# Could anyone explain how energy and momentum are conserved when an isolated neutron decays into a beta-minus particle?

I am not able to get to a reasonable explanation as to how momentum and energy are conserved when an electron, a proton, and a neutrino are created.

• Not clear what part you are having trouble with. – user93146 Sep 7 '18 at 20:10

I assume you're referring to the process I've drawn below (simplified, no quarks needed for this):

I'm not quite sure how detailed of an answer you want, but it's easy to get a feel for what's happening if we imagine we are moving with the neutron such that to us it looks like it isn't moving. Since it has no kinetic energy in this frame, its only energy is the rest mass, and there is no momentum.

Now after the neutron decays, (let's ignore the $W$ boson, that just complicates things), it shoots out three particles. Separately their momenta may take a range of values, but adding them all together, their total momentum must be 0, since we had 0 momentum to start with.

The total energy of the proton, electron and neutrino must sum to the rest mass energy of the neutron, because again this is what we started with.

If we're in a frame where the neutron is moving, then note the total energies would be different, and you would have to add the initial momentum to all the momenta of the particles in the rest frame.