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Equation used to find kinetic energy of proton

  1. May 17, 2015 #1
    I am having trouble deciding when to use which equation.

    If you're given the wavelength of a proton, let's say 100 fm, and have to find the kinetic energy of it, how would you do this?

    Here are my ideas:

    Idea 1: Use lambda = h/p, where p = sqrt(2Em).

    Idea 2: Use E=(pc)^2+(mc^2)^2 = (mc^2)^2+(h/lambda * c)^2

    Then I'll use:

    K = E- E_o
    ==> (answer from idea 1 or 2) - mc^2


    Which should I use? I personally think idea 2 is correct because it accounts for the relativisitic effects.

    thank you!
     
  2. jcsd
  3. May 17, 2015 #2
    In your idea 1 you've already given the wavelength to momentum relationship---and you're given the wavelength. That's all you need.

    Edit: looks like I misread the question......
     
    Last edited: May 17, 2015
  4. May 17, 2015 #3
    but is the equation correct?
    I actually forgot how I got p = sqrt(2Em)...I think I derived it earlier in my work.

    Also I asked my friend who is learning this in school and he said that you have to use idea 2 because it is a particle?
     
  5. May 17, 2015 #4

    jtbell

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    Staff: Mentor

    The relativistic equation is correct in general. Your method 1 is basically non-relativistic, so it's "correct enough" only for low-energy (low-velocity) particles. But it's hard to tell in advance whether the velocity is "low enough" unless you have a lot of experience in doing these kinds of problems. So I would go with your method 2. If you have time, try method 1 also and see how close together the results are.
     
  6. May 17, 2015 #5

    jtbell

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    Staff: Mentor

    Hint: start with the non-relativistic formulas for momentum and kinetic energy, p = mv and E = (1/2)mv2.
     
  7. May 17, 2015 #6
    Thank you everyone! My answer using method 2 was actually 1000 times larger than the answer using method 1. I guess you have to take into account relativity!
     
  8. May 17, 2015 #7

    jtbell

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    Staff: Mentor

    I suggest that you check your calculations and particularly your units carefully. My results for the two methods differ by only about 0.004%.

    As a check, calculate the proton's speed assuming the classical formula. What % is it of the speed of light?
     
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