Photoelectric Effect Calculator mechanism

Model scope

The threshold formulas f0=φ/h and λ0=hc/φ are standard, and the positive-excess photoelectric relation is standard after converting wavelength with f=c/λ. The implementation is not acceptable as specified because the raw KE formula lacks the required physical max(0,...) constraint, and the wavelength/frequency conversion, unit handling, invalid-input behavior, and work-function-table provenance are not explicitly defined.

• KE_max=hf−φ is only the unconstrained excess-energy expression. The physical maximum kinetic energy must be KE_max=max(0,hf−φ), with ejection=no when hf<φ.
• V_stop=KE_max/e must be reported as zero or not applicable when hf<φ; a negative stopping voltage would be physically misleading for the stated output.
• The specification accepts wavelength or frequency but does not explicitly state the required conversion f=c/λ when wavelength is supplied.

Units and conventions

• h=6.62607015×10^-34 J·s exactly, c=299792458 m/s exactly, and e=1.602176634×10^-19 C exactly.
• Work function φ and photon energy must use the same energy units. Test vectors use φ in eV and convert with 1 eV=e joules.
• For electron photoelectric emission, V_stop=KE_max/e uses the magnitude of the electron charge, so KE expressed in joules gives V directly.
• Wavelengths are in vacuum and must be converted to metres before using f=c/λ or E=hc/λ.
• The numerical work functions used below are assumed material-table values; the actual lookup table must identify its source and acknowledge material/surface-condition variation.

Inspectable vector

One of 4 source-bound review vectors:

{
  "inputs": {
    "material": "Na",
    "work_function": "φ=2.28 eV",
    "incident_wavelength": "λ=400 nm"
  },
  "expected_outputs": {
    "photon_energy": "4.9661146425×10^-19 J = 3.0996049608 eV",
    "threshold_frequency": "f0=5.5130154718×10^14 Hz",
    "threshold_wavelength": "λ0=543.790344 nm",
    "ejection": "yes",
    "KE_max": "1.31315191698×10^-19 J = 0.8196049608 eV",
    "stopping_voltage": "0.8196049608 V"
  },
  "working": "1. Convert wavelength: λ=400 nm=4.00×10^-7 m. 2. Photon energy: E=hc/λ=(6.62607015×10^-34)(299792458)/(4.00×10^-7)=4.9661146425×10^-19 J. 3. Convert photon energy: E/e=(4.9661146425×10^-19)/(1.602176634×10^-19)=3.0996049608 eV. 4. Excess energy: KE=3.0996049608−2.28=0.8196049608 eV. 5. Convert KE to joules: 0.8196049608(1.602176634×10^-19)=1.31315191698×10^-19 J. 6. Stopping voltage: V=KE/e=0.8196049608 V. 7. Threshold frequency: f0=φ/h=(2.28 eV)(1.602176634×10^-19 J/eV)/(6.62607015×10^-34 J·s)=5.5130154718×10^14 Hz. 8. Threshold wavelength: λ0=c/f0=543.790344 nm. Since 400 nm<543.790344 nm, emission occurs."
}

Failure boundary

BREAK_CLAIMED · SELF_FLAGGED

A zero incident wavelength creates the undefined operation f = c/lambda. The instrument should reject this input; returning infinity, a numeric photon energy, or an ejection result would be a failure.

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-tranche6/tranche6-results.json
• BOUNDARY_HAZARD_CATALOG.json