Only some energy steps fit.
Discrete atomic energies produce line spectra. Emission occurs when an electron moves to a lower energy state and a photon carries the energy difference. Absorption requires a matching available upward energy step. The Bohr model describes hydrogen energy levels but is not a general model for many-electron atoms.
The standing-wave condition around a Bohr orbit is nλ = 2πr, giving mvr = nh/(2π). Matter has de Broglie wavelength h/p. Electron diffraction supports wave behaviour of matter, while localised detection and the photoelectric effect demonstrate particle-like behaviour.
Hydrogen energy levels
Explore the relationship
Allowed initial and final levels are integers. The continuous line is only a guide between allowed transitions.
Tap or focus a plotted point to read its values.
View plotted data as a table
| Series | Initial principal level | Photon energy magnitude / eV |
|---|---|---|
| Photon energy magnitude / eV | 4 | 2.55 |
| Photon energy magnitude / eV | 4.06667 | 2.57764 |
| Photon energy magnitude / eV | 4.13333 | 2.60395 |
| Photon energy magnitude / eV | 4.2 | 2.62902 |
| Photon energy magnitude / eV | 4.26667 | 2.65293 |
| Photon energy magnitude / eV | 4.33333 | 2.67574 |
| Photon energy magnitude / eV | 4.4 | 2.69752 |
| Photon energy magnitude / eV | 4.46667 | 2.71833 |
| Photon energy magnitude / eV | 4.53333 | 2.73824 |
| Photon energy magnitude / eV | 4.6 | 2.75728 |
| Photon energy magnitude / eV | 4.66667 | 2.77551 |
| Photon energy magnitude / eV | 4.73333 | 2.79298 |
| Photon energy magnitude / eV | 4.8 | 2.80972 |
| Photon energy magnitude / eV | 4.86667 | 2.82578 |
| Photon energy magnitude / eV | 4.93333 | 2.8412 |
| Photon energy magnitude / eV | 5 | 2.856 |
| Photon energy magnitude / eV | 5.06667 | 2.87022 |
| Photon energy magnitude / eV | 5.13333 | 2.88389 |
| Photon energy magnitude / eV | 5.2 | 2.89704 |
| Photon energy magnitude / eV | 5.26667 | 2.90969 |
| Photon energy magnitude / eV | 5.33333 | 2.92188 |
| Photon energy magnitude / eV | 5.4 | 2.93361 |
| Photon energy magnitude / eV | 5.46667 | 2.94491 |
| Photon energy magnitude / eV | 5.53333 | 2.95581 |
| Photon energy magnitude / eV | 5.6 | 2.96633 |
| Photon energy magnitude / eV | 5.66667 | 2.97647 |
| Photon energy magnitude / eV | 5.73333 | 2.98626 |
| Photon energy magnitude / eV | 5.8 | 2.99572 |
| Photon energy magnitude / eV | 5.86667 | 3.00486 |
| Photon energy magnitude / eV | 5.93333 | 3.01369 |
| Photon energy magnitude / eV | 6 | 3.02222 |
| Photon energy magnitude / eV | 6.06667 | 3.03048 |
| Photon energy magnitude / eV | 6.13333 | 3.03847 |
| Photon energy magnitude / eV | 6.2 | 3.0462 |
| Photon energy magnitude / eV | 6.26667 | 3.05369 |
| Photon energy magnitude / eV | 6.33333 | 3.06094 |
| Photon energy magnitude / eV | 6.4 | 3.06797 |
| Photon energy magnitude / eV | 6.46667 | 3.07478 |
| Photon energy magnitude / eV | 6.53333 | 3.08138 |
| Photon energy magnitude / eV | 6.6 | 3.08779 |
| Photon energy magnitude / eV | 6.66667 | 3.094 |
| Photon energy magnitude / eV | 6.73333 | 3.10003 |
| Photon energy magnitude / eV | 6.8 | 3.10588 |
| Photon energy magnitude / eV | 6.86667 | 3.11157 |
| Photon energy magnitude / eV | 6.93333 | 3.11709 |
| Photon energy magnitude / eV | 7 | 3.12245 |
| Photon energy magnitude / eV | 7.06667 | 3.12766 |
| Photon energy magnitude / eV | 7.13333 | 3.13273 |
| Photon energy magnitude / eV | 7.2 | 3.13765 |
| Photon energy magnitude / eV | 7.26667 | 3.14245 |
| Photon energy magnitude / eV | 7.33333 | 3.14711 |
| Photon energy magnitude / eV | 7.4 | 3.15164 |
| Photon energy magnitude / eV | 7.46667 | 3.15606 |
| Photon energy magnitude / eV | 7.53333 | 3.16036 |
| Photon energy magnitude / eV | 7.6 | 3.16454 |
| Photon energy magnitude / eV | 7.66667 | 3.16862 |
| Photon energy magnitude / eV | 7.73333 | 3.17259 |
| Photon energy magnitude / eV | 7.8 | 3.17646 |
| Photon energy magnitude / eV | 7.86667 | 3.18024 |
| Photon energy magnitude / eV | 7.93333 | 3.18391 |
| Photon energy magnitude / eV | 8 | 3.1875 |
Explore: Compare transitions to different final levels. Which emits the highest-energy photon?
An electron drops from −1.5 eV to −3.4 eV.
- Photon energy = (−1.5) − (−3.4) = 1.9 eV.
- A positive photon energy is released.
Assumed knowledge
Energy conservation and negative energy levels.
Learning checkpoints & source
YOUR LEARNING CHECKPOINT- Connect atomic levels with absorption and emission spectra.
- Use de Broglie wavelength and the hydrogen model.