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Homework Help: Finding momentum of muon

  1. Sep 27, 2015 #1
    1. The problem statement, all variables and given/known data
    pi-meson's rest energy is 139.57MeV, it decays into a muon and a neutrino. The muon has a rest energy of 105.45MeV, and a proper lifetime of 2.197*10^-6. The neutrino's mass can be treated as massless in the process.

    1) Assuming the pi-meson decays at rest, what is the momentum of the muon?

    2. Relevant equations
    E_muon + E_neutrino = E_pi-meson
    E_muon = c^2* ((m_pi-meson)^2 - (m_muon)^2)) / (2m_pi-meson)
    E_muon = sqrt((P_muon^2 c^2) + (m_muon c^2)^2)
    3. The attempt at a solution
    Ok I used used the second equation and it gives about 9.866*10^18, then, use this value in the 3rd equation and solving for the momentum, I get a negative value under the square root, which doesn't make sense. In the 2nd equation, the values I plugged in for m_pi-meson and m_muon are just 139.57 and 105.47, and used 3*10^8 for c. Where did I go wrong?
    Last edited: Sep 27, 2015
  2. jcsd
  3. Sep 27, 2015 #2


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    Staff: Mentor

    Where do those equations come from?
    9.866*1018 what? Kilometers, apples, ...? Units are important.
  4. Sep 27, 2015 #3
    The first equation is based on the conservation laws, you can see from here https://teachers.web.cern.ch/teache...h/mbitu/energy_and_momentum_conservation1.htm I used equation (2.5)
    For the second equation, I used the fact that E^2 = p^2 c^2 + m^2 c^4 , squared both sides to get E, and tried to solve for the momentum from here
  5. Sep 27, 2015 #4
    Oh never mind, I solved it. Thanks for the help.
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