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Question about de broglie wavelengths

  1. Mar 8, 2013 #1
    1. The problem statement, all variables and given/known data
    Assume that the total energy E of an electron greatly exceeds its rest energy E0. If a photon has a wavelength equal to the de Broglie wavelength of the electron, what is the photon’s energy? Repeat the prob- lem assuming E = 2E0 for the electron.

    I need help with the first part of the problem--I included my answer to the second part in case it is relevant to the first.


    2. Relevant equations

    de Broglie wavelength λ=h/p

    E^2 = p^2c^2 + m^2c^4

    E=hf=hc/λ



    3. The attempt at a solution

    Part one of the problem:

    Knowing that E>>Erest, I can use the mass-energy relation to show that E^2 = P^2c^2, such that E=pc. From this I know that p=E/c

    I used this to show that the energy of the photon must be equal to the energy of the electron as follows:

    λelectron = λphoton
    λelectron = h/p = h/(E/c) = hc/Eelectron
    λphoton = hc/Ephoton
    hc/Eelectron = hc/Ephoton ---> Eelectron = Ephoton

    From here all I can see is that there is an infinite number of solutions. I don't understand how to winnow my process down so that it yields only one solution. That said, I don't even know if my process is 100% correct.

    Part two of the problem:
    λ=h/pelectron=hc/Ephoton
    Ephoton=c/pelectron

    E^2 = p^2c^2 + E0^2 = (2Eo)^2 = 4Eo^2
    3Eo^2 = p^2c^c
    p=√3 * (Eo)/c

    such that:
    Ephoton=c/pelectron = c/(√3 * (Eo)/c), all of which are constants that I know the values of and which give me a real answer.

    What say you all about the first part of the problem?
     
  2. jcsd
  3. Mar 8, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    You got the correct, unique solution: Ephoton=Eelectron=E.

    For the second problem, the units in your answer do not match, there has to be some error.
     
  4. Mar 8, 2013 #3
    Ahh thank you very much, I made a writing mistake with the second problem that I corrected in my homework. I didn't realize that the first solution was the solution--again, thanks.
     
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