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Physics · Ch 8 — Atomic and Nuclear Physics

Beta decay

8.6.2

Beta decay

In beta decay, a radioactive nucleus emits either an electron or a positron; both are collectively called beta particles, with the positron being the electron's antiparticle - identical mass, but opposite (positive) charge.

Beta-minus (β−\beta^-) decay. Here an electron (e−e^-) is emitted, the nucleus's atomic number increases by one while its mass number stays the same:

ZAX ⟶ Z+1AY+e−+νˉ(8.28){}^{A}_{Z}X\ \longrightarrow\ {}^{A}_{Z+1}Y+e^-+\bar{\nu}\qquad (8.28)

At the level of individual nucleons, this happens because one neutron inside nucleus XX converts into a proton, emitting an electron and an antineutrino: n→p+e−+νˉn\to p+e^-+\bar{\nu}. A concrete example is carbon-14 decaying to nitrogen-14: 614C→714N+e−+νˉ^{14}_{6}C\to{}^{14}_{7}N+e^-+\bar{\nu}.

Beta-plus (β+\beta^+) decay. Here a positron (e+e^+) is emitted, and the atomic number decreases by one while the mass number stays the same:

ZAX ⟶ Z−1AY+e++ν(8.29){}^{A}_{Z}X\ \longrightarrow\ {}^{A}_{Z-1}Y+e^++\nu\qquad (8.29)

Here a proton inside XX converts into a neutron, emitting a positron and a neutrino: p→n+e++νp\to n+e^++\nu. A concrete example is sodium-22 decaying to neon-22: 1122Na→1022Ne+e++ν^{22}_{11}Na\to{}^{22}_{10}Ne+e^++\nu. Note that a single free proton, isolated outside any nucleus, cannot undergo β+\beta^+ decay by itself (energy conservation forbids it, since a free neutron is heavier than a free proton); by contrast, an isolated free neutron can and does undergo β−\beta^- decay on its own, with a half-life of about 13 minutes. It is important to note that the emitted electron or positron was never sitting inside the nucleus beforehand - it is created at the instant of the neutron-to-proton (or proton-to-neutron) conversion. …