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A particle at rest decays into 2 particles

  1. Sep 13, 2012 #1
    1. The problem statement, all variables and given/known data
    A particle at rest with mass M decays into 2 particles, one with mass m1 and the other with mass m2. Use conservation of energy and momentum to show that E1=((M^2+m1^2-m2^2)c^2)/(2M)


    2. Relevant equations
    E=√((p^2)(c^2)+(m^2)(c^4))=γmc^2
    p=γmv

    3. The attempt at a solution
    Energy is conserved, so E0=E1+E2
    The mass is initially at rest so E0=M(c^2)
    E2=√((p2^2)(c^2)+(m2^2)(c^4))

    So, I need to get
    M(c^2)-√((p2^2)(c^2)+(m2^2)(c^4))
    to look like
    ((M^2+m1^2-m2^2)c^2)/(2M)
     
  2. jcsd
  3. Sep 14, 2012 #2

    vela

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    You need to use conservation of momentum as well.
     
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