Beta Decay<=>Positron emission

[Gnomie27]

I'm in high school chem. and we are learning about nuclear chemistry (it's more of a physics topic
in my opinion), but we learned that in beta decay a neutron loses mass (e- & anti-neutrino) and becomes a proton. We also learned that in positron emission a proton loses mass (positron & neutrino) and becomes a neutron. So, my question is...How is it that a neutron and proton can both become each other by losing mass?!? It's not balanced.

 

[snorkack]

How is it that a neutron and proton can both become each other by losing mass?!? It's not balanced.

It is balanced by binding energy. Proton can only become a neutron by losing mass if the resulting neutron is bound in a nucleus, so much stronger than proton was that due to binding energy the mass of the neutron is smaller than the mass of proton was. Proton cannot become neutron if the neutron is too weakly bound, or if the original proton is too strongly bound.

 

[mathman]

The main point is that these processes depend on the composition of the nucleus. Free protons do not decay, free neutrons do.

 

[Gnomie27]

let me see if i understand this correctly. energy is making up for the lost mass due to E=MC^2, right? so a free proton can not decay because there's no binding energy to make up for the loss in mass, however in a nucleus with too much energy it can become more stable by releasing the energy in the form of a positron, and the same thing occurs with a neutron releasing an electron. so what i still don't understand is how can a lone neutron decay if there's no binding energy to make it unstable? also how are the quarks effected in these decay modes, won't one of the ups or downs, depending on the decay, have to switch?

 

[Bill_K]

A proton weights 938.3 MeV, while a neutron weighs 939.5 MeV. Therefore a free neutron can decay into a proton, with about 1 MeV energy to spare, which goes into the kinetic energy of its decay products. But a proton can't decay into a neutron because it doesn't have enough energy unless it can grab 1 MeV from somewhere. So a proton contained in a nucleus can decay into a neutron if the difference in binding energy between the original nucleus and the nucleus that's left is at least 1 MeV.

 

[mfb]

also how are the quarks effected in these decay modes, won't one of the ups or downs, depending on the decay, have to switch?

Sure, that is the decay process on a quark level. up->down+positron+neutrino or down->up+electron+antineutrino

 

[Viracocha]

how can a lone neutron decay if there's no binding energy to make it unstable?

It's really particle physics. It has nothing to stabilty, it occurs due to a probabilistic interaction that can occur in the neutron. A down quark emits a negatively charged W boson (purely by chance) that turns it into an up quark and the neutron into a proton. This emission also accounts for the mass loss

 

[llynne]

Does the down quark actually emit a W boson or does the boson appear from interactions with fields.

 

[mfb]

Physics is not about "actually". The emission of a virtual W boson is a good model, but you can view it as an interaction with the field as well.

 

[llynne]

Thanks. I get hung up on theory laden terms I guess. The only way I can make sense of bosons and fermions is to see them as field interactions.