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Wavelength of an electron homework

  1. Jun 9, 2009 #1
    1. The problem statement, all variables and given/known data

    -Electron has 3.00 MeV (or 4.8*10^-13 Joules)
    -it's relativistic
    -finding λ.

    2. Relevant equations

    h=6.63*10^-34

    λ=h/p (obviously)

    And I'm not sure if they're needed, but the relativistic eq's are:

    KE = mc^2/sqrt(1-(v/c)^2)
    p = mv/sqrt(1-(v/c)^2)

    I'm not sure if this one applies to relativistic speeds:

    E = hc/λ

    3. The attempt at a solution

    Attempt 1:

    E = hc/λ

    4.8E-13 = (6.63E-34)(3E8)/λ
    λ = (6.63E-34)(3E8)/(4.8E-13)
    λ = 4.14E-13 m

    BUT answer key says 3.58E-13

    If you could help, that would be great.
    Sorry if it's too long, and I'm a little unfamiliar with relativistic eqn's so forgive me if I screwed up on them.
     
  2. jcsd
  3. Jun 9, 2009 #2

    diazona

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    Homework Helper

    The equation you used, [itex]E = hc/\lambda[/itex], only applies to photons (or massless particles in general). So you're not going to need that one here. If you're familiar with the equation
    [tex]E^2 = p^2c^2 + m^2c^4[/tex]
    I'd use that. If not, you can get the velocity from
    [tex]E = \frac{mc^2}{\sqrt{1 - v^2/c^2}}[/tex]
    (note that that's total energy, not kinetic energy) and compute the momentum from that.
     
  4. Jun 10, 2009 #3
    Thanks very much for the help.
     
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