Bohr Model Hydrogen Energy Levels Calculator implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-clean

Evidence ID

t6-107

Effect

Computation or source lookup only

Input and validation requirements

• Reject n=0, negative, noninteger, or otherwise invalid principal quantum numbers because n² appears in a denominator for energy.
• Reject Z≤0; require a positive integer Z.
• The formulas are physically applicable only to one-electron hydrogen-like ions, not neutral multi-electron atoms with the stated atomic number.
• A transition with n1=n2 gives ΔE=0 and causes division by zero when calculating wavelength; it must be rejected or reported as no photon.
• Wavelength calculations require an explicit energy unit and a matching hc constant; mixing joules with eV·nm produces incorrect results.
• Very large n or Z values may expose floating-point rounding; displayed precision should not imply precision beyond the constants used.
• The energy-level diagram should label the Bohr-model approximation and should not imply full quantum-mechanical accuracy, especially for multi-electron atoms, fine structure, Lamb shifts, reduced-mass corrections, or external-field effects.

Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "Z": 1,
    "n1": 2,
    "n2": 1,
    "transition": "emission",
    "wavelength_units": "nm"
  },
  "expected_outputs": {
    "E_initial_eV": -3.4,
    "E_final_eV": -13.6,
    "radius_initial_m": 2.116708e-10,
    "radius_final_m": 5.29177e-11,
    "delta_E_eV": -10.2,
    "photon_energy_eV": 10.2,
    "wavelength_nm": 121.553135686,
    "wavelength_m": 1.21553135686e-7,
    "spectral_series": "Lyman"
  },
  "working": "E_initial=−13.6×1²/2²=−13.6/4=−3.4 eV. E_final=−13.6×1²/1²=−13.6 eV. r_initial=2²a0/1=4(5.29177×10^-11)=2.116708×10^-10 m. r_final=1²a0=5.29177×10^-11 m. ΔE=E_final−E_initial=−13.6−(−3.4)=−10.2 eV. Emitted photon energy=|ΔE|=10.2 eV. λ=hc/E=1239.841984/10.2=121.553135686 nm=1.21553135686×10^-7 m. The lower level is n=1, so this is Lyman."
}

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