Nuclear Binding Energy Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Physics — Kinematics/Projectiles/Orbits, Forces/Energy/Momentum, Rotational Dynamics, Gravitation, Oscillations/Waves, Optics, E&M Fields, Relativity, Quantum, Statistical Thermo

Tranche

tranche-6

Evidence ID

t6-126

Ledger rows

1

No ledger note is attached.

Review findings

The energy relation E_b=Δm c² is standard, but the mass convention is not. The instrument should explicitly branch between nuclear-mass input, using Z m_p+N m_n−M_nucleus, and atomic-mass input, using Z m_H+N m_n−M_atom. Because the current specification claims to accept atomic masses while prescribing only the nuclear-mass formula, it fails verification. The honest label should disclose the atomic-versus-nuclear mass convention, the isotope-table source/version, and the neglected electron-binding-energy correction.

Formula and scope findings

• The stated mass-defect formula Δm=Z m_p+N m_n−M_nucleus is correct only when M_nucleus is a nuclear mass excluding electrons. The inputs explicitly allow measured atomic masses and isotope-table presets, which normally are atomic masses including Z electrons.
• For an atomic mass M_atom, the standard formula is Δm=Z m_H+N m_n−M_atom, where m_H is the neutral hydrogen-atom mass; equivalently, electron masses and electron binding-energy corrections must be handled explicitly.
• The specification does not state the formula for binding energy per nucleon; it should be BE/A, with A=Z+N.
• The specification does not define the mass unit or the exact isotope-table mass convention, so numerical results are ambiguous.

Unit assumptions

• Test vectors use atomic masses in unified atomic mass units (u), with m_H=1.00782503223 u, m_n=1.00866491595 u, and 1 u c²=931.49410242 MeV.
• Atomic masses include the electrons associated with the Z protons; the corrected atomic-mass formula therefore uses neutral hydrogen-atom mass m_H rather than bare proton mass m_p.
• A=Z+N is dimensionless, mass defect is reported in u, total binding energy in MeV, and binding energy per nucleon in MeV/nucleon.
• Electron binding energies are neglected, as is standard for nuclear binding-energy calculations at this precision.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The specification exposes a division-by-zero case at A=Z+N=0 and does not clearly define whether the supplied measured mass is atomic or nuclear. Applying the stated nuclear-mass formula directly to an atomic mass produces materially incorrect binding energies.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "Z": 1,
    "N": 0,
    "A": 1,
    "mass_type": "atomic",
    "measured_atomic_mass_u": 1.00782503223
  },
  "expected_outputs": {
    "mass_defect_u": 0,
    "binding_energy_MeV": 0,
    "binding_energy_per_nucleon_MeV": 0
  },
  "working": "Use Δm=Z m_H+N m_n−M_atom. Δm=(1)(1.00782503223)+(0)(1.00866491595)−1.00782503223=0 u. BE=0×931.49410242=0 MeV. BE/A=0/1=0 MeV/nucleon. This is the zero-binding edge case."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json