Bohr Uses Quantum Theory to Identify Atomic Structure

Niels Bohr applied the quantum theory to Ernest Rutherford’s nuclear model of the atom, providing a theoretical explanation for a variety of atomic phenomena and a program for further research.

Summary of Event

In the first decade of the twentieth century, physics was not dominated by the quantum, introduced by Max Planck in 1900, or by relativity, introduced in 1905 by Albert Einstein. Rather, it was dominated by the electron, discovered in 1897 by Sir Joseph John Thomson. Theoreticians and experimentalists were busy developing an electromagnetic view of the world in which a wide variety of physical phenomena were explained in terms of electrons, Electrons their motions, and their interactions with the “ether.” The successes of the electromagnetic view of the world were such that its proponents believed that eventually it could explain everything. Atoms;structure
Molecules, structure
Quantum theory
Bohr model of the atom
[kw]Bohr Uses Quantum Theory to Identify Atomic Structure (1912-1913)
[kw]Quantum Theory to Identify Atomic Structure, Bohr Uses (1912-1913)
[kw]Atomic Structure, Bohr Uses Quantum Theory to Identify (1912-1913)
Molecules, structure
Quantum theory
Bohr model of the atom
[g]Denmark;1912-1913: Bohr Uses Quantum Theory to Identify Atomic Structure[02970]
[c]Science and technology;1912-1913: Bohr Uses Quantum Theory to Identify Atomic Structure[02970]
[c]Physics;1912-1913: Bohr Uses Quantum Theory to Identify Atomic Structure[02970]
Bohr, Niels
Rutherford, Ernest
[p]Rutherford, Ernest;nuclear model of the atom
Thomson, Joseph John
Darwin, Charles Galton

A number of atomic models were developed during this period, but there was little concern for working out the details. The atomic model developed by Thomson was widely accepted. It consisted of a set of coplanar rings of electrons moving within a uniformly positively charged sphere. The electrons in Thomson’s model made up much of the mass of the atom. Unlike other atomic models, Thomson’s model had the advantage of mechanical stability: Electrons slightly displaced in the plane of their orbit would not tear the atom apart.

It was in this intellectual atmosphere that Niels Bohr completed his doctoral dissertation in 1911 on the electron theory of metals. Electron theory of metals Bohr spent the first part of the academic year 1911-1912 in Cambridge, England, with Thomson. He then went to Manchester in the spring of 1912 to work with Ernest Rutherford, who had recently proposed a model of the atom in which a positively charged nucleus much smaller than the size of the atom is surrounded by electrons. (Contrary to Thomson’s model, in Rutherford’s model, much of the mass of the atom is located in the nucleus.) Bohr began a normal course of laboratory exercises, and by the end of May, 1912, he was still working primarily on the electron theory of metals and not on the central problems of radioactivity and Rutherford’s nuclear model.

Bohr read a paper by Charles Galton Darwin (grandson of the evolutionist Charles Darwin), who was also working with Rutherford at Manchester, concerning the absorption by matter of “alpha particles” (helium atoms with both electrons removed). Bohr noticed an error in Darwin’s study and began compiling his own ideas. He developed an analogy between the passage of alpha particles through matter and his own work on the electron theory of metals. The problem of the mechanical stability of Rutherford’s model appeared when Bohr tried to calculate the effect of a passing charged particle on the electron’s orbit. The question of stability was important because of the way Bohr solved it: by fiat. As classical mechanics could not provide a condition of stability for Rutherford’s model, Bohr turned to Planck’s quantum theory. Bohr assumed that for stable orbits of electrons, there exists a definite ratio between the kinetic energy of the electrons in an orbit and their frequency of rotation. The value of this ratio is Planck’s constant. Planck’s constant[Plancks constant] Bohr called these stable orbits “stationary states.”

In Bohr’s model of the atom, electrons orbit the nucleus in discrete energy states. When an electron moves from a higher energy orbit to a lower-energy orbit, the extra energy is released as a photon of light.

Bohr submitted these ideas to Rutherford in a memorandum, but that document was not discovered until after Bohr’s death in 1962. This was only a beginning: Many aspects essential to Bohr’s completed theory had yet to appear. The material in this memorandum reappeared in the second and third parts of Bohr’s trilogy of papers.

Bohr knew he was on the right track when he was able to fit the large number of “radioelements” Radioelements (elements chemically similar to known elements but with vastly different radioactive properties) into the periodic table. He suggested that radioactive properties could be relegated to the nucleus, whereas chemical properties were the result of the number of electrons in an atom. The radioelements could then be explained as elements that had heavier nuclei than usual. This would give the radioelements different radioactive properties but would keep their same chemical properties. Bohr also demonstrated that atomic number—and not atomic weight—governs the chemical properties of the elements. Bohr’s theory also gave a straightforward explanation of the well-known periodicity of chemical elements.

Bohr grappled in late 1912 with John W. Nicholson’s Nicholson, John W. earlier atomic theory, which included Planck’s quantum, and an explanation of the spectra of atoms. In the late nineteenth century, astronomers noticed lines, or gaps, in the spectrum of light from the sun. Further investigation showed that each element had its own unique set of lines. Johann Jakob Balmer Balmer, Johann Jakob developed a formula that accounted for known frequencies, but this equation had no physical significance. Nicholson’s theory accounted for experimental results quite well. Bohr was briefly troubled by the inconsistencies between his theory and Nicholson’s, but by early 1913, he had resolved the inconsistencies.

Up to this time, Bohr had considered atoms only in their lowest energy state. In Nicholson’s theory, electrons in the atom could have energies greater than the lowest energy possible. Bohr saw a use for Nicholson’s idea of using the higher energy levels and incorporated them into his theory. Adapting Nicholson’s theories gave Bohr his most distinct break with classical physics. It was widely believed that the mechanical frequency of the electron as it orbited the nucleus was equal to the frequency of the spectral line that atoms would emit. Instead, Bohr equated the differences in the frequencies of two stationary states of the atom with the frequency of the emitted spectral line. Electrons jumping from one stationary state to another emitted radiation with a frequency independent of the electron’s mechanical frequency.

In a letter to a colleague written in February, 1913, Bohr indicated that he had completed work on the topics that were eventually to compose the second and third published parts of the trilogy: the periodicity of the elements, the volume of the atoms, the conditions of atomic combination, energies of X rays, dispersion, and radioactivity.

During February and March, Bohr included a discussion of the spectra of atoms. He had, in fact, ruled out consideration of the optical spectrum. What led him to include spectra was his realization that his theory could explain Balmer’s formula, which was expressed as a difference of two quantities. Bohr associated that difference with the difference in frequency of two stationary states.

Niels Bohr.

(The Nobel Foundation)

Bohr managed to solve the problem of spectra in a manner that was convincing to him, but he had yet to provide a mathematical derivation of his results. In the early part of the first paper of the trilogy, Bohr provided three such derivations; however, they were incompatible because Bohr compiled his results on spectra with great speed. The draft of the first part of the trilogy that Bohr sent to Rutherford in early March was modified only slightly and was published in July, 1913. The second and third parts of the trilogy, published in September and November of 1913, presented solutions to the problems contained in the Rutherford memorandum.


Immediate reactions to Bohr’s trilogy were mixed. Many physicists still did not consider Planck’s quantum to have any physical significance. Those who, like Nicholson, were willing to consider the quantum questioned portions of Bohr’s approach. In particular, in the second and third parts of his trilogy, Bohr extended his theory to atoms with more than one electron. Although Bohr tried to present quantitative support for the result, he often had to rely on qualitative arguments to achieve the correct results. Even the first part did not escape criticism for its incompatible derivations of Balmer’s formula and its tradition-breaking assumptions about atoms.

Acceptance increased, however, as Bohr’s theory accounted for details of spectra that had eluded explanation by other models. An early victory was Bohr’s attribution of a set of spectral lines called the “Pickering series” to ionized helium instead of to hydrogen. Spectroscopists examined helium and found the lines. The agreement between Bohr’s prediction and the experimental results was numerically very close.

What became known as the “correspondence principle” Correspondence principle appeared in the first part of the trilogy. It became an important tool in the early development of quantum theory. The correspondence principle asserted that the results of quantum mechanics do not conflict with those of classical mechanics in the realm where classical mechanics is valid. In practice, the correspondence principle was used as a tool in order to justify using the results of classical mechanics in the calculation of quantum mechanical properties. Through the use of this principle, Bohr’s original theory was extended to other areas. The long-term impact of Bohr’s trilogy on physics and physicists can be gauged from the comment of one of Bohr’s fellow physicists: “There is hardly any other paper in the literature of physics from which grew so many new theories and discoveries.”

Bohr’s groundbreaking trilogy of 1913, although flawed, made way for quantum mechanics. Bohr’s trilogy was generally considered to be conceptually confusing in places but able to make remarkably accurate predictions for single-electron atoms. Bohr’s predictions began to break down when applied to atoms with more than one electron, and some problems associated with spectral lines resisted solution. Also, although Bohr’s ideas on atomic structure in the second and third papers were highly suggestive, many of the details were incorrect. He returned to atomic structure around 1920 and presented a consistent theory.

Bohr not only continued to contribute to many aspects of physics but also played a major role in educating the new generation of physicists who went on to develop quantum mechanics. Although well known among physicists, Bohr never became as well known to the public as Einstein. His trilogy represents only the first stage of a scientific career that spanned more than fifty years. Atoms;structure
Molecules, structure
Quantum theory
Bohr model of the atom

Further Reading

  • Bohr, Niels. On the Constitution of Atoms and Molecules. New York: W. A. Benjamin, 1963. Reprints Bohr’s trilogy of papers. Includes an introduction by the physicist Leon Rosenfeld. Moderately technical, but an essential source for information about Bohr and the science of his day.
  • _______. “Reminiscences of the Founder of Nuclear Science and Some Developments Based on His Work.” In Rutherford at Manchester, edited by J. B. Birks. London: Heywood, 1962. Paper originally presented at a meeting of the Physical Society of London. Gives Bohr’s nontechnical version of how he developed his theory.
  • Cropper, William H. Great Physicists: The Life and Times of Leading Physicists from Galileo to Hawking. New York: Oxford University Press, 2001. Presents portraits of the lives and accomplishments of important physicists and shows how they influenced one another with their work. Chapter 16 is devoted to Niels Bohr. Includes glossary and index.
  • French, A. P., and P. J. Kennedy, eds. Niels Bohr: A Centenary Volume. Cambridge, Mass.: Harvard University Press, 1985. Discusses Bohr’s early years in a manner accessible to the general public, professional physicists, and teachers of science.
  • Heilbron, John L., and Thomas Kuhn. “The Genesis of the Bohr Atom.” Historical Studies in the Physical Sciences 1 (1969): 211-290. Attempts a plausible and comprehensive treatment of Bohr’s route to the quantized atom. Critically synthesizes suggestions in the existing literature and elaborates some previously neglected strands in Bohr’s scientific development. Moderately technical.
  • Moore, Ruth. Niels Bohr: The Man, His Science, and the World They Changed. 1966. Reprint. Cambridge, Mass.: MIT Press, 1985. Although historians have questioned some of the interpretations of events in this book, it remains one of the most popular works on Bohr and his science.
  • Polkinghorne, John. Quantum Theory: A Very Short Introduction. New York: Oxford University Press, 2002. Aims to make quantum theory accessible to the general reader. Among the concepts discussed are uncertainty, probabilistic physics, and decoherence. Includes mathematical appendix and index.
  • Rozental, Stefan, ed. Niels Bohr: His Life and Work as Seen by His Friends and Colleagues. 1967. Reprint. New York: Elsevier, 1986. Succeeds in its attempt to describe the scientific work of Niels Bohr so that it is understandable to members of the general public. Conveys the depth of respect Bohr received from his fellow physicists.

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