Calculator Input
Example Data Table
| Transition | Photon Energy (eV) | Wavelength (nm) | Series |
|---|---|---|---|
| n=1 to n=2 | 10.2000 | 121.5531 | Lyman series |
| n=3 to n=2 | 1.8889 | 656.3869 | Balmer series |
| n=4 to n=2 | 2.5500 | 486.2125 | Balmer series |
| n=5 to n=2 | 2.8560 | 434.1183 | Balmer series |
Formula Used
The calculator follows the Bohr model for hydrogen energy states.
Eₙ = -13.6 / n² eV
ΔE = 13.6 × |1 / nf² - 1 / ni²| eV
λ = hc / ΔE
f = ΔE / h
rₙ = a₀n²
vₙ = αc / n
Eionization = 13.6 / n² eV
These relations estimate bound-state energies, emitted photons, orbit radius, electron speed, and ionization thresholds for one-electron hydrogen calculations.
How to Use This Calculator
- Enter the initial principal quantum number.
- Optionally enter a final level for transitions.
- Choose the maximum level shown in the graph.
- Select your preferred wavelength display unit.
- Set the decimal precision you want.
- Press Calculate to display results above the form.
- Review the summary table, chart, and comparison table.
- Use the export buttons to save CSV or PDF files.
Frequently Asked Questions
1. What does this calculator measure?
It calculates hydrogen energy levels, orbit radius, electron speed, ionization energy, and photon properties for transitions between two Bohr levels.
2. Why are hydrogen energies negative?
Negative energy means the electron is bound to the nucleus. Energy must be supplied to move the electron from that level to the ionization limit.
3. What happens when the final level is lower?
A lower final level produces emission. The atom releases a photon whose energy equals the difference between the two allowed energy states.
4. What happens when the final level is higher?
A higher final level represents absorption. The atom must receive a photon with exactly the required energy gap to complete the upward transition.
5. What does the wavelength tell me?
The wavelength identifies the spectral line from the transition. It also shows whether the photon falls in ultraviolet, visible, or infrared regions.
6. Is this based on quantum mechanics?
Yes. It uses the Bohr energy relations for hydrogen. Those formulas match the main quantum result for one-electron hydrogen energy levels.
7. Can I use it for other atoms?
It is intended for hydrogen. The same structure works best for one-electron systems, but multi-electron atoms need more advanced corrections.
8. Why does the graph flatten at higher n values?
Energy levels crowd together as n increases. Each new level approaches zero energy, so the spacing shrinks near the ionization limit.