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Broglie wavelength - calculate electric potential difference

  1. Jul 26, 2013 #1
    1. The problem statement, all variables and given/known data
    In a TV tube, an electric potential difference accelerates electrons from a rest position towards a screen. Just before striking the screen, the electrons have a wavelength of [itex]1.0 x 10^{-11} m [/itex]. Find the electric potential difference.


    2. Relevant equations
    [itex]λ = h/mv [/itex]
    [itex] ΔE_k = qΔV [/itex]


    3. The attempt at a solution
    [itex] v = h/λm = (6.63x10^{-34}Js)/(1.0x10^{-11}m)(9.11x10^{-31})[/itex]
    [itex] = 7.3 x 10^7 m/s[/itex]
    I rearranged the second equation to solve for ΔV
    [itex] ΔV = ((1/2)(9.11x10^{-31}kg)(7.3x10^7m/s))/(1.60 x 10^-19c)[/itex]
    [itex] = 2.1 x 10^{-4} V[/itex]

    I was just wondering if someone could let me know if I'm doing this right? Sorry for not using latex properly, I'm not really sure how to make fractions.
     
    Last edited: Jul 26, 2013
  2. jcsd
  3. Jul 26, 2013 #2

    TSny

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    Homework Helper
    Gold Member

    Hello.

    Your method looks good. But you need to check your calculation of the kinetic energy of the electron.
     
  4. Jul 26, 2013 #3
    Units

    Another good way to see that your calculation went awry is to check your units instead of just writing Volts as the units for the answer.

    kg*(m/s)/C are the units on your product in the final line of your calculation before the answer. But Volts are J/C

    We know that a Joule is not a kg*m/s, but should be a kg*m2/s2.

    Hope this helps.

    Dr Peter Vaughan
    BASIS Peoria Physics
     
  5. Jul 26, 2013 #4
    Ah thank you both very much. I wrote down the 1/2mv^2 in my actual work but forgot to do the calculation.

    Thank you:)
     
  6. Jul 26, 2013 #5

    TSny

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    Gold Member

    Good work!

    Note that you got a speed of the electron that is about 24% the speed of light. This is encroaching on the domain of relativity. But your non-relativistic answer is accurate to within 2% error.
     
    Last edited: Jul 26, 2013
  7. Nov 17, 2017 #6
    i think for the Ek formula should be 1/2mv^2 and seems you missed the to square the 7.3E7m/s
     
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