Bohr’s model explains hydrogen’s spectral lines by giving its electron only certain allowed energy levels. When the electron moves between levels, it absorbs or emits a photon whose energy equals the difference between them. Since only particular energy differences are possible, hydrogen produces particular wavelengths—not a continuous spectrum.
What Bohr meant by electron shells
In Bohr’s 1913 model, an electron in hydrogen could occupy only certain allowed states, each with a fixed energy. Bohr pictured these states as circular orbits around a central nucleus. The school term “shell” commonly refers to a principal energy level labeled by the number n.
Unlike a planet orbiting the Sun, an electron in one of Bohr’s allowed stationary orbits does not continuously radiate energy. It changes energy only by moving between allowed levels. That restriction was central to Bohr’s explanation of why atoms remain stable and why hydrogen’s spectrum contains distinct lines.
How energy-level changes produce spectral lines
An electron can absorb energy and move to a higher level, or move to a lower level and emit a photon. The photon’s energy equals the magnitude of the difference between the two levels:
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|ΔE| = hν = hc/λ
Here, h is Planck’s constant, ν is the photon frequency, c is the speed of light, and λ is its wavelength. Each possible transition has a particular energy difference, so it produces or absorbs light at a particular frequency and wavelength. A spectral line therefore records the energy difference between two allowed levels.
Hydrogen’s energy levels
For hydrogen, Bohr’s energy for level n is:
En = −13.6 eV/n², where n = 1, 2, 3, …
The lowest-energy state, called the ground state, is n = 1 at −13.6 eV. As n increases, the energy approaches zero. Zero marks the ionization limit: the point at which the electron is no longer bound to the atom.
Example: a transition from n = 3 to n = 2
When hydrogen’s electron drops from n = 3 to n = 2, it emits a photon with energy equal to the magnitude of the difference between those levels. A transition between another pair of levels has a different energy difference and therefore a different spectral line. For downward transitions, OpenStax gives the wavelength relation 1/λ = R(1/nf² − 1/ni²), with ni > nf.
Hydrogen’s spectral series
Lines are grouped into series according to the level where the transition ends:
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- Lyman series: transitions ending at n = 1.
- Balmer series: transitions ending at n = 2.
- Paschen series: transitions ending at n = 3.
The shared endpoint gives each series a common pattern, while different starting levels produce different lines within it.
Where the model works—and where it does not
Bohr’s equations work especially well for hydrogen and hydrogen-like ions: systems with one electron and a nucleus of charge Z. For those ions, the energy levels follow En = −Z²E₀/n², and the orbit radius follows rn = (n²/Z)aB. The stronger nuclear attraction shifts their spectra relative to hydrogen’s.
Those simple formulas should not be applied unqualified to ordinary atoms with multiple electrons. Bohr’s model does not give a complete account of larger atoms or all their spectral details.
Bohr’s orbits versus the modern picture
Bohr’s circular paths are part of a historical model, not a literal modern map of electron motion. Modern quantum mechanics describes electrons using quantum states and orbitals rather than little planets traveling along definite paths. Bohr’s model remains a useful first explanation of hydrogen’s discrete energy levels and line spectrum, but it is not the current description of where an electron travels.
Why Bohr developed the model
Bohr combined Rutherford’s nuclear atom with the idea that electron energies are quantized. Under classical expectations, Rutherford’s orbiting electrons would make the atom unstable; Bohr instead proposed allowed stationary orbits and transitions between them. The American Physical Society dates Bohr’s letter explaining the hydrogen spectrum to Rutherford to March 6, 1913.
The University of Copenhagen’s Niels Bohr Institute recounts that, after returning to Copenhagen in 1912, Bohr’s colleague H. M. Hansen drew his attention to Balmer’s empirical formula for hydrogen. Bohr recognized that his theory could account for it and published three articles in 1913. The Institute attributes the later recollection “As soon as I saw Balmer’s formula, it was immediately clear to me” to Bohr; it is not identified as a contemporaneous statement from 1913.
Seeing a line spectrum
A discharge tube, slit and diffraction grating can be used in a spectroscope to view emission lines, as described by OpenStax. Such a demonstration makes the discrete lines visible; it does not demonstrate that electrons follow Bohr-style circular paths.
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