1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    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


    User Avatar
    Science Advisor
    Homework Helper
    2017 Award

    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


    User Avatar

    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! :)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted