Hydrogen Atom Energy Levels
Visualize hydrogen electron energy levels and spectral lines. Select transitions to see photon wavelengths for Lyman, Balmer, and Paschen series.
The Bohr Model of Hydrogen
In 1913, Niels Bohr proposed a quantum model of the hydrogen atom in which the electron orbits the nucleus only in discrete 'allowed' orbits, each with a specific energy. When an electron jumps from a higher energy level n₂ to a lower level n₁, it emits a photon whose energy equals the energy difference.
Energy Levels
The energy of level n is E_n = −13.6/n² eV. The ground state (n=1) has E = −13.6 eV. The ionization energy (n → ∞) is +13.6 eV. Negative energies mean the electron is bound — it needs energy to escape.
| n | Energy (eV) | Orbit radius (pm) |
|---|---|---|
| 1 | −13.60 | 52.9 (Bohr radius) |
| 2 | −3.40 | 211.6 |
| 3 | −1.51 | 476.1 |
| 4 | −0.85 | 846.4 |
| 5 | −0.54 | 1322.5 |
| 6 | −0.38 | 1904.4 |
Spectral Series
Transitions to different lower levels produce different spectral series, each in a different region of the electromagnetic spectrum.
| Series | Lower level n₁ | Region | Discovered |
|---|---|---|---|
| Lyman | 1 | Ultraviolet (UV) | 1906 |
| Balmer | 2 | Visible light | 1885 |
| Paschen | 3 | Near infrared (NIR) | 1908 |
| Brackett | 4 | Infrared (IR) | 1922 |
| Pfund | 5 | Far infrared | 1924 |
Hydrogen Atom Formulas
Energy Levels (Bohr)
Photon Energy of Transition
Rydberg Formula (Wavelength)
The Rydberg constant R_H = 1.097 × 10⁷ m⁻¹. The wavelength λ = hc/ΔE where h = 6.626 × 10⁻³⁴ J·s and c = 2.998 × 10⁸ m/s.
Bohr Orbit Radius
| Symbol | Name | Value |
|---|---|---|
| R_H | Rydberg constant | 1.097 × 10⁷ m⁻¹ |
| a₀ | Bohr radius | 52.9 pm = 0.529 Å |
| E_∞ | Ionization energy | +13.6 eV |
| h | Planck's constant | 6.626 × 10⁻³⁴ J·s |
Frequently Asked Questions
Why are hydrogen spectral lines discrete rather than a continuous spectrum?
In the Bohr model (and quantum mechanics), electrons occupy quantized energy levels. Only specific energy differences ΔE are allowed, so only photons of those exact frequencies/wavelengths are emitted. A continuous spectrum would require continuous energy levels, which classical physics predicts but experiment disproves.
Why is the Balmer series in visible light?
The Balmer series corresponds to transitions down to n=2. The smallest energy gap (n=3→2) gives 1.89 eV → 656 nm (red). The next (n=4→2) gives 2.55 eV → 486 nm (blue-green). These energies fall in the visible range 1.77–3.10 eV. Transitions to n=1 (Lyman) release much more energy, putting them in UV.
Can electrons absorb photons as well as emit them?
Yes — absorption is the reverse process. An atom in a low energy state can absorb a photon of exactly the right energy to jump to a higher level. This produces dark absorption lines in a continuous spectrum (Fraunhofer lines). The sun's spectrum shows hundreds of dark lines from hydrogen and other atoms in its atmosphere.
What is the ionization energy of hydrogen?
13.6 eV. This is the energy needed to remove the electron from the ground state (n=1, E = −13.6 eV) to infinity (E = 0). This can be supplied by a photon of wavelength λ = hc/(13.6 eV) = 91.2 nm (UV).
Does the Bohr model work for atoms other than hydrogen?
Only for hydrogen-like ions (one electron): He⁺, Li²⁺, etc., with modification E_n = −13.6Z²/n² eV where Z is the atomic number. For multi-electron atoms, electron-electron repulsion makes the simple Bohr picture inaccurate; full quantum mechanics is needed.