# Solving energy-momentum equations for lamba decay

1. Apr 7, 2013

### jturko

1. The problem statement, all variables and given/known data
A lambda particle decays into a proton (at rest) and a pion. The rest masses are:
lambda: 1116 MeV/c^2
pion: 140 MeV/c^2
proton: 938 MeV/c^2

we want to find the energy of the
a) pion
b) lambda (before decay)

2. Relevant equations
I am assuming we need to use the energy-momentum 4-vector equation
E2=(mc2)2 + (pc)2

3. The attempt at a solution
So I think we know in the lab frame that the momentum of the pion and the lambda are the same, since the proton is at rest. So the energy of the pion must be its rest mass plus the mass deficit from the lambda; 140+(1116-(140+938))=140+38=178 , but there must be some energy that is from the initial momentum of the lambda. Could there be a missing parameter? I am unsure how you would figure out how much energy would be from the momentum without any other information.

2. Apr 7, 2013

### jambaugh

You must also conserve momentum, write a 4-vector eqn 4-momentum in = 4-momentum out. That will also handle energy conservation.

3. Apr 7, 2013

### jturko

Awesome! thank you, I was just regrouping my terms sloppily. Once looking at the 4 momenta it became clear very quickly!