Physics

Physics

Problem

Consider the following two-step decay sequence: 818O→  β−  918F→  β+  818O.^{18}_{8}\text{O} \xrightarrow{\;\beta^-\;} ^{18}_{9}\text{F} \xrightarrow{\;\beta^+\;} ^{18}_{8}\text{O}. In the first step, the emitted electron is accompanied by lepton AA. In the second step, the emitted positron is accompanied by lepton BB. Determine the symbols of leptons AA and BB that are required for each step to satisfy conservation laws.
Intuitive explanation

Beta decay conserves both charge and lepton number, so you need to track what happens to each when a quark transforms inside the nucleus. In β−\beta^- decay, a neutron becomes a proton and emits an electron—but that's only two particles, so a third must carry away "missing" lepton number to keep the total constant. In β+\beta^+ decay, a proton becomes a neutron and emits a positron; again, a partner particle is needed to balance lepton accounting. Identify what lepton number each emitted particle carries, then determine what the companion lepton must be.

Intuitive explanation

Beta decay conserves both charge and lepton number, so you need to track what happens to each when a quark transforms inside the nucleus. In β−\beta^- decay, a neutron becomes a proton and emits an electron—but that's only two particles, so a third must carry away "missing" lepton number to keep the total constant. In β+\beta^+ decay, a proton becomes a neutron and emits a positron; again, a partner particle is needed to balance lepton accounting. Identify what lepton number each emitted particle carries, then determine what the companion lepton must be.

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