Bohr model

The Bohr model, also known as the Rutherford–Bohr model, represents one of the most significant developments in early atomic theory. Formulated between 1911 and 1918 by Niels Bohr, it expanded upon Ernest Rutherford’s nuclear model and marked a pivotal moment in the transition from classical to quantum physics. Although later superseded by quantum mechanical models, the Bohr model successfully explained several atomic phenomena, most notably the spectral lines of hydrogen, and introduced the concept of quantised electron energies.
The model depicts the atom as a small, dense, positively charged nucleus encircled by negatively charged electrons constrained within discrete orbits. These circular orbits resemble a miniature Solar System, but the electron–nucleus interaction is governed by Coulomb attraction rather than gravity. Only specific orbits corresponding to distinct energy values are permitted, and transitions between these orbits give rise to the emission or absorption of electromagnetic radiation.

Background and Early Atomic Models

Before the second decade of the twentieth century, atomic models were speculative and lacked a firm experimental foundation. Even the atomic concept itself faced opposition from some scientists. Various structural models were proposed, often drawing on analogies with macroscopic systems.
In the late nineteenth century, theorists began to consider planetary-style atoms in which electrons orbited a central charge. However, classical electrodynamics introduced a major difficulty. Joseph Larmor demonstrated in 1897 that any accelerating charge emits radiation. Because electrons in orbit are continuously accelerating, they would rapidly lose energy and spiral into the nucleus. Atomic systems, therefore, appeared mechanically and electromagnetically unstable unless special arrangements of multiple electrons could cancel the expected radiation.

Thomson’s Plum Pudding Model

When Bohr began developing his atomic theory, the most influential model was J. J. Thomson’s plum pudding model. Thomson proposed that electrons rotated in coplanar rings within a positively charged sphere, which held almost all the atom’s mass. Early calculations suggested mechanical stability under the assumption of thousands of electrons per atom, and Thomson linked particularly stable electron configurations to the chemical properties of elements. He also developed an expression for beta scattering that seemed initially promising.
However, Thomson later demonstrated that atoms contained far fewer electrons than previously assumed, undermining the stability of his model. Moreover, the design could not account for the extensive structure observed in atomic spectral lines.

Rutherford’s Nuclear Model

Experimental results obtained by Hans Geiger and Ernest Marsden in 1908 showed that alpha particles occasionally scattered at very large angles when passing through thin metal foils. This outcome was irreconcilable with Thomson’s diffuse positive sphere. In 1911, Rutherford proposed a new model featuring a compact, positively charged nucleus containing most of the atom’s mass. Electrons were assumed to orbit this nucleus, but the model did not address how such orbits could remain stable or how atomic spectra arose.
Bohr’s early work explicitly built upon Rutherford’s nuclear structure but sought to incorporate quantum principles in order to overcome classical deficiencies.

Atomic Spectra and Quantum Constraints

Atomic spectra provided a powerful clue to the atom’s structure. Empirical relations such as the Balmer and Rydberg formulae described the wavelengths of light emitted by hydrogen with remarkable accuracy, yet their theoretical basis remained unknown. Classical models predicted spectral lines dependent on the square of vibrational frequencies, contradicting observed linear dependencies.
Advances by Arthur W. Conway and others suggested that individual electron oscillations might produce spectral series. Meanwhile, the Rydberg–Ritz combination principle demonstrated that spectral line frequencies corresponded to differences between characteristic terms later interpreted as quantised energy levels.
The old quantum theory, emerging between Planck’s work on blackbody radiation in 1900 and the advent of modern quantum mechanics in 1925, supplied the conceptual foundation for Bohr’s approach. Quantisation of energy, guided by Planck’s constant, provided a mechanism for stable electron orbits and discrete spectral transitions.

The Haas Model and Early Quantum Ideas

Arthur Erich Haas proposed a pioneering quantum model of the hydrogen atom in 1910. His design resembled Thomson’s sphere of positive charge but introduced the crucial idea that the electron’s potential energy on this sphere was linked to the Planck constant. By combining energy constraints with centrifugal balance, Haas identified a relationship between atomic dimensions and quantum constants. Although initially rejected, this model was discussed extensively at the 1911 Solvay Conference and anticipated several aspects of Bohr’s later formulation.
Bohr adopted similar equations but reversed the logic: instead of solving for the Planck constant using assumed atomic dimensions, he treated the constant as known and derived the radius of the hydrogen atom’s ground-state orbit. This radius is now termed the Bohr radius, a fundamental atomic constant.

Development of the Bohr Model

Bohr’s model introduced several key postulates:

• Electrons move in stable orbits around the nucleus without radiating energy.
• Only specific orbits with quantised angular momentum are allowed.
• Radiation is emitted or absorbed only when an electron transitions between these orbits, with the photon energy given by hν, the product of Planck’s constant and the frequency of the emitted radiation.

The radius of each permitted orbit increases as n², where n is the principal quantum number. Transitions between these levels produce spectral lines such as those in the Balmer series. The model successfully explained the origin of the Rydberg formula and provided theoretical justification for its constants by relating them to fundamental physical quantities.

Comparison with Other Models

The Bohr model represents a significant improvement over the Rutherford atom. It incorporates quantisation, avoids the instability predicted by classical electrodynamics, and matches observed spectral patterns. Nonetheless, it remains a simplified and approximate description of atomic structure. It is particularly effective for hydrogen and hydrogen-like ions, where a single electron is present. For multi-electron atoms, the model becomes inaccurate because it cannot account for electron–electron interactions or the full complexity of atomic energy levels.
Compared with later quantum mechanical models, the Bohr picture is primitive. Quantum mechanics, through Schrödinger’s wave equation and subsequent developments, offers a far more precise account, with electrons occupying orbitals rather than fixed circular paths. The Bohr model can be derived as a first-order approximation within full quantum theory, highlighting its pedagogical value even as an obsolete scientific theory.

Influence of the Solvay Conference and Subsequent Developments

The 1911 Solvay Conference played a formative role in directing early quantum research. Although Bohr did not attend, he read the conference proceedings and discussed their implications with Rutherford. The meeting focused on radiation theory and quantised oscillators, including debates on atomic composition. Hendrik Lorentz raised questions concerning models based on Haas’ ideas, highlighting the growing interest in integrating quantum principles.