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Unique λ at which X-ray and electron have same energy

  1. Sep 21, 2008 #1
    1. The problem statement, all variables and given/known data
    This is from Advanced Physics by Adams and Allday. Spread 8.34, Q 4.

    Derive an equation to show that there is a unique wavelength at which X-ray photons and electrons have the same energy. Calculate this wavelength and energy.

    2. Relevant equations
    For photons: E = hf = h c / λ

    For electrons:
    λ = h / p (de Broglie)
    K.E. = ½ mv^2
    p = mv

    3. The attempt at a solution
    p = √(2mE)
    Substituting in de Broglie
    λ = h / √(2mE)
    E = h^2 / 2mλ^2

    Equating energies
    (h c / λ)X-ray = (h^2 / 2mλ^2)electron
    Separating out the constants c, h, 2 and m (where m is the rest mass of an electron)
    (λ)X-ray = (h / 2cm) * (λ^2)electron

    ... which does not have a unique solution :-(
    Last edited: Sep 21, 2008
  2. jcsd
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