Electron Capture vs Positron Emision

[FireStorm000]

I'm having some slight confusion over what seems to be a violation of conservation of mass: Both electrons and positrons have positive mass, so now consider an atom that undergoes a beta decay, and so has it's mass changed by the difference in mass between a proton and a neutron. How does it work that you can have the same initial mass, same final mass, and get there by both gaining mass(EC), or loosing mass (β+). What gives?
-FireStorm-

 

[snorkack]

Gives kinetic energy of the emitted particles.

Take a nucleus which can decay both ways, like potassium 40.

In case of positron emission, the difference between the masses of K-40 and Ar-40 is split between the 3 major components of
1) positron rest mass (511 keV)
2) positron kinetic energy
3) neutrino kinetic energy
and the minor components of
4) neutrino rest mass (unknown but small)
5) Ar-40 nucleus recoil

Eventually the positron is annihilated, emitting 2 or 3 photons whose combined energy shall be 1022 keV plus whatever the positron kinetic energy was.

If, however, the K-40 nucleus manages to capture an electron, then there is no positron emitted. But a neutrino is emitted.

The whole mass difference between K-40 and Ar-40 nuclei, plus the mass of electron (usually somewhat less than 511 keV), have to be carried away by the emitted neutrino. Only the recoil of the Ar-40 nucleus goes elsewhere.

It follows that the neutrinos emitted on electron capture are much more energetic than the neutrinos emitted by positron emission. The capture neutrinos have to take the 1022 keV of electron-positron pair energy, plus the positron´s share of kinetic energy.

Electron capture neutrinos also have a narrow line spectrum, because they cannot share their energy with positron.

 

[FireStorm000]

Ah, that makes much more sense; considering the neutrino in there gives you much more wiggle room.