Balance nuclear identities and a complete mass-energy account

State the event and measurement model

A nucleus has proton number Z and nucleon number A, with neutron count A−Z. Isotopes share Z but differ in neutron count. The abstract parent in this ledger has A40,Z20; selecting a mode is a bookkeeping experiment, not a claim that a particular real isotope has all those decay channels. Alpha emission removesA4,Z2. Beta minus changes a neutron into a proton while emitting an electron and antineutrino; beta plus changes a proton into a neutron with a positron and neutrino. Gamma emission changes excitation without changing A or Z.

Reconcile the quantitative evidence

Identity balance and energetic permission are distinct. The supplied complete mass difference is total initial rest mass minus all final rest masses, including emitted charged leptons and excitation conventions. Q=Δm c² gives available energy using the rounded1 u c²=931.5 MeV. Negative Q forbids that isolated decay under the stated initial conditions; zero Q does not establish a finite decay rate. Positive Q still does not prove a channel exists or identify its probability. Momentum requires recoil, and beta energy is shared with a neutrino rather than fixed entirely by the charged particle.

Preserve limits and alternative explanations

Binding energy is the energy required to separate a nucleus into its constituent free nucleons. A bound nucleus has less rest mass than those separated particles. For a supplied abstract nucleus with mass defect 0.03 u andA4, binding energy is27.945 MeV and energy per nucleon6.98625 MeV. Doubling that defect at the same A doubles both values. Nuclear fusion or fission can release energy when products have lower total rest mass or greater total binding, but the amount must be computed for the complete products rather than inferred from the words split or combine. No practical reaction procedure is part of this lesson.

Worked original case

For abstract beta-minus conversion ofA40,Z20, daughterA40,Z21 has19 neutrons; its charge plus the emitted electron remains20e. With complete mass difference0.002 u, Q=1.863 MeV shared among the final particles. This does not state a real isotope half-life or a unique electron energy.

Investigation

Compare all four identity modes at fixed mass difference, then vary the difference through negative, zero and positive values. State which balances survive and which conclusions about real decay remain unestablished. Contrast nuclear and neutral-atomic mass conventions before using a table.

Changed-case practice

Sources and boundaries

Original cases checked 31 October 2026 against the primary explanation. These are bounded virtual models, not instructions to illuminate, accelerate, collect or expose real material. No real laboratory participation, detector certification, personal medical conclusion or independent mastery is claimed. Keep first work, critique, revision and genuinely new assigned evidence separately from public practice.

Supplemental source checks, 31 October 2026: Binding energy and mass conventions. Numerical cases remain original supplied models.