Niels Bohr’s 1913 model explained hydrogen’s spectral lines: electrons occupy fixed energy levels and emit or absorb light of precise wavelengths when they jump. It works perfectly for one-electron atoms.
How to use the Bohr Model Calculator
- Atomic number Z
- Initial level n_i
- Final level n_f
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the atomic number (1 for hydrogen) and the initial and final principal quantum numbers.
Inputs explained
| Field | What to enter |
|---|---|
| Atomic number Z | A number |
| Initial level n_i | A number |
| Final level n_f | A number |
What each result means
- Initial energy E_i = -13.605693×[Atomic number Z]^2÷[Initial level n_i]^2
- Final energy E_f = -13.605693×[Atomic number Z]^2÷[Final level n_f]^2
- Photon energy |ΔE| = abs([Final energy E_f] – [Initial energy E_i])
- Photon frequency = [Photon energy |ΔE|]×1.602176634e-19÷6.62607015e-34
- Photon wavelength = 6.62607015e-34×299792458÷([Photon energy |ΔE|]×1.602176634e-19)
Example values
How the main result changes when Atomic number Z changes and everything else stays at the example values above:
| Atomic number Z | Photon energy |ΔE| (eV) |
|---|---|
| 1 | 1.8897 |
| 1.25 | 2.9526 |
| 1.5 | 4.2518 |
| 2 | 7.5587 |
Formula
E_n = −13.6057 eV·Z²/n², ΔE = E_f − E_i, λ = hc/|ΔE|
Worked example
Inputs — Atomic number Z: 1; Initial level n_i: 3; Final level n_f: 2.
Results — Initial energy E_i = -1.511744 eV; Final energy E_f = -3.401423 eV; Photon energy |ΔE| = 1.88968 eV; Photon frequency = 456,922,490,348,751 Hz; Photon wavelength = 656.112282 nm; Transition = Emission.
Key terms
- Energy level
- Allowed energy of a bound electron.
Frequently asked questions
What is the ground-state energy of hydrogen?
−13.6 eV.
Why is the 3 → 2 line red?
It emits 656 nm light – the Balmer H-alpha line.
Does the Bohr model work for helium?
Only for one-electron ions such as He⁺.
What replaced the Bohr model?
Quantum mechanics (Schrödinger's equation).