Track nuclear identity through four decay types

Begin with evidence

Radioactive decay changes an unstable nuclear state to a lower-energy final state, possibly with a different nucleus and emitted particles. A gamma transition can leave proton and neutron counts unchanged while reducing excitation energy. Thus “decay always creates a different element” is false. Whether a particular isotope can undergo a channel depends on its actual energy structure; balanced symbols alone do not establish instability.

Connect the model

Alpha emission removes a helium-4 nucleus: daughter mass number A decreases by four and proton count Z by two. Beta-minus conversion changes a neutron into a proton while emitting an electron and an antineutrino, so A stays fixed and daughter Z increases by one. Beta-plus conversion changes a proton into a neutron with a positron and a neutrino, so A stays fixed and Z decreases by one. The emitted beta electron is not a preexisting orbital electron simply escaping.

Interpret the ledger

Charge bookkeeping must include emitted particles. In beta-minus decay, the daughter’s extra +e balances the emitted −e. In beta-plus decay, the daughter loses +e while the positron carries it. Neutrinos carry no electric charge but contribute energy and momentum. The lepton ledger assigns opposite signs to a lepton and its antiparticle; the paired beta emissions sum to zero in these examples.

Test the boundary

The workbench’s generic parent choices are stipulated accounting exercises, not claims that each displayed A,Z combination physically supports all four modes. Gamma emission leaves A and Z fixed and lowers excitation, with recoil allowed by conservation. No specific isotope half-life memorization, electron-capture channel or neutron-emission decay is required here. There is no source handling or radiation exposure activity.

Worked original case

For a generic parent A=80,Z=40, alpha gives daughter 76,38; beta-minus gives 80,41 plus electron and antineutrino; beta-plus gives 80,39 plus positron and neutrino; gamma retains 80,40 with lower nuclear excitation.

Predict, compare and retain evidence

Can a nucleus release energy while keeping its element and isotope identity? Hold one parent choice fixed and compare all four channels. Predict daughter A and Z and the emitted charge before checking. For each channel show where charge and nucleon number reside, then explain why the bookkeeping is not a stability prediction.

Changed-case practice

A generic A=120,Z=60 nucleus emits an alpha particle, then its daughter undergoes beta-minus decay. Find final A and Z and total emitted electric charge.

Check the reasoning after your attempt

After alpha the daughter is 116,58; after beta-minus it is 116,59. Emitted alpha charge +2e and electron charge −e total +e, balancing parent +60e with final nucleus +59e. This does not establish an actual allowed chain.

Retain lepton identity as well as charge and nucleon number

For these alpha and beta nuclear accounts, lepton-number conservation is a required bookkeeping check, not an optional substitute for energy and momentum. Assign +1 to an electron or electron neutrino and −1 to its antiparticle. Beta-minus emits an electron and antineutrino, totaling zero; beta-plus emits a positron and neutrino, also totaling zero. A positron has the electron’s mass and opposite electric charge. Neutrinos have extremely small nonzero mass, no electric charge and very weak interactions with ordinary matter through weak and gravitational interactions in this introductory model.

Predict and check: replacing the antineutrino in a proposed beta-minus account with a neutrino would leave charge and nucleon sums unchanged but produce emitted lepton number +2 rather than zero, rejecting that proposed channel. In the alpha-then-beta-minus transfer above, explicitly list emitted lepton numbers 0,+1,−1 and verify their zero sum. This bookkeeping does not establish the actual isotope’s rate, stability or a detector’s ability to observe every product. (Current clause 15.8.A.)

Reflect and source-check

Why does unchanged mass number in beta decay not mean unchanged neutron count?

Original prose and supplied numerical evidence; checked 30 October 2026 against the current AP Physics 2 framework, fall 2026 clarifications and OpenStax. Virtual-only: no physical source, exposure or apparatus is requested. Public examples and model captures are not independent mastery or supervised laboratory participation.

Clause-level source/action reconciliation checked 31 October 2026 against the linked current framework and Fall 2026 clarification. Added packets are original virtual comparisons; no new practical or learner-completion claim.