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A nucleus stability is judged by it's n/p ratio, which it prefers to be ~1. If n/p ratio is much less than 1, an atom tries to increase neutrons and decrease protons present in the nucleus. My physics teacher had taught this, in the β- decay lecture. Later, I found some details about electron capture, where a proton captures an electron orbiting it, and turns into a neutron.

Both of them achieve the common goal of decreasing protons and increasing neutrons. Then why two paths to achieve it ? Why do we know and study more about β- decay than electron capture ? In what conditions, and for what reasons is one preferred above the other ?

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  • $\begingroup$ Nuclear physicists don’t prefer one over another, but in an introductory course one might well talk mostly about one and just mention other reactions. Why a given nucleus might show one pathway more than another is, well, difficult to describe in detail. $\endgroup$
    – Jon Custer
    Commented Jul 8, 2022 at 21:37
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    $\begingroup$ Should the body of your question also say $\beta^+$ decay? It currently says $\beta^-$, which is also a decay mode, but which sends the nuclear charge in the other direction. $\endgroup$
    – rob
    Commented Jul 9, 2022 at 2:07

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The competing factors are that to achieve positron emission the energy for the creation of an electron mass must be available.
If that amount of energy is not available positron emission cannot occur.

For there to be electron capture one of the electrons, usually in the K-shell, has to have a reasonably probability of being inside the nucleus ie within the range of the weak force.
Since the probability is low, electron capture is difficult and thus rare.
Electron capture happens most often in the heavier neutron-deficient elements where the mass change is smallest and positron emission is not possible.

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