How does mass change during beta decay?

[Anonymous No.9809200]

I know this is probably a super brainlet question, but whenever I try to calculate the mass after beta decay I mess up.

Say I have hypothetical nucleus with the mass 20000MeV. It goes through beta decay and gives off an electron with the maximum kinetic energy of 2MeV. The mass of the new nucleus should be 20000 - 2 - 0,511 (mass of an electron) MeV = 19997,489 MeV.

My textbook says you should only subtract the 2MeV of kinetic energy. Why shouldn't you also subtract the mass of the electron? The original nucleus loses an electron as well as the other energy, right? Please help a brainlet out.

[Anonymous No.9809257]

wot about binding energy?

[Anonymous No.9810111]

>>9809200
Even bigger brainlet here so correct me if im wrong. I think it's because the electron can't pre-exist inside the nucleus. That's fucking with the calculations

[Anonymous No.9810709]

>>9809200
I have no authority in anything, but i think your problem is Units.
The mass of nucleus and kinetic energy of electron are expressed in energy units, but an electron at rest is expressed in kilograms (Mev/c)??

[Anonymous No.9810717]

>>9810111
A neutron transforms into a proton and shoots out an electron in beta decay.
Would appreciate it if a nonbrainlet could dwscribe the transformation (magic?) process in laymen terms.

[Anonymous No.9810944]

>>9810717
I was thinking of this

[Anonymous No.9810949]

>>9809200

Essentially beta decay means a neutron transforming to a proton, emitting an electron and an electron neutrino. The neutrino has a negligible mass, so we ignore it for now, same with the electron. An neutron and a proton are roughly the same weight( neutrons are about 1 MeV heavier iirc). So the nucleus' weight is, as a rough estimate, the same after the decay, except for the binding energy electron and neutron take out of the core. I suppose your problem is thinking to deeply about it when your book just wants to do this "rough estimate"-kind of calculation.

[Anonymous No.9810954]

>>9810717

essentially, i can't do it easier than this :

nature has 4 forces, strong nuclear force, weak nuclear force, electromagnetic force and gravity. The Strong nuclear force is what binds Protons and neutrons( that consist of quarks) together internally and, over residue processes, in the nucleus. The weak nuclear force allowes quarks to transform into others, so one of the three quarks in the neutron, a down quark, transforms to an upquark. since the charge has to be preserved, this process emits a W- boson that is really short lived and itself decays into an electron ( taking the negative charge with it) and an anti electron neutrino because the number of leptons has to be conserved as well.

[Anonymous No.9810961]

>>9809200
Neutrons are more massive than protons, and there's nuclear binding energy.