On the quantum theory of radiation and the structure of the atom. Offprint from: Philosophical Magazine, 6th series, Vol. 30.

[London: Taylor & Francis], 1915.

First edition, author’s presentation offprint, inscribed by Bohr to his friend from student days and brother-in-law Poul Nørlund, of this important paper in which Bohr confronts experiments by Moseley and by Franck and Hertz, and introduces the seminal idea of a ‘stationary state’. “The central assumption [in the Bohr model] that ‘stationary electron orbits’ exist in atoms (and molecules) received justification in the crucial experiments of James Frank (1882-1964) and Gustav Hertz (1878-1975) in Berlin, although at the time the authors misinterpreted their results. They noted that ‘electrons in mercury vapor undergo elastic collisions with the molecules until they obtain a critical velocity, [and this] velocity is equivalent to the one obtained by electrons that have gone through a potential of 4.9 volts’ … Though the authors claimed until 1916 that the 4.9 V represented the ionization potential of mercury, [in the paper being offered] Bohr argued rather: ‘It seems that their experiments may possibly be consistent with the assumption that this voltage corresponds only to the transition from the normal state to some stationary state of the neutral atom’ [pp. 410-411] (our italics). Hence, he considered the Frank-Hertz experiment to give strong support to his atomic theory, and the experimentalists finally agreed with him. A decade later they received the Nobel Prize for physics ‘for their discovery of the law governing the impact of an electron upon an atom' and in particular for their verification of Bohr’s hypothesis of stationary states and the frequency condition’” (Brown, Pais, et al. Twentieth Century Physics). Bohr also showed in this paper that his theory supported Kossel’s interpretation of Moseley’s important findings about X-ray spectra. OCLC lists copies in US at Florida, Oregon State, Pierpoint Morgan and Smithsonian. One copy on ABPC/RBH.

Provenance: Inscribed in upper corner of front wrapper by Bohr, ‘Til Poul fra Niels’, to Poul Nørlund (1888-1951), historian and later director (1938-1951) of the Danish National Museum, and the brother of Bohr’s wife Margrethe. Bohr enrolled at the University of Copenhagen in 1903 where he was taught physics by Christian Christiansen and philosophy by Harald Høffding, a friend of his father. A group of 12 students began to meet after Høffding’s lectures to continue the discussion of various topics in philosophy. This group, which called itself ‘Ekliptika’, included Bohr and Poul Nørlund, as well as their brothers Harald and Erik, both mathematicians. Bohr met Poul’s sister Margrethe in 1910 and they were married two years later.

“A little after the publication of his trilogy [‘On the constitution of atoms and molecules’], Bohr expressed in private great doubts about the ‘horrid assumptions’ of his new theory and about the possibility of a generalization to systems more complex than the hydrogen atom or the harmonic oscillator:

‘I tend to believe that in this problem there are buried very considerable difficulties, which can be avoided only by departing from the usual considerations to an even greater extent than has been necessary up to now, and that the preliminary success is due only to the simplicity of the systems considered.’

“The main object of the 1913 trilogy was to develop a new ring model, a substitute for Thomson's models of atoms and molecules, in an endeavor to recover the properties of Mendeleev’s table of elements. This part of Bohr’s work was too speculative to receive unambiguous empirical confirmation. Nevertheless, in the years 1913-1914, various events improved Bohr’s confidence in the basic truth of at least part of his ‘horrid assumptions.’ These assumptions appeared to give the first germs of a successful theory of atomic spectra when applied to the spectra of one-electron systems (H, He+) and to the new field of X-ray spectra” (Darrigol, From c-numbers to q-numbers, pp. 89-90).

This theory was outlined in the present paper, which originated partly as a response to criticisms of Bohr’s 1913 theory by the British physicist John Nicholson (1881-1955), who was actually the first to propose that the momentum of electrons in an atom is quantized (Bohr openly acknowledged this point in all his early papers). “In this paper, probably due to Nicholson’s criticism, we find the first indication that Bohr’s theory could work only when applied to periodic systems. In connection with the discussion of the Stark effect [the splitting of spectral lines caused by an electric field], Bohr made the following remark [p. 404]:

‘In a discussion of such non-periodic orbits, however, the general principles applied are no longer a sufficient guidance.’

“Likewise new was his attempt to explain the two spectral systems of ortho- and parhelium by the assumption of different orbits of the innermost electron” (Collected Papers 2, pp. 334-335). The spectrum of helium consists of two complete systems of lines, the frequencies of each of which are given by a formula similar to the Balmer formula for the spectrum of hydrogen that had originally led to Bohr’s theory of atomic structure. Because of this helium had been assumed to be a mixture of two different gases, ‘orthohelium’ and ‘parhelium’, although all attempts to separate them had failed. Bohr now realised that the explanation was that the binding of the innermost electron can occur in two different ways.

“In addition, the Einstein-de Haas effect [the phenomenon whereby a change in the magnetic moment of a body can cause it to rotate] seemed to prove that there are indeed rotating electrons in the interior of the atoms, which, in accordance with Bohr’s fundamental assumption, do not radiate. Stark’s continued experiments showed that, in all cases to which Bohr’s calculation could be applied, there was an agreement between theory and experiment within an error of about 20%.

“Above all, in his paper of August 1915 [offered here], Bohr gave the correct interpretation of the Franck-Hertz experiments [as described above] ... Finally, Bohr took up W. Kossel’s ideas concerning the mechanism of the characteristic X-radiation” (ibid.).

In 1913, Bohr’s younger colleague at Manchester, H. G. J. Moseley (1887 – 10 August, 1915), observed and measured the X-ray spectra of various chemical elements (mostly metals) by the method of diffraction through crystals. Moseley discovered a systematic mathematical relationship between the wavelengths of the X-rays produced and the atomic numbers of the metals that were used as the targets in X-ray tubes. This has become known as Moseley’s law – it is similar to the Balmer formula for atomic spectra. “Walther Kossel (1888-1956), a young Munich physicist trained by Lenard in Heidelberg, adopted Bohr’s ring model of the atom but argued that the emission of X-rays was preceded by an ionization process that caused an inner ring to lose an electron. The resultant ‘hole’ would then be filled by an electron coming from an outer ring, with the energy difference between the rings appearing in the form of a distinct X-ray … The mechanism proposed by Kossel was quickly adopted by Bohr, who in 1915 [in the offered paper] introduced it to physicists with no command of German or without access to the Verhandlungen of the German Physical Society” (Kragh, Niels Bohr and the Quantum Atom, p. 107). Bohr pointed out in the present paper that Kossel’s theory predicts certain relations between the frequencies of the X-ray lines which are in agreement with Moseley’s measurements. He also noted that it explained some recent observations by W. L. Bragg on X-ray spectra.

Offprint from the Philosophical Magazine, vol. xxx, September 1915, pp. [i], 394-415 [1:blank], 8vo (222 x 145 mm), original printed orange wrappers, with inscription in Bohr's hand.

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