Momentum of a massless particle?

[phosgene]

Homework Statement

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).

Homework Equations

Relativistic momentum = $\gamma(mv)$

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..

 

[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?

 

[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.