Niels Bohr and the Quantum Atom: The Bohr Model of Atomic Structure 1913-1925

206 Pages·2012·13.395 MB·English

by  Helge Kragh

NIELS BOHR AND
THE QUANTUM
ATOM
The Bohr Model of Atomic Structure
1913-1925
HELGE KRAGH
Aarhus University, Denmark
OXFORD
UNIVERSITY PRESS
OXFORD
UNIVERSITY PRESS
Great Clarendon Street, Oxford OX2 6DP,
United Kingdom
CONTENT
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© Helge S. Kragh 2012 Preface iv
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1. Atomic Theories Before 1913
First Edition published in 2012
Impression: I 2. On the Constitution of Atoms and Molecules 39
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7. A Theory of the Chemical Elements 271
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Preface v
While technical in places, the book offers a broader picture of Bohr's theory than the
one which can be found elsewhere in the scholarly literature. Thus, it deals extensively
PREFACE with the reception of the theory (Chapter 3) and also with the criticism launched against
it by physicists of a more conservative inclination (Section 4.5). To get a full impression
of a new scientific theory, one needs to look not only at its followers but also at its
critics. Bohr's theory scored its most important victories in atomic structure and related
Modern physics is essentially based on a remarkable series of discoveries and theories
spectroscopic experiments, which were also the fields that led to its decline in about
dating from the two decades between 1895 and 1915. Integrating Rutherford's nuclear
1924. However, as originally conceived it was not limited to the domain of atomic
model with elements of Planck's quantum theory, Niels Bohr's theory of the atom
architecture but was ambitiously announced as a theory of the constitution of matter,
paved the way for the later quantum mechanics, but the atomic theory itself had but a
whether atomic or molecular. The chemical aspects of Bohr's theory are rarely given
short lifetime. This makes it only more attractive from a historical point of view,
much attention in the writings of either physicists or historians of science, which in my
because one is able to follow the theory through its entire life, from its birth in 1913
view tends to distort the overall picture and impact of the theory. Molecular spectros
through its adolescence around 1918 to its declining years in 1924-1925. The present
copy was almost as important in the development as atomic spectroscopy, and the
work is largely limited to this period. It is a fairly detailed and complete account of how
views of the chemists are as enlightening as those of the physicists. Major parts of the
a most important scientific theory came into being, how it was further developed, and
Chapters 6 and 7 deal with the chemical aspects and the ways in which the chemical
how it eventually was abandoned to be replaced by an even better theory that in
community responded to the theory.
important ways built on it. Of course, this better theory is still with us.
The book is chronologically organized, describing how Bohr and his colleagues,
The book is written in connection with the 2013 centennial of Bohr's theory, which
especially in Germany, thought about and developed the surprising new quantum
does not, however, imply that it is of a celebratory nature. Although there are good
theory of atoms. It starts however with a chapter outlining earlier atomic theories
reasons to celebrate Bohr and his theory, these reasons are not what motivated the
that to some extent, if mostly indirectly, provided the background for Bohr's break
book. It is primarily a detailed history of Bohr's atomic theory and only secondarily
through in 1913. Of these earlier theories, the nuclear atom of Rutherford was of direct
about the physicist who created the theory. In other words, it is not biographical,
and crucial significance to Bohr, while].]. Thomson's mechanical model of the atom
although it can perhaps be characterized as a biography of a scientific theory. Because
and later J. Nicholson's atomic model inspired him in both a positive and negative
this theory was the brainchild of and so intimately connected with the physicist Niels
sense. Bohr's theory was highly original, but of course it was not created out of nothing.
Bohr, he cannot avoid appearing prominently throughout the book. If there is another
The picture of the young Bohr that emerges in this book is one of an extremely hard
main figure in the book, it will be Arnold Sommerfeld, the German physicist who did so
working, competitive, ambitious, and determined physicist. In his later years Bohr
much to promote and develop Bohr's ideas.
became a quantum sage, the oracle from Blegdamsvej in Copenhagen, and is often
The historical study of Bohr's theory of atomic structure is far from new. In fact,
portrayed as more a philosopher than a physicist. Although Bohr in a sense always
some of the finest historical studies, due in particular to Leon Rosenfeld, John Heilbron,
thought 'philosophically' about foundational problems in physics, in his younger days
Thomas Kuhn, Paul Forman, and Ulrich Hoyer, were published less than a decade after
he was unquestionably and solely a physicist. He was a visionary physicist, but his
Bohr's death in 1962. Since then, historians of science have continued to investigate the
visions were restricted to the realm of physics. Although a theorist, he was almost
old quantum theory of atoms, molecules, and radiation, but at a slower pace. Of course,
obsessively occupied with experimental tests, which to him counted more than (but
the present book draws on the extensive secondary literature, including some papers I
were not, of course, contrary to) philosophical reflections. His famous correspondence
wrote on the subject many years ago. Niels Bohr and the Quantum Atom aspires to give a
principle, which is detailed in Chapter 5, could not be tested experimentally, yet its
comprehensive picture of the theory in all its major facets, although with a focus on
consequences could and were tested. The correspondence principle is one of the most
those parts of the theory which were due to Bohr or in which he was significantly
fascinating parts of Bohr's theory, not least because it was so closely connected to his
involved. It is impossible to write such a history without taking into regard the complex
personal way of thinking. It was a prime example of what Einstein called Bohr's
technical and conceptual matters that were in many ways the very heart of the theory.
'musicality' and 'unique instinct and tact'.
On the other hand, I do not deal with technicalities for the sake of technicalities.
From a philosophical point of view, the Bohr atom of the old quantum theory is far
A substantial part of the book will be accessible to readers with no background in
physics. less interesting than the mature quantum mechanics that emerged in 1925 and since
then has served as a stable foundation of physics. Indeed, during the lifetime of the Bohr
atom it was ignored by professional philosophers, many of whom may have been
vi
Preface
unaware of it. All the same, later philosophers have taken a keen interest in Bohr's
theory and analyzed it from different points of view. In an appendix of the book
(Chapter 9) I offer an overview of some of these considerations, which include how
Bohr's theory appears in the theories of scientific development argued by T. s. Kuhn,
1
I. Lakatos and other philosophers. I am well aware that this topic is covered onl
incompletely and provisionally. y
An important source for any serious study of Bohr's physics is the many letters that
are preserved a.t the Niels Bohr Archive in Copenhagen, appropriately located in the Atomic Theories Before 1913
histonc mstitut10n that was established for Bohr in 1921. Some of these letters, if far
from all of them, are reproduced in the invaluable 12-volume series Niels Bohr's Collected
Works (1972-2007), the first volumes of which I have used extensively. I am grateful to
Fmn Aaserud, director of the Niels Bohr Archive, for granting me access to the rich
The first really successful theory of atomic structure was proposed by Niels Bohr in an
materials included in the archive. Much of this material, if not all of it, is included in the
epoch-defining paper in Philosophical Magazine of July 1913. It was this theory that
Archive for History of Quantum Physics to which I have had electronic access through
established atomic theory as a fundamental and progressive field of physics intimately
the Max Planck Institute for History of Science in Berlin.
connected with spectroscopy and the new and still mysterious quantum theory. But
Helge Kragh although rational atomic theory, in the sense of a scientific theory dealing with the internal
Aarhus University, Denmark structure of the atom, dates from the beginning of the twentieth century, ideas of complex
atoms and their structure can be found much earlier. 1 Many of the theories of this earlier
period were speculative suggestions with little or no foundation in experiment. Some of
them were of a philosophical rather than scientific nature. They were all short-lived, but of
course some of the theories lived longer and were developed to a higher level than others.
The vortex theory of the second half of the nineteenth century and].]. Thomson's
electron theory were among the more successful of the pre-Bohr atomic theories. The
Bohr atom, revolutionary as it turned out to be, was part of a long tradition in atom
building and to some extent influenced by earlier conceptions of atomic architecture.
It is important to realize that until about World War I atomic theory was not only a
small field of physics, it was also not highly regarded in the physics community. It is
telling that at the first (and only) International Congress of Physics, held in Paris in 1900
in connection with the World Exhibition, only one of the 92 invited papers, namely the
one of]. ]. Thomson, dealt explicitly with atomic structure. The models proposed in
the early period were rarely meant to be realistic pictures of the atom, but merely
illustrations of mechanisms that might help in understanding some aspect or other of
physical phenomena. Referring to the period around 1910, it has been said that 'for the
average physicist of the time, speculations about atomic structure were something like
speculations about life on Mars- very interesting for those who liked this kind of thing,
but without much hope of support from convincing scientific evidence and without
much bearing on scientific thought and development'.2 A decade later the situation was
quite different, the change in attitude being to a large extent a result of Bohr's quantum
theory of atomic structure.
Not only were internally structured atoms not universally accepted in the first decade
of the twentieth century, there was in the period still scattered opposition to the very
existence of atoms and molecules, ranging from uncompromising anti-atomism to
2
Niels Bohr and the Quantum Atom
Atomic Theories Before 1913 3
cautious scepticism. Some positivistic minded physicists and chemists, including Pierre
All the same, the general idea of a material unity in nature-that all matter ultimately
Duhem in France, Ernst Mach in Austria, and Georg Helm and Wilhelm Ostwald in
consists of structures made up of a primitive particle or protyle-remained popular. The
Germany, rejected a realist interpretation of atomic theory. The unobserved atoms
hypothesis was widely conceived as too attractive to be wrong. The ~ntroduct10n of
might be heuristically useful concepts, but they regarded them as 'metaphysical' rather
spectroscopy and the periodic system of the elements inspired further interest m neo
than real constituents of matter. Although opposition was declining, in 1913 Jean Perrin
Proutean hypotheses, which more often than not were seen in connection with the
in France still felt it necessary to emphasize that atoms do exist and that the opponents
evolutionary worldview that was so popular during the Victorian era.
of the atomic theory, 'which until recently were numerous, have been convinced and
In some cases atomic speculations related to the Proutean tradition had a distinct air
have abandoned one after the other the sceptical position that was for a long time
of Pythagoreanism, as in the works of the Danish-American chemist and polymath
legitimate and no doubt fruitful'.3 This was true in the case of Ostwald, who in 1908
Gustavus Hinrichs, one of several precursors of the periodic system. Hinrichs, who
admitted the existence of atoms, but not in the cases of Duhem and Mach: they both
combined his atomic theory with numerological considerations of spectroscopic and
died in 1916, convinced that atoms were nothing but constructs of the human mind.
astronomical data, was convinced that all chemical elements were composed of a single
In 1913-the year that Bohr published his atomic theory-Duhem criticized the
substance. 6 For this basic element he proposed the name pantogen, assuming it to have
confidence with which the 'school of neo-atomists' spoke of their hypotheses of the
an atomic weight of either 0.5 or 0.25. While Hinrich's works were not well known, and
inner structure of matter. 'We do not share this confidence', he wrote. 'We are not able
'pantogen' never caught on, somewhat similar ideas were suggested by several leading
to recognize in these hypotheses a clairvoyant vision of what there is beyond sensible
scientists in England in particular. The astronomer Joseph Norman Lockyer and the
things; we regard them only as models.'4 Bohr, too, regarded his theory of the atom as a
chemists William Crookes and Thomas Carnelley were among the most articulate and
model. The crucial difference was it was not only a model, but a model of something
visionary advocates of evolutionary neo-Prouteanism. However, although this tradition
that really existed. As to Duhem, he never mentioned Bohr's atomic theory, of which
in speculative atomic theory significantly influenced the first electron models of the
he may have been unaware.
atom, it did not include definite models of the composition of atoms. Moreover, neo
Prouteanism and related ideas were mainly of interest to chemists, astronomers and
amateur scientists, whereas most physicists chose to ignore them. For this reason they
need not be further examined.
1.1 PRE-ELECTRON ATOMIC SPECULATIONS
Models of the internal architecture of atoms were proposed many years before the
discovery of the electron. Some of them were based on hypothetical electrical particles,
The Daltonian atom of the early nineteenth century was a primitive elementary body
while other models assumed neutral but equally hypothetical subatomic constituents.
with no internal constitution, the atoms of the different elements having nothing
These early atomic models had in common that they were speculative, and some of
structural in common. What distinguished a hydrogen atom from an atom of lead
them very much so, and also that they made very little impact on mainstream science.
was solely its atomic weight, a measurable property. Although this was the kind of
In some cases they were merely casual speculations of a philosophical nature. For
atom that appealed to most chemists, from an early date there were suggestions that
example, this was the case with the ideas of the Danish physicist and engineer Ludvig
the atoms themselves were somehow complex bodies. The English physician and
August Colding, who is better known for his contributions to 'the imperishability of
chemist William Prout argued in 1815-1816 that the atomic weights indicated a
forces' or what became known as the law of energy conservation. In an unpublished
common composition of the elements, namely that all atoms were made up of unit
note of 1854, he pictured atoms, or what he called 'molecules', as analogous to
particles, which he identified with hydrogen atoms. Prout's hypothesis was taken up
planetary systems. 'Many facts seem to me to indicate that every molecule constitutes
and modified in various ways by several chemists, first and most effectively by the
an infinitely small planetary system, be it with or without a central body', he wrote.
Scotsman Thomas Thomson who promoted it in a work of 1825 ambitiously entitled
'Each of these small planets has a characteristic rotation about its axis, and this rotation
An Attempt to Establish the First Principles of Chemistry by Experiments. However, the
determines both the electric tension and magnetic polarity of the particle.'7
hypothesis remained controversial throughout the century and was rejected by leading
By the mid-nineteenth century the ether was generally assumed to play an important
chemists from Berzelius to Mendeleev.5 Not only was it speculative, but increasingly
role in microphysics, whether based on atoms or not. While the ether was usually
accurate determinations of the atomic weights contradicted the original form of the
considered a homogeneous imponderable medium, there was no scarcity of ideas
hypothesis. Thus the atomic weight of chlorine turned out to be close to 35 .5 (in terms
assuming other forms-for example a corpuscular ether. To get an impression_ of
of the weight of hydrogen), a value which evidently posed problems for believers in
Prout's hypothesis. mechanical ether atoms in the speculative tradition, consider the ideas of two scientists
from German-speaking Europe. In 1857, Ferdinand Redtenbacher, an Austrian-born
Atomic Theories Before 1913 5
4 Niels Bohr and the Quantum Atom
Let e be the positively charged electrical particle, and let the negative particle, carrying an
director of the Polytechnic College in Karlsruhe, announced an atomic theory based on
what he called 'dynamids'.8 According to his model, matter consisted of ponderable opposite charge of equal amount, be denoted -e. Let only the latter be associated with the
massive atom, whose mass is so large that the mass of the positive particle may be
atomic particles surrounded by shells of imponderable ether. The material particles
considered negligible. The particle -e may then be considered as being at rest, while just
were kept together by a hypothetical mechanical force analogous to Newtonian
the particle e moves around the particle -e. 12
gravitation, while the ether particles were assumed to be mutually repulsive and
attracted by the massive atomic core. It was such a system of a massive core and Weber came to the conclusion that the chemical elements were composed of an equal
minute ether particles, arranged in shells, that he called a dynamid. Redtenbacher number of positive and negative particles revolving around each other and possibly also
related his dynamid theory to contemporary ideas of heat, gases, elasticity, and optics, performing vibrations. In this way he thought that the mass might be explained in terms
and discussed on this basis various expressions for the dispersion of light. It was a of electricity and that an understanding of the periodic system was within reach.
speculative atomic theory, but one with physical applications. Moreover, he speculated that the chemical elements, if they were composites of
About thirty years later the respected Swiss botanist Carl Wilhelm von Nageli electrical particles, might possibly be decomposed into lighter elements. The dream
proposed a detailed atomic theory that had some qualitative features in common of the alchemists received justification from electrodynamics! According to Maxwell's
with the older one of Redtenbacher, in particular that it was based on a corpuscular electromagnetic field theory a circulating electrical particle would lose energy and
ether governed by mechanical forces of both a repulsive and attractive nature.9 Nageli hence cause the atom to become unstable and eventually collapse, but this problem
pictured the atom as a tightly packed system of billions of tiny ether particles ('amers'), (which later appeared prominently in atomic theory) did not appear in Weber's
some of which were ponderable and would therefore tend to agglomerate into an alternative theory.
atomic core. The ponderable ether core was surrounded with an ether atmosphere of Independent of Weber, Robert Grassmann, a brother and collaborator of the mathe
density decreasing with the distance, a Schwerii.therhulle. According to Nageli, his matician Hermann Grassmann, developed somewhat similar ideas of ether atoms
etherial atomic model offered an explanation of several chemical problems, including consisting of electrical doublets. He considered chemical atoms to be composed of a
the nature of affinity and the combination of atoms into molecules. He also thought positive particle surrounded by a spherical shell of polarized ether doublets. Although
that it was suggestive with regard to physiology and biology in general. Robert Grassmann's ideas received little attention, they were critically reviewed by the
From about 1850 views of ether and matter became increasingly based on electrical physicist and pioneering psychologist Gustav Fechner, a close friend of Weber and
rather than mechanical theory. One of the first suggestions of electrical atoms was himself an advocate of atomism.13 Fechner had for a long time been interested in
made by Richard Laming, an English physician and amateur physicist, who between atomic theory, both in its scientific and philosophical aspects. As early as 1828 he
1828 and 1851 postulated the existence of subatomic, unit-charged particles. According suggested a dynamical model of the atom in close analogy to the solar system and
to Laming, the atom was composed of a material core surrounded by an 'electrosphere' governed by Newton's law of gravitation. The atoms, he said in this early work,
of concentric shells of electrical particles of both charges. 10 This kind of corpuscular 'simulate in small dimensions the situations of the astronomical objects in large
electrical theory was unusual in England but fairly popular among those German dimensions, being animated m. any case b y t h e same ico rces '1. 4
physicists in favour of electrical actions propagating instantaneously over a distance. The theories of Weber, Grassmann, and other German scientists were based on
In 1846 a fundamental force law of this kind was proposed by Wilhelm Weber, who at hypothetical electrical particles. When the electron was turned into a real particle at the
the time served as professor of physics in Leipzig. Weber conceived his force law as the end of the century, physicists were generally puzzled that it existed in a negative form
core of a unified theory of the future that might possibly lead to an explanation of all of only. The neutrality of the ether seemed to require complete charge symmetry and yet
nature. By the 1860s he had developed an electrical theory according to which the the positive electron was conspiciously missing. Apparently without knowing of the
neutral ether consisted of positive and negative particles orbiting around each other. earlier work of Weber and Grassmann, the British-Australian physicist William Suther
Moreover, he extended his picture of the ether to an analogous picture of the chemical land suggested in 1899 that the ether consisted of doublets of negative and positive
atoms.11 electrons held tightly together, particles for which he coined the name 'neutron'. As he
In his later work, some of it unpublished and of a fragmentary nature only, Weber wrote in a paper two years later, 'In the free <ether the positive and negative electron
considered the ponderable atom to be structured like a planetary system, with a large revolving ... round their centre of inertia form what I have proposed to call the
number of tiny electrically charged particles revolving around a heavy massive part. neutron, the electric doublet, which gives the <ether its chief electric and magnetic
The system was kept together by electrical forces satisfying his force law. In a paper of properties'.15 By that time atomic models were no longer based on purely hypothetical
1871 he explained: entities. It was now generally agreed that atoms contained a large number of electrons,
6
Niels Bohr and the Quantum Atom
Atomic Theories Before 1913 7
all of them carrying the same negative charge, but there was no agreement as to the
said, 'is that its success in explaining phenomena does not depend on the ingenuity with
number or arrangement of the electrons.
which its contrivers "save appearances", by introducing first one hypothetical force and
then another'.18
Among those who found the vortex atom attractive was also the mathematician and
statistician Karl Pearson, who however preferred an alternative version of the ultimate
1.2 FROM VORTEX ATOM TO ELECTRON ATOM
tom. In 1885 he proposed than an atom might be a differentiated spherical part of the
a 19
ether, or perhaps a vacuum within the ether, pulsating with a natural frequency. He
The atomic model developed by the famous Cavendish physicist Joseph John Thomson
found the conception of spherical atoms to be promising with respect to the under
in the early years of the twentieth century can with some justification be called the first
standing of a wide range of phenomena, including chemical affinity and spectral lines.
modern model of the atom. Contrary to earlier models it was based on an experimen
Six years later he modified his ideas into a theory of 'ether squirts', point atoms from
tally known entity, the electron, and for this and other reasons it could be subjected to
which ether continuously flowed into space.20 In addition to the ether squirts, acting as
experimental tests. While Thomson's electron dates from his celebrated investigation of
points of positive matter, he postulated the existence of negative matter in the form of
cathode rays in 1897, his electron atom did not simply grow out of these experiments.
sinks that absorbed ether. Although Pearson developed his ambitious atomic ether
There were other and even more important roots, for Thomson had for several years
theories in considerable mathematical detail and attempted to link them to experimen
been convinced that the atom was a complex body made up of a single primordial
tal knowledge, compared to the vortex atom they attracted very little interest.
particle or substance. He was in important respects a loyal follower of Prout, a heritage
In a prize essay of 1882 young].]. Thomson examined theoretically the question of
he proudly admitted. Moreover, as a theoretical entity the electron antedates the 1897
the stability of vortices arranged at equal intervals around the circumference of a
experiments, which explains why we can find ideas of electrons and electron atoms
circle.21 Using standard perturbation theory he found after lengthy calculations that
(as well as the name 'electron') in the literature even before that year. =
the configurations with n 2, 3, 4, 5, and 6 vortices would be dynamically stable, but
The leading electron theorist Joseph Larmor argued in 1894 that electrons-which he
that seven vortices on the same ring could not form a stable system. For larger n he
pictured as 'singular points in the ether'-were the primordial units of all matter. The
relied on an analogy with experiments with floating magnetized needles, which the
following year he went a step further, now suggesting 'a molecule [atom] to be made
American physicist Alfred Mayer, at the Stevens Institute of Technology in Hoboken,
up of, or to involve, a steady configuration of revolving electrons'.16 His picture was not
New Jersey, had made in 1878 (Figure 1.1). That Mayer's experiments could be taken to
unlike the one that Weber had earlier proposed on a non-Maxwellian and more
illustrate the periodic system of the elements had first been pointed out by Kelvin.
speculative basis. In 1894 Larmor did not make it clear whether or not he conceived
Although Thomson, like most other physicists, abandoned the vortex atom programme
of the electron as a subatomic particle, and it is quite possible that at the time he did not.
about 1890, the idea continued to guide him and appeal to him. Thus, in a paper of 1890
However, two years later he did.
he linked the periodic system with the vortex atomic model and pointed out the
Thomson's unitary idea of matter consisting of subatomic electrical charges owed a
suggestive similarity between an arrangement of vortices and the regularity found
debt to his general predisposition toward neo-Prouteanism and, in particular, to his
among the chemical elements.
earlier work on the vortex theory of atoms. According to this theory, first proposed by
The vortex atom approach greatly influenced Thomson's thinking about the
William Thomson (Lord Kelvin) in 1867, atoms might be conceived of as vortical
complexity of the elements. In 1897 he no longer thought of the vortex atom as a
modes of motion in a perfect, all-pervading fluid.17 The fluid was generally taken to be
realistic model, yet his new primordial particle, the electron, had more than a little
identical to the ether. For about two decades the ambitious and mathematically
similarity with the vortices of the old theory. In his seminal paper of October 1897,
complex vortex theory attracted much interest among mathematically inclined British
Thomson suggested that that the atom consisted of a large number of electrons
physicists, including Peter G. Tait, Augustus Love, William Hicks, Micaih Hill, and]. J.
(which he insisted on calling 'corpuscles'), possibly held together by an unspecified
Thomson. It was applied to a variety of physical and chemical problems, such as line
central force. In this first version of the Thomson model, the atom was pictured as just
spectra, affinity, chemical combination, the behaviour of gases, and even gravitation.
an aggregation of electrons and so, assuming Coulomb forces between the electrons,
Although not convinced of its truth, Maxwell was full of praise of the vortex theory
there was no attractive force to keep the atom from exploding. Thomson had to
because of its methodological virtues and ontological parsimony. In a deservedly
invent the needed attractive force, and this he did. 'If we regard the chemical atom as
famous article on 'Atom' for the 1875 edition of Encyclopaedia Britannica, he singled
an aggregation of a number of primordial atoms [electrons]', he wrote, 'the problem
out Kelvin's vortex model as by far the most attractive picture of atomic constitution.
of finding the configurations of stable equilibrium for a number of equal particles
'The greatest recommendation of this theory, from a philosophical point of view', he
acting on each other according to some law of force ... is of great interest in
8 Niels Bohr and the Quantum Atom Atomic Theories Before 1913 9
It was this picture that Thomson developed into a quantitative and sophisticated atomic
model over the next few years (Section 1.4). In his book Electricity and Matter, based on
the Silliman lectures he gave at Yale University in May 1903, he provided a full if mostly
qualitative account of the theory.
Thomson's model was the most important of the electron atomic models of the early
twentieth century, but it was not the only one. Shortly after Thomson's announcement
of the cathode-ray electron in the spring of 1897, Kelvin suggested his 'Aepinus atom',
named after Franz Aepinus, a eighteenth-century natural philosopher from Germany
who had pioneered a one-fluid electrical theory. Kelvin pictured the atom as a number
of' electrions' embedded in a globe of positive electricity, a picture which had much in
common with Thomson's but nonetheless differed from it. For example, Kelvin's
hypothetical electrions did not have the same mass and charge as the electrons, and
they were thought to be subject to an ad hoc force law more complicated than the
ordinary Coulomb force. In work between 1902 and 1907 Kelvin applied the Aepinus
model in an attempt to explain or illustrate the puzzling phenomenon of radioactivity,
which according to him was probably triggered by etherial waves or some other
external agency.24 Very few physicists found the Aepinus model to be of any value.
In spite of being the most elaborate attempt of the period to explain radioactivity in
intra-atomic terms, and in spite of being proposed by a physicist of the highest possible
Fig. 1.1. Mayer's experiments with magnetized needles. To the left,].]. Thomson's illustration in distinction, the ideas of the aging Kelvin had almost no impact on the further develop
Thomson. 1907, p. 111. To the right, some of Mayer's magnet configurations. Some of the ment of atomic theory. British physicists referred respectfully to it, but without taking it
configurations are unstable. For example, five needles may arrange themselves in a square with a
seriously or developing it.
central needle but a slight mechanical disturbance will make the system turn into the stable
pentagon configuration. In his book Electrons of 1906, the physicist Oliver Lodge, then at Birmingham
University, surveyed the various candidates of atomic structure at the time. Apart
connection with the relation between the properties of an element and its atomic from the ideas of the Thomson-Kelvin type he mentioned the possibility that the
weight'.22
atom 'consists of a kind of interlocked admixture of positive and negative electricity,
In 1897 Thomson only knew the charge-to-mass ratio elm of the cathode ray indivisible and inseparable into units'.25 This may have been a reference to the picture
electrons and therefore had to assume that the particles were subatomic, with a charge of the atom favoured by Philipp Lenard, at the time professor of physics at the
numerically equal to that of the hydrogen ion. Two years later the assumption was University of Kiel and the recipient of the 1905 Nobel Prize for his work on cathode
confirmed when he and his research students at the Cavendish Laboratory succeeded in rays. Based on his studies of the absorption of cathode rays in gases, Lenard suggested
determining the charge of the electron, which led to a mass for the particle of the order in 1903 that the interior of the atom was mostly empty space.26 To explain the
of one-thousandth of a hydrogen atom. The same year, in an address to the British experimental results he assumed the atom to be composed of impenetrable 'dyna
Association for the Advancement of Science, Thomson expounded his atomic model in mids', a dynamid being a kind of tightly bound neutral doublet consisting of a
a fuller and more confident way. What became sometimes known (rather inappropri negative and a positive electron. As mentioned, the idea of intra-atomic dynamids,
ately) as the 'plum pudding' model, he explained as follows:
or at least the name, had been introduced by Redtenbacher half a century earlier, but
Lenard did not refer to his predecessor. The constituent dynamids were much smaller
I regard the atom as containing a large number of smaller bodies which I shall call
corpuscles; these corpuscles are equal to each other; the mass of a corpuscle is the mass than the atom. He estimated the radius of a dynamid to be at most 3 x 10-12 cm,
of the negative ion in a gas at low pressure, i.e. about 3 x 10-26 of a gramme. In the normal implying that the atom was nearly empty: 'The space occupied by a cubic metre of
atom, this assemblage of corpuscles forms a system which is electrically neutral. ... [T]he solid platinum is empty, in the same sense that celestial space traversed by light is
negative effect is balanced by something which causes the space through which the empty, except for the proper volume of the dynamids, which cannot in all exceed a
corpuscles are spread to act as if it had a charge of positive electricity equal in amount to cubic millimetre.'27 In this respect, if in no other, he anticipated the later Bohr
the sum of the negative charges on the corpuscles. 23 Rutherford atom. Indeed, this is what a few patriotic German physicists claimed after
-
10 Niels Bohr and the Quantum Atom
Atomic Theories Before 1913 11
World War I, suggesting that Rutherford's atom was merely a particular version of
thorium, and uranium. Models of the type suggested by Jeans and Lodge were short
Lenard's.28
lived. Their explanatory force was limited, they made use of ad hoc assumptions, and
Lenard found that the number of dynamids in an atom was proportional to the
they presupposed the existence of positive electrons for which there was no experi
atomic weight, but did not offer a value for the factor of proportionality. Moreover, mental evidence. (There were, however, a few claims of evidence32 Compared to
.)
he assumed the dynamids to be in rapid rotation, which he thought might cast light on
Thomson's model, the Jeans-Lodge atom had little to offer.
the nature of radioactivity. Although he was little concerned with spectroscopic
Atomic models such as those mentioned, and most of those to be mentioned, were
evidence, he outlined a mechanism according to which the atom would emit charac
very much a British speciality. According to the Victorian tradition, models served
teristic spectral lines when free electrons returned to equilibrium in the dynamic atomic
heuristic purposes rather than representing some reality of nature. They were first of all
structure. Lenard's atomic hypothesis of 1903 was qualitative and rather vague. Not mental illustrations, formulated mathematically and based on the established laws of
only did it not address spectroscopic issues, it also did not connect with issues of
mechanics and electrodynamics, if often supplemented with hypothetical forces.
chemistry. For example, he did not give the number of dynamid units in either
A model were not to be taken literally, but were seen as a method or picture that
hydrogen or other elements, nor did he suggest how his atoms might combine into
offered some insight into the inner workings of nature. Speaking of the vortex model of
molecules. For these and other reasons Lenard's work exerted but little influence on the
atoms, Larmor said in an address of 1900 to the British Association for the Advance
further development of atomic structure and almost none on the British atom builders.
ment of Science:
~is model of the atom was no more successful than Kelvin's Aepinus atom in attracting
mterest from other physicists. The value of such a picture may be held to lie, not in any supposition that this is the
mechanism of the actual world laid bare, but in the vivid illustration it affords of the
Yet another conception of the atom, for a brief while popular among some physicists,
fundamental postulate of physical science, that mechanical phenomena are not parts of a
was to view it as, in the words of a French amateur physicist, 'a miniature solar system
scheme too involved for us to explore, but rather present themselves in definite and
composed of particles revolving round one another without touching and incessantly
consistent correlations, which we are able to disentangle and apprehend with continually
pursuing their eternal course under the influence of the forces which direct them'. 29 In
increasing precision.33
this case the positive electricity was assumed to be located in the hypothetical positive
electrons that could still be considered plausible particles, if undetected ones, in the This was a philosophy that governed British physics not only in the era of the vortex
early years of the new century. Primarily with the aim of explaining the mechanism of model, but also in the first two decades of the twentieth century. We shall meet it in
line spectra, 24-year-oldJames Jeans proposed in 1901 that the atom consisted of a large later chapters.
number of positive and negative electrons, supposedly differing only in the sign of their Philosophical Magazine, a commercially published journal founded in 1798, emerged
ch arge. 30 Jeans speculated that the electrons formed shells of alternating charges in the as the premier journal for atom-builders in the British tradition. Models of a similar kind
atoms, with the outermost layer consisting purely of negative electrons. To secure were rare among French and German physicists, who generally favoured a more
dynamical equilibrium he furthermore suggested modifying Coulomb's law at very phenomenalist approach and looked upon dynamical models with some distrust.
small distances, which he did by introducing in an ad hoc manner a repulsive force They might share the Britons' enthusiasm over the new physics based on electrons
independent of the sign of the electronic charges. Although Jeans' s atom was ephem and ether, but typically without engaging in model making of the elaborate kind
eral, it was the first attempt to interpret spectral laws on the basis of a definite model of favoured by British physicists. For example, the atomic models of Lenard and Stark
atomic structure. completely lacked the mathematical framework that was such a characteristic feature of
An atomic model similar to the one ofJ eans was argued by Lodge, who thought that British models of the Kelvin-Thomson tradition.
'The whole of the atom may be built up of positive and negative electrons interleaved In 1901 Walter Kaufmann, a physicist at the University of Bonn, gave an address to
together, and nothing else'.31 Electrons in a state of violent motion would imply a loss the Association of German Scientists and Physicians (Versammlung deutscher Natur
of radiation energy, causing the atom to decay in a kind of atomic earthquake. To forscher und Artzte) in which he surveyed the state and promises of electron physics.
Lodge's mind this did not speak to the disadvantage of the model, for in that way he Much in the spirit of Thomson and Lodge he concluded that 'the electrons would be
could offer a qualitative explanation of radioactivity of a kind similar to the one the long-sought-for "primordial atoms" whose different groupings would form the
proposed by Kelvin. Of course, on this picture one would expect all elements to be chemical elements, and the old alchemists' dream of the transformation of the elements
radioactive, but this was just what many physicists believed at the time. In the first would be brought a good deal nearer realisation'.3 4 He added that a mathematical
decade of the twentieth century it was often assumed that radioactivity was a common treatment of the stability of the intra-atomic electrons might even lead to an explana
property of atoms, only exhibited more strongly in heavy elements like radium, tion of the periodic system. Yet Kaufmann refrained from advocating a particular model
12 Niels Bohr and the Quantum Atom Atomic Theories Before 1913 13
0
of the atom corresponding to an arrangement of the electrons, and he did not engage in
@
the mathematical work to find the electron configurations.
Augusto Righi, a prominent professor of physics at the University of Bologna, may .•
,
serve as another example of how physicists on the Continent conceived the structure of ...
the atom. Electrons, he said in a popular book of 1909, are 'the elements of construction
@ @
in the architecture of the atom', which at the time was completely uncontroversial.
---~'· ®:·:.t:-:~.
More specifically, 'It may be admitted that a material atom is nothing but a system
•.-".;<: .t.> :;. ·. ·.. . ., ·4- : ·:,.
consisting of a certain number of positive and an equal number of negative electrons,
\·~/···;'
and that the latter, or at least some of them, move about the remaining portion like
satellites'.35 Characteristically, he did not go further than such generalities and felt no
0 0 @
desire to construct definite models out of the positive and negative electrons.
1.3 THE RISE AND FALL OF THE THOMSON MODEL
Fig. 1.2. Thomson atoms in three dimensions, as pictured by J. J. Thomson in a lecture to the
In work performed between 1903 and 1904, Thomson transformed his crude picture of Royal Institution in 1905.
the atom into a quantitative and sophisticated atomic model.36 From a physical point of
view, the model consisted of a sphere of atomic dimension and uniformly filled with a
positive fluid of uniform charge density; within the sphere a large number of point-like
negative electrons moved in rings around the centre. Unlike the electrons, the positive
sphere was hypothetical, assumed to be frictionless and without mass. Chemically and
spectroscopically inert, its only function was to provide an elastic force upon the where c denotes the velocity of light in vacuum and y is the acceleration. In the case of
electrons and thus keep the atom together. According to Thomson and most contem a single electron of charge e revolving with speed v on a circle of radius a, meaning that
porary physicists, even the lightest atoms were highly complicated structures, the y = v2 I a, the energy loss would be
=
simplest one (hydrogen) being a congeries of about n 1000 electrons.
The models that Thomson examined mathematically were mostly planar, but this
was merely a simplifying assumption. He was well aware that to obtain more realistic
models he would have to consider three-dimensional structures, as he did for a small Larmor realized that if atoms were composed of orbiting electrons, as he believed
number of electrons, from n = 1-8 (Figure 1.2). In any case, the function of his model they were, they might quickly lose their orbital energy through radiation.38 However,
was basically heuristic, to help physicists visualizing physical phenomena and thereby he did not consider this an insurmountable problem, among other reasons because he
suggest new experimental and theoretical ideas. 'My object', he said, 'has been to show could prove that for extra electrons the effect will not be additive. On the contrary,
that stable arrangements of corpuscles would have many properties in common with for a large number of orbiting electrons the amount of energy radiated could be made
real atoms, and I have attempted to illustrate the properties by considering a special arbitrarily small. The same kind of argument was used by Thomson with respect to
case chosen solely on the ground of simplicity'.37 his model atom. Considering the case of n electrons on the same ring, he proved that
It was an important feature of the 1904 model that the electrons were arranged on the radiation drain catastrophe reduced drastically with n. For example, taking the
rings with circular motion providing the necessary centrifugal force. However, accord radiation from a single revolving electron as unity, he found that the radiation from a
ing to Maxwellian electrodynamics accelerating electrons will emit radiation energy circle with six electrons moving with a speed of v = O.OOlc would be only 10-16. For
and so, it would seem, the atom would eventually collapse. This problem had been the general case of n equidistantly placed electrons on a single ring he derived the
considered by Larmor in an important paper of 1897 in which he calculated the power
expression
radiated by an accelerated charge to be