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Particle decays

  1. Jun 4, 2009 #1
    1. The problem statement, all variables and given/known data
    a neutral kaon at rest decays to pion- and pion+ , if kaon rest mass is 497.7MeV/c^2, and the pions rest mass is 139.6MeV/c^2, what are the kinetic energies of the resulting pions?

    Im very stuck with this, and not sure where to start, how can i find Ek of pions, if i dont know their velocities? ive searched thorugh my textbook but can find any similar examples, please someone help.
     
  2. jcsd
  3. Jun 4, 2009 #2

    Cyosis

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    Use conservation of energy and momentum.
     
  4. Jun 4, 2009 #3

    malawi_glenn

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    and conservation of momentum.

    What are the relation between momentum and kinetic energy in relativistic dynamics?
     
  5. Jun 4, 2009 #4
    i dont need to use invarient mass E^2=(pc)^2+(mc^2)^2?
     
  6. Jun 4, 2009 #5

    Cyosis

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    Just write down the conservation equations in terms of [itex]E_0=mc^2, \; E=\gamma mc^2, \; T=(\gamma-1)mc^2[/itex].
     
  7. Jun 4, 2009 #6

    malawi_glenn

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    maybe, there are several ways to do this, i would just to what Cyosis suggested.
     
  8. Jun 4, 2009 #7
    so Ef=E1+E2=497.7MeV=.5mv^2+.5mv^2???? i cant do anything from there...
     
  9. Jun 4, 2009 #8

    Cyosis

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    You will have to use special relativity here. The total energy on one side equals the total energy on the other side. Total energy includes rest mass.

    Edit: While your equation is wrong I don't see how you can say that you can't do anything from there. You already assumed that both speeds are equal (something you should show) so just solving for 1/2 m v^2 would give you the answer, albeit the wrong answer, because you're working classically.
     
  10. Jun 4, 2009 #9
    so 497.7MeV=mv^2+2mc^2??? im sorry i completely dont understand... could you tell me the formula im supposed to use, im unfamiliar with this relativistic part
     
  11. Jun 4, 2009 #10

    Cyosis

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    Where does this mv^2 come from. Relativistic kinetic energy is not 1/2 mv^2. In a collision we have three types of energies. Total energy, E, relativistic kinetic energy, T and rest energy E_0. Therefore we know that [itex]E=T+E_0[/itex]. So what is the relativistic expression for kinetic energy?
     
    Last edited: Jun 4, 2009
  12. Jun 4, 2009 #11
    so Ek=T-Eo? my book says Ek=mc^2(gamma-1)
     
  13. Jun 4, 2009 #12

    Cyosis

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    I defined T as the kinetic energy so no. If [itex]E=T+E_0[/itex] then [itex]T=E-E_0[/itex]. You can call T E_k if you prefer that it does not matter as long as you don't mix them up.
     
  14. Jun 4, 2009 #13
    ok then T=gamma*mc^2-mc^2? but how do i find the gamma value, sine i dont know u?
     
  15. Jun 4, 2009 #14

    Cyosis

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    You are asked to find the kinetic energy not the velocity.

    Can you please just write down the momentum conservation equation first, then the energy conservation equation?
     
  16. Jun 4, 2009 #15
    Pf=Pi? E/c=E/c+E/c and Ef=Ei
     
  17. Jun 4, 2009 #16

    Cyosis

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    A little bit more specific to this problem perhaps? What is the value of p-initial?
     
  18. Jun 4, 2009 #17
    p initial = 0, since the particle is at rest, therefore p final also has to equal 0?
     
  19. Jun 4, 2009 #18
    so are you saying that for the system total energy is m(k)c^2=2m(pi)c^2+2*gamma*m*u^2?
     
  20. Jun 4, 2009 #19

    Cyosis

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    You have way more information than that. You need to make use of it. I will list you all the variables you need to put in your equations.

    [itex]
    E_{kaon},T_{\pi^-},T_{\pi^+},E_{0,\pi^-},E_{0,\pi^+},p_{kaon},p_{\pi^-},p_{\pi^+}
    [/itex]

    The first thing you do when solving a problem is writing down all the variables that are relevant to the problem. Now use these variables to write down the conservation of momentum equation and the conservation of energy equation.
     
  21. Jun 4, 2009 #20

    Cyosis

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    Where does the u come from? And secondly how do you know that both pions have the same kinetic energy (it's true)?
     
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