A pion at rest decays into a muon and an antineutrino. The mass of the antineutrino is zero, find the energies and momenta of the muon and antineutrino. Mass of the pion is 139.57 MeV/c^2 and the mass of the muon is 105.66 MeV/c^2
pion -> muon + antineutrino
(3) E^2 = (pc)^2 + (mc^2)^2
The Attempt at a Solution
Conservation of energy: E(pion) = E(muon) + E(antineutrino)
Using equation 1 and the given masses:
E(pion) = 139.57 MeV
E(muon) = 105.66 MeV (?)
so E(antineutrino) = E(pion) - E(muon) = 33.91 MeV
Use equation 2 for the massless antineutrino and get p = 33.91 MeV/c
since momentum is conserved and p(pion) = 0 (at rest),
p(muon) = -p(antineutrino) = -33.91 MeV/c
I don't think I'm right because if the muon has momentum it is moving and thus I can't find its energy by simply plugging its mass into equation 1.
Thanks for any help.