5
    It makes more sense now. I guess I was all the time applying the energy of a photon, not an electron. Thank you, now I can sleep restfully at night.
     
  7. Nov 20, 2011 #6
    De Broglie was a strange character!!! When he came up with his hypothesis, as part of his thesis, his professor did not think much of it and showed it to Einstein.
    Einstein accepted the thesis completely !!!!
    There but for fortune......
    Sleep tight
     
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