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Kaon Decay -- Special relativity

  1. Oct 27, 2015 #1
    1. The problem statement, all variables and given/known data
    A K0 particle is unstable and has a mass of 8.87x10-28 kg. It can decay into π+ and π- particles, each of mass 2.49x10-28 kg. Suppose that a K0 is moving in the +x direction and decays by this process, with the π+ moving off at 0.9c and the π- moving off at 0.8c.
    a) What was the speed of the K0 before the decay?
    b) In what directions do each of the π particles move after the decay?

    2. Relevant equations
    Pinitial=P1+P2

    3. The attempt at a solution
    I assume that the momentum is conserved thus Pinital=P1+P2. I also know that P=gamma*mass*velocity
    So with that information, I can solve for the momentum of the two particles. P1+P2=2.12*10^-19
    Now I know my total momentum, thus I isolate for velocity. HOWEVER, the original mass of the kaon is 8.87*10^-28, but the masses of the two particles do not add up to the total mass, where did the lost mass go? Energy? If so, how do I solve th problem?

    Also, for part b) do I just say, they are in opposite directions?
     
  2. jcsd
  3. Oct 27, 2015 #2

    BvU

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    Science Advisor
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    Gold Member

    Hello Sophia, welcome to PF :smile: !

    You'll have to do momentum conservation in two directions (longitudinal and transverse).
    And (b) is right in the Kaon rest frame, but not in the lab frame !
    In that rest frame the leftover energy from the decay is converted into kinetic energy of the pions. Equally - from momentum conservation :smile:
     
  4. Oct 27, 2015 #3

    jtbell

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    Staff: Mentor

    Correct. More precisely, some of the rest-energy (mc2) of the kaon becomes part of the kinetic energy of the pions. Total energy is conserved. Therefore you have three conservation equations:

    • Conservation of energy
    • Conservation of x-momentum
    • Conservation of y-momentum

    Set them up and identify your unknown quantities.
     
  5. Oct 27, 2015 #4
    Thank you!
     
  6. Oct 27, 2015 #5
    That was very helpful! :)
     
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