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Finding Electron Speed and Wavelength

  1. Jun 11, 2010 #1
    1. The problem statement, all variables and given/known data
    The wavelength of an electron is 4.4 × 10−7 m.
    How fast is it moving? The Planck’s con-
    stant is 6.62607 × 10−34 J · s .
    Answer in units of m/s.
    013 (part 2 of 2) 10.0 points
    If the electron has a speed of 9 × 106 m/s,
    what is its wavelength?
    Answer in units of m.


    2. Relevant equations
    Thats what I need help on.


    3. The attempt at a solution
    I tried E = hc / λ
    Then E = 1/2mv^2

    But that didnt work. Any ideas? Thanks
     
  2. jcsd
  3. Jun 11, 2010 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Use the de Broglie relation between momentum p and wavelength λ:

    λ=h/p.

    ehild
     
  4. Jun 12, 2010 #3
    OK you're not too far off the right method so that's good :smile:

    So these are the things you already know:

    Planck's Constant: [itex]h=6.62607\times 10^{-34} J s^{-1} [/itex]

    Electron Wavelength: [itex]\lambda_{e} = 4.4\times 10^{-7} m[/itex]

    For the first part you need to find the velocity of the electron.

    As ehild said you should use the de-Broglie relation for the wavelength of an electron, which is:

    [tex]\lambda = \frac{h}{p}[/tex]

    You can just quickly look up the mass of an electron (if you can't remember it) and then you know everything you need to know in order to calculate the speed of the electron, through inputting the values and rearranging the equation.

    For the second part you are now given the electron speed and need to find wavelength. This is a similar method just slightly different.

    So now you know:

    Electron Speed: [itex]v = 9\times 10^{6}ms^{-1}[/itex]

    Again you can use the de-Broglie relation, just rearrange it as required, input values, and there you go. :biggrin:
     
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