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Hydrogen-Like Atom Energy Transition — result sheet
Calculate Bohr-model energy levels, orbit radii, and photon wavelength for a one-electron ion transition.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Eₙ = −13.6 Z²/n² eV; rₙ = a₀n²/Z; photon energy = |Eᵢ − Eꜰ| and λ = hc/ΔE.
A hydrogen-like atom has one electron and a nucleus with charge Z. In the Bohr model, the allowed energy and radius depend on the principal level n and scale with the nuclear charge; a transition emits or absorbs a photon whose energy equals the level difference.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Nuclear charge Z — minimum 1; maximum 92
- Initial level nᵢ — minimum 1; maximum 1000
- Final level nꜰ — minimum 1; maximum 1000
Worked example
| Input | Value |
|---|---|
| Nuclear charge Z | 1 |
| Initial level nᵢ | 3 |
| Final level nꜰ | 2 |
Photon energy about 1.889 eV and wavelength about 656.1 nm
Assumptions and limits
- The atom or ion has exactly one electron and is modeled with the nonrelativistic Bohr approximation.
- The nucleus is treated as fixed and isolated, with no reduced-mass, fine-structure, external-field, or Lamb-shift correction.
- The transition wavelength is a vacuum value and the photon energy is the magnitude of the level difference.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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