Radioactive Decay / Half-Life Calculator mechanism

Model scope

The decay and activity formulas are standard under the stated assumptions, but the specification does not define what N means when it says remaining quantity, does not state the age-dating inversion, and does not define unit conversion rules for Bq. The honest-label text appropriately excludes clinical dosimetry, but should also state that age-dating results are educational estimates and not a substitute for calibrated laboratory dating or nuclear-data analysis.

• N=N0·e^(-λt) and λ=ln(2)/t½ are standard first-order radioactive-decay formulas, provided t and t½ use the same time unit.
• A=λN is valid only when N is the number of radioactive parent atoms and λ uses inverse seconds for activity in becquerels. If N means mass, volume, moles, or an unspecified remaining quantity, an atom-count or amount-to-activity conversion is required.
• The age-dating inversion formula is missing. For a measured target quantity N with known initial quantity N0, the required formula is t=ln(N0/N)/λ=t½·log2(N0/N).

Units and conventions

• The elapsed time t and half-life t½ must use identical time units when calculating remaining quantity.
• For activity in Bq, λ must be in s^-1 and N must be the number of radioactive parent atoms.
• If N is supplied in moles, use N_atoms=n·NA before calculating activity; if supplied as mass, use isotope-specific molar mass and Avogadro's constant.
• The example C-14 half-life is taken as 5730 years, with 1 year=365.25 days=31,557,600 seconds for Bq conversion.
• The selected isotope's half-life must be clearly identified and sourced from a maintained nuclear-data table; rounded tabulated values affect calculated results.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "isotope": "C-14",
    "half_life": 5730,
    "half_life_unit": "years",
    "initial_parent_atoms": 1000000,
    "elapsed_time": 5730,
    "elapsed_time_unit": "years"
  },
  "expected_outputs": {
    "decay_constant_per_year": 0.000120968094,
    "remaining_parent_atoms": 500000,
    "activity_per_year": 60.484047
  },
  "working": "1. λ=ln(2)/t½=0.69314718056/5730=0.000120968094 year^-1. 2. λt=0.000120968094×5730=0.69314718056. 3. N=N0e^(-λt)=1,000,000×e^(-0.69314718056)=1,000,000×0.5=500,000 atoms. 4. A=λN=0.000120968094×500,000=60.484047 decays/year. This is not Bq because λ is per year."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero half-life causes division by zero and must be rejected. The probe also exposes a convention hazard: negative elapsed time yields an apparent quantity greater than the initial quantity unless the instrument rejects or explicitly labels backward-time extrapolation.

Other records

Sources and evidence

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

• VERIFIED_LEDGER.json
• evidence-tranche5/tranche5-results.json
• BOUNDARY_HAZARD_CATALOG.json