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What am I doing wrong?

  1. Dec 6, 2012 #1
    Hello! I'm solving problems which come with their answers... but I get different results! Can you help me, please?
    The problem statement and equations are in the attached images.

    1. The problem statement, all variables and given/known data
    (Image)
    Also:
    U=energy in Joules
    β=v/c≈1 (relativ. particles)
    μ0=4π×10-7
    2. Relevant equations
    (Image)
    uB=B2/(2μ0), B=magnetic field in Teslas

    3. The attempt at a solution
    (a) Only substitute the values. I obtain -4.05×10-16 W= -2531 eV/s.

    (b) [itex]\frac{(dU/dt)proton}{(dU/dt)electron}[/itex], only the term γ2proton2electron remains and it is equal to (mc2)2proton/(mc2)2electron=2.96×10-7!
    And it yields 1.86×10-8 for α particles. :-s

    (c) Like process in (b), but equating instead of dividing. This gives γproelect, and Uprot/Uelect= (mc2)prot/(mc2)elect = 1.84×103...

    I have spent several hours in problem solving, now I'm tired and sleepy and can't see where is the mistakes(s), please, help!
     

    Attached Files:

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    • 1.png
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  2. jcsd
  3. Dec 6, 2012 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    If you use the classical electron radius re for electrons, you should substitute this for other particles. This should give two additional factors of ##\frac{m_e}{m_p}##.
     
  4. Dec 6, 2012 #3
    Ohhh!!! You're right! I didn't consider that, only took the given value for σT...:blushing:
    Thanks!!!!!!!!
     
  5. Dec 6, 2012 #4
    Wait... How to obtain m_p from r_p (or viceversa) if don't know density?
    I found already values for r_p and r_α, ~10^-16,-15 m, but I would like how to deduce them. Substitute p & α parameters into expression for r_e gives me radius ~10^-37!
     
    Last edited: Dec 6, 2012
  6. Dec 6, 2012 #5

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    The classical radius (as calculated with the electromagnetic field energy) is proportional to the inverse mass.
    Classical electron radius
     
  7. Dec 6, 2012 #6
    Thanks, I have the value of class. e- radius, r_e= 2.818e-15, rather I need right values for radii of proton and alpha particles, because those I found are... odd:
    r_p=2.1e-16
    r_α=2.1e-15
    How can be possible r_p<r_e?!
    Another founded value for r_p is 8.6e-16, and r_alpha =4r_p...

    I've tried to calculate them from formulae in http://en.wikipedia.org/wiki/Thomson_scattering and http://en.wikipedia.org/wiki/Classical_electron_radius:

    http://upload.wikimedia.org/math/f/1/9/f196c5b29b4e0fed8f4710bedc522016.png & http://upload.wikimedia.org/math/5/3/d/53dc80a0e75009917114d545c93fc0a4.png=mc^2 without the factor 1/2, as it is said there... and I got 4.51E-034 for r_e & 8.72E-061 for sigma_T! :'(

    I am increasingly confused!:( HEEEEEEELP!!!!
     
    Last edited: Dec 6, 2012
  8. Dec 6, 2012 #7
    Oh, I have it!, I have it! other factors are eliminated leaving only masses quotint^4!
     
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