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Bohr Model Energy and Radius Calculator — result sheet
Estimate a hydrogen-like electron energy level and orbital radius from nuclear charge and principal level.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Eₙ = −13.6Z²/n² eV; rₙ = a₀n²/Z, with a₀ = 0.0529177 nm.
The simplified Bohr model gives quantized energy and radius estimates for a one-electron, hydrogen-like system.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Nuclear charge Z — minimum 1; maximum 118
- Principal level n — minimum 1; maximum 100
Worked example
| Input | Value |
|---|---|
| Nuclear charge Z | 1 |
| Principal level n | 1 |
Energy = −13.6 eV; radius ≈ 0.05292 nm.
Assumptions and limits
- Atomic number and principal level are positive whole numbers.
- The result uses the hydrogen-like Bohr approximation rather than a many-electron quantum calculation.
- Fine structure, electron spin, shielding, and relativistic effects are not modeled.
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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