Source: https://guthlabs.ai/docs/instruments/radioactive-decay-half-life-calculator/
instrument / verified-clean
# Radioactive Decay / Half-Life Calculator
The current ledger marks this instrument verified clean within the source-bound verification corpus.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Inspectable records
[01**Overview**Purpose and lifecycle]()[02**Mechanism**Method and assumptions]()[03**Implementation**Binding and validation]()[04**Qualification**Evidence and errata]()
## Ledger state
The current ledger marks this instrument verified clean within the source-bound verification corpus.
**Area**: Chemistry & Materials
**Tranche**: tranche-5
**Evidence ID**: t5-003
**Ledger rows**: 1
No ledger note is attached.
## Review findings
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.
### Formula and scope findings
- 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).
### Unit assumptions
- 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.
## Boundary hardening
**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.
## 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": {
"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."
}
````
## 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-tranche5/tranche5-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`