# Energy and Momenta of a muon? Relativity!

1. Feb 8, 2010

### sutupidmath

1. The problem statement, all variables and given/known data

A pion spontaneously decays into a muon and a muon antineutrino. Recent experimental evidence indicates that the mass m of the antineutrino is no larger than about 190 keV/c^2 and may be as small as zero. Assuming that the pion decays at rest in the laboratory, compute the energies and momenta of the muon and muon antineutrino (a) if the mass of the antineutrino were zero and (b) if its mass were 190keV/c^2.

3. The attempt at a solution
The mass of the pions is 139.56755MeV/c^2 and the mass of the muon is 105.65839MeV/c^2.
(a)

For the energy of the muon i simply used E=mc^2=105.65839MeV.
For the energy of the antineutrino i found the difference in mass before and mass after the decay which is m=33.90916MeV/c^2, and similarly applied the formula E=mc^2=33.90916MeV

For momenta of the antineutrino then i used the formula E=pc=> p=33.90916MeV/c.

I am thinking to do a simmilar thing for (b) also, but i have a strong feeling that (a) isn't even close to being correct.

Any help would be appreciated!

2. Feb 8, 2010