# Momentum of a massless particle?

1. Oct 18, 2012

### phosgene

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

Consider a neutron which decays at rest. Calculate the momentum of the electron in MeV/c when the proton is produced at rest. (You may assume that the anti-neutrino has zero mass).

2. Relevant equations

Relativistic momentum = $\gamma(mv)$

3. The attempt at a solution

Since the neutron is at rest, it has zero momentum. So I'm guessing that the electron has an equal and opposite momentum to the anti-neutrino...but if it has zero mass, how do I work out the momentum? I've also tried playing around with the equation

$E^2 = p^2c^2 + m^2c^4$

but I still get equations involving the mass, which just give me back zero momentum. I'm also assuming that the electron doesn't just have zero momentum, otherwise it seems like a silly question..

2. Oct 18, 2012

### Dickfore

How many particles are the products of the decay? What laws of conservation hold during this decay? How many equations between how many unknowns does this give you?

3. Oct 18, 2012

### phosgene

The products are a proton, an electron and an anti-neutrino, andI believe that conservation of energy and momentum laws hold during this process. The equations I get out of this are

momentum of neutron = 0 = total momenta of decay products

as the proton is at rest its momentum = zero

the electron's momentum = unknown

the anti-neutrino's momentum = unknown, but its mass is assumed to be zero.

This is the part where I get stuck. Combining the above equations, I get that the momentum of the electron should be equal and opposite to the momentum of the anti-neutrino..but I don't know how to proceed as I'm not sure how to handle the case where a massless particle has momentum.