The gallery of failed atomic models, 1903-1913

It is often said that history is “written by the victors”. While this statement is usually referring to the winners of a military or political conflict, a similar effect occurs in the history of science. Physics textbooks, for instance, often describe the development of a theory in a highly abbreviated manner, omitting many of the false starts and wrong turns that were taken before the correct answer was found. While this is perfectly understandable in a textbook (it is rather inefficient to teach students all of the wrong answers before teaching them the right answer), it can lead to an inaccurate and somewhat sterile view of how science actually works.

Science is all about testing ideas via experiment: ideas which match the current experimental evidence can be overturned when new experiments come to light. Even a good scientist will come up with many wrong turns in trying to understand a complicated phenomenon. Unfortunately, many people, including many scientists, feel that science is about ‘always being right’. This attitude can be stifling, as it prevents researchers from suggesting answers for fear of being ‘wrong’.

To counter this attitude, I present the following post: The gallery of failed atomic models.

Back in April, I wrote a post about a 1910 paper written by Ehrenfest on charge distributions which can accelerate without radiating. At that time, before Bohr came up with his model of the atom and ushered in the era of quantum mechanics, most atomic models involved electrons accelerating in some manner. According to electromagnetic theory, point charges always radiate, but Ehrenfest demonstrated that an extended charge distribution could accelerate without radiation. This is one way to ‘save’ a lot of atomic models from being completely unrealistic. But how many atomic models were there?

A lot. Most people in physics are taught Thomson’s ‘plum pudding’ model of the atom, but a little investigating* turned up no less than eight distinct pictures of atomic structure**.

The late 1800s and early 1900s was the breakthrough period of atomic research. A number of tantalizing pieces of experimental evidence suggested a nontrivial internal structure to the atom. Among them, the following three were perhaps the most significant:

  1. The presence of electrons. In 1897, J.J. Thomson performed experiments with cathode rays and demonstrated conclusively that atoms contained negatively-charged ‘corpuscles’, which we now call electrons. Any atomic model would not only need to include electrons, but an equal amount of positive charge to make the entire atom electrically neutral.
  2. The periodic table. In 1869, Dmitri Ivanovich Mendeleev developed the periodic table of elements, which ordered elements roughly in terms of increasing mass and vertically arranged them in the table according to their chemical properties. This regular structure of the elements suggested that the elements were themselves made up of some sort of more fundamental building blocks, and an atomic model needed to account for this.
  3. The Balmer formula/Rydberg formula. In 1814, Joseph von Fraunhofer invented the spectroscope, a device to analyze the ‘colors’ of light. Looking at the Sun’s spectrum, he observed isolated dark lines in the otherwise continuous solar spectrum, as shown in his original (hand-drawn) figure below:

    The upper part of the figure indicates the relative brightness of each color of the spectrum. The lower part of the figure shows the appearance of each color in the spectrum. There are numerous isolated frequencies (colors) which have no brightness at all. It was later determined that these missing colors were due to absorption of the Sun’s light by atoms.
    Atoms evidently absorb light, and emit light, only at certain isolated frequencies. Physicists were at a loss to explain the origin of this behavior, but in 1885 Johann Balmer empirically determined a formula that matched one collection of the spectral lines of hydrogen. In 1888 Johannes Rydberg extended this formula to incorporate every observed frequency of hydrogen, and closely matched the frequencies of other atoms as well. These formulas were unexplained by the turn of the century, and it was clear that any theory of atomic structure would have to produce them.

Any atomic model would therefore need to incorporate one or more of these three elements: 1. The presence of electrons, 2. The periodic table, 3. The Rydberg formula. Let us take a look at what solutions were proposed, in roughly chronological order:

1. The dynamid model, by P. Lenard (1903).

(P. Lenard, “Über die Absorption der Kathodenstrahlen verschiedener Geschwindigkeit,” Ann. Physik 12 (1903), 714-744.)

Philipp Lenard was a Hungarian-German physicist who did extensive experimental investigations of the properties of “cathode rays” (what we now know to be beams of electrons); this work earned him the 1905 Nobel Prize in Physics “for his important work on cathode rays.” (His Nobel lecture may be read here.)

Lenard made numerous profound observations of electron behavior, several of which contributed to his conception of the atom. He demonstrated that the ability of a material to absorb electrons depended almost entirely on the mass of the material, and hardly at all on its specific chemical properties: this suggested that atoms were all made of the same fundamental pieces, and the only difference between different elements was the presence of more or less of these fundamental pieces. He demonstrated that electric forces were the “active ingredient” in chemical interactions, and also demonstrated that the amount of solid matter in an atom is extremely small.

From these observations, he postulated that the fundamental building block of all elements is what he called the “dynamid”: a positive and negative charge bound together. The atomic mass of an atom is simply proportional to the number of dynamids present, i.e. a hydrogen atom is a single dynamid, helium would evidently be four dynamids, and so on. The binding force which holds these dynamids together was not explained. An electron impinging on an atom could collide with the negative part of the dynamid (another electron) and liberate it.

This theory gave at least a partial explanation for the structure of the periodic table, and the presence of electrons in the atom, but could not explain the Rydberg formula. Another significant limitation was the lack of observation of the positive part of the dynamid: if a negative half could be stripped off, why not a positive part?

Lenard himself, though an important and distinguished physicist, was a major asshole outside of science. He became an avid German nationalist during the Nazi regime and the greatest proponent of “Deutsche Physik”, the idea that “Jewish science” had corrupted the “purity” of scientific endeavor. Though I’ve already said that it’s okay to be wrong in science, I still get a small bit of satisfaction knowing that a jerk like Lenard has a Nobel lecture filled with wrong ideas, including the dynamid as well as much discussion of the aether.

2. The ‘plum pudding’ model, by J.J. Thomson (1904).

(J.J. Thomson, “On the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with application of the results to the theory of atomic structure,” Phil. Mag., Ser. 6, Vol. 7 (1904), 237-265.)

Thomson’s model was the most highly-regarded of its time, and is usually the only failed model discussed in modern physics classes (an excerpt of his original paper can be read here). The original idea, however, was apparently suggested by the other Thomson, William Thomson aka Lord Kelvin. J.J. Thomson’s role was to actually make quantitative calculations that demonstrated the model’s stability.

Stability was an important consideration in early atomic models. Very early on, scientists such as Jean Baptiste Perrin had proposed an atom of ‘nucleo-planetary’ form***, in which negative electrons orbit a centrally located positive nucleus, much as the planets orbit the Sun in the solar system. However, electrons in orbit should constantly radiate energy, and since there is a force of attraction between the nucleus and the orbiters, the electrons should rapidly lose their energy and ‘crash-land’ into the nucleus.

Thomson’s partial solution was to replace the nucleus with an extended distribution of positive charge. The electric force F within a uniform sphere of charge increases with the distance from the center, while the electric force outside a positive nucleus would increase inversely with the distance from the center, as shown below:

An electron moving towards the center of Thomson’s atom would feel less of an attractive force as it moved closer to the center; simultaneously, it would experience more of a repulsive force from the other electrons. These two effects combined result in a system in which a ring of moving electrons are in stable equilibrium at some radius from the center of the atom.

Thomson provided roughly thirty pages of calculations on the stability of such atoms, considering in detail the cases of 2, 3, 4, 5, and 6 electrons. He demonstrates that the system is stable as long as the velocity of the electrons lies above some threshold; below this velocity, the stability breaks down, and Thomson suggests that this breakdown might be a manifestation of atomic radioactivity:

Consider now the properties of an atom containing a system of corpuscles of this kind, suppose the corpuscles were originally moving with velocities far exceeding the critical velocity; in consequence of the radiation from the moving corpuscles, their velocities will slowly – very slowly – diminish: when, after a long interval, the velocity reaches the critical velocity, there will be what is equivalent to an explosion of the corpuscles, the corpuscles will move far away from their original positions, their potential energy will decrease, while their kinetic energy will increase. The kinetic energy gained in this way might be sufficient to carry the system out of the atom, and we should have, as in the case of radium, a part of the atom shot off.

Thomson’s model was well-received because it offered at least a crude explanation of atomic stability, and almost as a side-effect radioactivity seemed to appear. The model had no explanation of the Rydberg formula, however, and the “sphere of uniform positive electrification” was not well-defined.

It’s worth noting that Thomson himself does not call his model the ‘plum pudding’ model; this name was introduced by others, possibly not in a positive way.

Although his atomic model was unsuccessful, Thomson himself certainly was; he won the 1906 Nobel prize “in recognition of the great merits of his theoretical and experimental investigations on the conduction of electricity by gases.”

3. The Saturnian model, by H. Nagaoka (1904).

(H. Nagaoka, “Kinetics of a system of particles illustrating the line and the band spectrum and the phenomena of radioactivity,” Phil. Mag., Ser. 6, Vol. 7 (1904), 445-455.)

Another approach to solving the stability problem was suggested by the Japanese scientist Nagaoka. In 1859 James Clerk Maxwell solved a dispute about the nature of Saturn’s rings by demonstrating theoretically that they had to be composed of a collection of relatively small satellites. Maxwell showed with a detailed calculation that slight disturbances of such a ring would result in oscillations of the ring, but not its destruction.

Nagaoka brought this analogy to the problem of atomic stability (an excerpt of his paper can be read here). He follows Maxwell’s calculations, but with repelling electrons in the ring rather than attracting masses, and demonstrates theoretically that the oscillations of the ring result in both a line spectrum similar to atomic spectra as well as a continuous band structure. Furthermore, he demonstrates that the line spectrum undergoes a Zeeman-like splitting effect in the presence of a magnetic field. Nagaoka even endeavors to explain radioactivity as a resonance effect between pairs of rings around the same atom; in essence, the different rings tear each other apart.

Nagaoka’s model seems to not have attracted significant attention, with one important exception to be mentioned later, which is somewhat ironic considering it was qualitatively close to the ‘true’ nuclear model.

4. Electron fluid model, by Lord Rayleigh (1906).

(Lord Rayleigh, “On electrical vibrations and the constitution of the atom,” Phil. Mag., Ser. 6, Vol. 11 (1906), 117-123.)

Lord Rayleigh, super-physicist, got himself into the atomic model game by considering a modification of Thomson’s ‘plum pudding’: he looked at the system in the limit as the number of electrons becomes so large that they may be approximated by a continuous electron ‘fluid’. In Rayleigh’s own words,

Some of the most interesting of Prof. Thomson’s results depend essentially upon the finiteness of the number of electrons; but since the experimental evidence requires that in any case the number should be very large, I have thought it worth while to consider what becomes of the theory when the number is infinite. The cloud of electrons may then be assimilated to a fluid whose properties, however, must differ in many respects from those with which we are most familiar.

Rayleigh is one of those physicists who, even when speculating wildly, manages to provide much food for thought and deep insights. He treats the electron cloud as irrotational fluid, which simplifies the calculations immensely, and then investigates the stability of this fluid when it is distorted from completely overlapping the positive electric sphere. Treating the electron fluid as also incompressible, he finds that it undergoes vibrations of discrete frequency, similar to the discrete frequency vibrations of a string or, more analogous, a drumhead. The frequencies he calculates, however, do not correspond to the Rydberg frequencies of the atom. Rayleigh tries to skirt this difficulty by suggesting,

A partial escape from these difficulties might be found in regarding actual spectrum lines as due to difference tones arising from primaries of much higher pitch…

…but he provides no clear prescription for doing so.

Some of his concluding remarks are worth reproducing almost in their entirety, as they relate to all models of the atom that involve orbiting electrons:

In recent years theories of atomic structure have found favour in which the electrons are regarded as describing orbits, probably with great rapidity.

An apparently formidable difficulty, emphasised by Jeans, stands in the way of all theories of this character. How can the atom have the definiteness which the spectroscope demands? It would seem that variations must exist in (say) hydrogen atoms which would be fatal to the sharpness of the observed radiation; and indeed the gradual change of an atom is directly contemplated in view of the phenomena of radioactivity. It seems an absolute necessity that the large majority of hydrogen atoms should be alike in a very high degree. Either the number undergoing change must be very small or else the changes must be sudden, so that at any time only a few deviate from one or more definite conditions.

It is possible, however, that the conditions of stability or of exemption from radiation may after all really demand this definiteness…

The argument here relates to the stability issues of orbital motion we mentioned above. Again making an analogy with planetary orbits, in principle a planet could form an orbit around the Sun with any orbital radius, and consequently with any orbital frequency. Assuming the frequency of radiation is related to the orbital frequency, this would imply that a ‘solar system’-like hydrogen atom should radiate over a range of frequencies, and not just a discrete set. Since every hydrogen atom seems to radiate in exactly the same way, something must restrict this ‘freedom’ of orbital frequency. Rayleigh’s last sentence seems to anticipate later quantum mechanical discoveries: in order for the atom to be stable, additional conditions must be satisfied, and these conditions are the first steps towards a quantum description of matter.

5. Vibrating electron model, by J.H. Jeans (1906).

(J.H. Jeans, “On the constitution of the atom,” Phil. Mag., Ser. 6, Vol. 11 (1906), 604-607.)

I’ve taken a few liberties in drawing Jeans’ model, as it seems that he made a number of suggestions for modifying Thomson’s model and did not necessarily put these suggestions together. In his own words,

… may I mention that in the Phil. Mag. for Nov. 1901, I attacked a problem similar in many respects to that which forms the main substance of Lord Rayleigh’s paper? The actual premises upon which I worked were different from those of Lord Rayleigh – his positive sphere being represented, in my work, by a crowd of positive electrons, and the definiteness of structure, which he obtains by regarding this sphere as rigidly fixed, being obtained in my work by using a law more general than ee’/r^2.

In the 1906 paper, however, Jeans follows up on Rayleigh’s comments about systems with orbiting electrons. In particular, he points out that one cannot arrive at a quantity which represents a frequency simply by using the usual electromagnetic laws. In his own words, quoting Rayleigh,

He goes on to say: “It is possible, however, that the conditions of stability or of exemption from radiation may after all really demand this definiteness…The frequencies observed in the spectrum may… form an essential part of the original constitution of the atom as determined by conditions of stability.”

If this were so, these frequencies would depend only on the constituents of the atom and not on the actual type of motion taking place in the atom. Thus if we regard the atom as made up of point-charges influencing one another according to the usual electrodynamical laws, the frequencies could depend only on the number, masses, and charges of the point-charges and on the aether-constant V. What I wish to point out first is that it is impossible, by combining these quantities in any way, to obtain a quantity of the physical dimensions of a frequency.

In brief, no equation involving charge, mass, and aether-constant V will ever result in a frequency. Since we know that atoms are emitting light with definite frequency, something is missing in the description.

Lord Rayleigh avoids this problem by introducing a definite electric charge density \rho_0 for the sphere of positive charge or, equivalently, a definite radius for the sphere. Jeans suggests that this may be inadequate,

If this positive electrification, instead of being limited to an invariable sphere, were supposed free to expand under its self-repulsion, Lord Rayleigh’s \rho_0 would be indefinite, as would consequently be the frequencies also.

Jeans’ suggestion to solve the problem:

It seems, then, that we must somehow introduce new quantities – electrons must be regarded as something more complex than point-charges. And when we have once been driven to surrendering the simplicity of the point-charge view of the electron, is there any longer any objection to putting the most obvious interpretation on the line-spectrum, and regarding its frequencies as those of isochronous vibrations about a position of statical equilibrium?

In simple words, if we imagine that the electron itself not as a point charge but as an object with its own internal structure, then the frequencies of light emitted from atoms could result from vibrations within this ‘structured electron’.

This is a fascinating observation, because it comes very close to addressing the real problem: new physics was needed in order to properly describe the behavior of the atom. We will address this at the end of the post.

6. Expanding electron model, by G.A. Schott (1906).

(G.A. Schott, “On the electron theory of matter and the explanation of fine spectrum lines and of gravitation,” Phil. Mag., Ser. 6, Vol. 12 (1906), 21-29.)

G.A. Schott was a curious fellow. He was a master of electromagnetic theory, and produced a number of important works on electromagnetic radiation from moving charges and the radiation reaction which can result. He could manipulate Maxwell’s equations with ease and develop amazing and counterintuitive results, as we will see in future posts.

On the other hand, he was perhaps the last respectable member of the anti-quantum crowd, and passed away in 1937 still trying to develop a purely classical theory of the atom. From his obituary (Obituary Notices of Fellows of the Royal Society, Vol. 2, No. 7, (Jan., 1939), pp. 451-454),

The first serious attack on the classical theory was made by Bohr in 1913. Although Planck’s constant appeared in the theory of light in 1900, Bohr was the first to use it to give an electrical explanation of line spectra. There were two violent departures from the classical theory. Firstly, the existence of radiationless electronic orbits, secondly the expression h\nu for the change in energy. Schott devoted the most of the remainder of his life attempting to fit both those in the classical theory… The mathematical difficulties are enormous, and the skill showed in getting numerical results shows Schott’s mastery at its highest. It might be called the supreme attack of a heroic defender before his death. Defeated? Who shall say? I like to think that in future years the work of Schott will always be consulted for inspiration to tackle the difficulties which come across the path of all theories.

Schott had a hand in investigations of atomic structure before the “Bohr revolution” as well. In 1906 he addressed the speculations of Rayleigh and Jeans and came up with his own take on them. In his typical and somewhat bizarre way of approaching problems, he suggests, like Jeans, that the electron must be more complicated than a point particle, but speculates that the special frequencies of the atom arise from the electron expanding at a very slow rate!

This causes problems with conservation of energy. In order to avoid these problems, Schott then suggests that this expansion must be countered by an internal stress, and that this stress is caused by pressure from the (hypothetical) aether.

Even more surprising, Schott provides calculations which suggest that this action of electrons on the aether results in an attraction between electrons, which he interprets as gravitation!

Schott’s work, while fascinating, also fails to produce the Rydberg formula for spectral lines, and he says nothing about the positive charge in the system. Each assumption he makes leads to an additional assumption to conform with experimental evidence, and this seems to be a good example of an ad hoc theory.

7. The archion model, by J. Stark (1910).

(J. Stark, Prinzipien der Atomdynamik: Die Elektrischen Quanten (Leipzig, Verlag von S. Hirsel, 1910).)

We now come to my personal favorite of all the failed atomic models: the archion! In his extremely detailed 1910 book Prinzipien der Atomdynamik, J. Stark proposed a fundamental positive component of the atom which differs from the dynamid discussed previously. He describes his reasoning in §13, “Hypothese über das Archion und die Struktur des Chemischen Atoms.”

Stark’s ideas are carefully described based on known and suspected properties of the elementary constituents of matter. We skip to his first definition of the archion:

Auf Grund der vorstehenden auf der Erfahrung basierten Folgerungen kann die nachstehende Definition eines neuen physikalischen Individuums kaum Bedenken erwecken. Wie festgestellt wurde, kann ein chemisches Atom mehrere voneinander trennbare positive Quanten enthalten, mit denen eine Masse von der Ordnung derjenigen des Wasserstoffatoms verbunden ist; wir dürfen nach dem jetzigen Stand unserer Erfahrung die Möglichkeit nicht ausschließen daß dies auch für das kleinste chemische Atom, das Wasserstoffatom, gilt. Als Archion definieren wir nun das Individuum, welches eine elektrische Ladung gleich derjenigen des positiven Elementarquantums besitzt und dessen mit dieser Ladung behaftete Masse nicht kleiner gemacht werden kann, ohne daß das Individuum als solches zu existierenaufhört. Die Bezeichnung positives Quantum soll lediglich die Größe der elektrischen Ladung, nicht die mit ihr verknüpfte Masse charakterisieren. Das Wort Archion soll, analog dem Wort Elektron, die Aussage über die Ladung und jene Aussage über die minimale mit der Ladung verbundene Masse vereingen.

In English:

Due to managing consequences based on experience the following definition of a new physical individual can hardly arouse doubts. As was determined, a chemical atom can contain several positive quanta, separable from each other, with which a mass is connected on the order of that of the hydrogen atom; we may not exclude after the current conditions of our experience the possibility that this also for the smallest chemical atom, which applies for hydrogen atom. As Archion we define now the individual which possesses an electrical charge equal that of the positive elementary quantity and whose mass afflicted with this charge cannot be made smaller, without the individual destroyed as such too. The designation positive quantity is to only characterize the size of the electrical charge, not those with it linked mass. The word Archion is, similar to the word electron, the statement about the charge and that statement about the minimum mass connected with the charge association towards.

The idea of an archion here is close to the modern day conception of a proton; however, Stark is unaware of both its electrically neutral counterpart the neutron and the nuclear force which holds the nucleus together. He instead seeks a purely electromagnetic explanation for the archion binding. It was already known in that day that atoms could possess magnetic dipole moments, like miniature “electric circuits”. Stark assumes that these dipole moments are contained within individual archions,i.e. that the individual archions act as microscopic permanent bar magnets. Each archion would therefore have a ‘north pole’ and a ‘south pole’, and two archions (magnets) put close together would experience a force lining them up. Quoting Stark again,

Hieraus folgt, daß sich mehrere Archionen dank ihrer wechselseitigen magnetischen Orientierung und Anziehung zu einem Individuum längs einer in sich zurücklaufenden Kurve so zusammenbauen können, daß längs derselben die Achsen der Archionen (Elementarmomente) in gleichem Sinne aufeinanderfolgen. Ein solches Individuum wird gegen eine Öffnung der Archionenkurve durch einen Eingriff von außen her mit einer Kraft reagieren, an welcher alle Archionen längs der Kurve mitwirken.

In English,

From this it follows that several Archions, owing to their mutual magnetic orientation and attraction to an individual along a curve running back in itself that along the same, can assemble themselves in such a way the axles of the Archions (elementary moments) in same sense sequences. Such an individual will react from the outside ago against an opening of the ‘Archion curve’ by an interference with a strength, in which all Archions participate along the curve.

In other words, the ‘bar magnets’ tend to line up, and what we call an ‘atom’ is a collection of bar magnets forming a closed curve:

There is a significant problem with this picture, however: the archions are all positively charged, and will repel each other, and that force is much greater than any magnetic dipole force which might hold it together. Stark solved this problem by adding the electrons somewhere in the vicinity of the archion connections, where they can neutralize the repulsion and hold the entire structure together.

Like all other models, this one could not explain the Rydberg formula, and would be rendered irrelevant in only a few years by Bohr’s monumental discovery.

Winner: The Bohr orbital model, by N. Bohr (1913).

(Niels Bohr, “On the Constitution of Atoms and Molecules (Part 1 of 3),” Phil. Mag. 26 (1913), 1-25.)

The beginning of the end of the ‘atomic model craze’ started in 1909 when students of Ernest Rutherford performed what is now known as the Geiger-Marsden experiment, or gold-foil experiment. The researchers fired high-energy alpha particles at a thin gold foil target. Alpha particles are now known to be helium atoms stripped of their electrons. According to the plum-pudding model, the alpha particles were expected to suffer only slight deflections on passing through the film: the positive ‘pudding’ was too spread out to deflect an alpha and the electron were much too light to deflect an alpha. Much to their surprise, however, they found that, occasionally, one of the alpha particles was completely reflected back towards its source. As Rutherford later commented, “It was almost as incredible as if you fired a fifteen-inch shell at a piece of tissue paper and it came back and hit you.”

By 1911, Rutherford had formulated his own model of the atom: it consisted of a heavy, positively-charged nucleus surrounded by electrons, with most of the atom consisting of empty space. Rutherford does not seem to have an idea of what exactly the electrons are doing, but he cites Nagaoka’s Saturnian model as an example of a stable model of a nuclear atom.

Following Rutherford’s lead, in 1913 Niels Bohr managed to derive the Rydberg formula with a modified “solar system” model of the atom. As mentioned earlier, the key step in accomplishing this feat was hinted at by Raleigh and Jeans: new physics needed to be introduced which constrains the motion of the electrons to certain special orbits around the nucleus.

Bohr suggested several new rules for the motion of electrons, none of which agree with classical physics:

  1. Electrons can only travel in stable orbits which possess quantized angular momentum, i.e. the orbital angular momentum of the electron satisfies the formula: L = nh/2\pi,where h is Planck’s constant, introduced in the study of blackbody radiation, and n = 1,2,3, and so forth. This in turn suggests that the electron travels only travel at certain orbital distances from the nucleus.
  2. An electron can only give up its energy “all at once” by jumping from a higher n-state to a lower n-state. The frequency \nu of the photon (light particle) released in jumping from level 2 to level 1, for instance, is given by h\nu = E_2-E_1, where E_1 is the energy of the particle in the n = 1 state.

In hindsight, Jeans was on the right track when he observed that something else needed to be added to the existing theory to produce the Rydberg formula. That ‘something’ was Planck’s constant, h.

With an atomic model that resulted in a near-perfect match to the experimental Rydberg formula, physicists now realized that they were exploring fundamentally new physics, and these new explorations developed into what we now know as quantum mechanics. For the most part, scientists accepted this new physics, and wild speculation of atomic structure was replaced with attempts to understand the consequences of the quantum theory****.


So what can we learn from all this? Hopefully the preceding discussion has made clear that science is just as much about being (constructively) wrong occasionally as it is about being right. Some hugely important names in physics – Rayleigh, Thomson, Kelvin, Stark, Lenard, Jeans – all eagerly contributed to the speculation about the inner workings of the atom. These speculations were often productive, too: Rutherford’s experiments were motivated by investigations of Thomson’s plum pudding model, and his nuclear model seems inspired by Nagaoka’s Saturnian model. Bohr’s model seems anticipated, if not inspired, by the earlier musings of Rayleigh and Jeans. We will see in later blog posts how Schott’s electromagnetic calculations led in surprising directions.

In the end, it is worth noting again that scientific research isn’t about having all the answers. Big discoveries come in bits and pieces, and through wrong turns and dead ends. Fortunately, the willingness of scientists to move past those faults and find new approaches pushes the boundaries of knowledge (mostly) in a forward direction.

* My investigations were helped immensely by an abbreviated description of numerous models in the book by Alex Keller, The Infancy of Atomic Physics: Hercules in his Cradle.
** I should mention that there is an even earlier atomic model, the ‘smoke ring’ model of William Thomson aka Lord Kelvin, proposed in 1867. In this model, all atoms are treated as stable vortices in the electromagnetic aether. This model was still seriously considered up through the early 1900s. For those with university library access, a nice historical article can be found here.
*** Keller’s book credits Perrin with the “nucleo-planetary” idea, but I have been unable to find a reference to it.
**** But not completely! In 1902, Gilbert Lewis developed a theory of a ‘cubical atom‘, which he did not get around to publishing until 1916. This model sought to explain atomic bonding; the original paper can be read here.
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38 Responses to The gallery of failed atomic models, 1903-1913

  1. dr. dave says:

    Definitely a book-marker! Wish I had found this when I was teaching my “QM for Poets” class last semester. It’s nice to show students that science doesn’t progress in a linear way from Model A to Model B

  2. CCPhysicist says:

    Very nice!

    Two observations:

    1) The Lenard model is particularly interesting, because it is the first to assume that positive charge also comes in quanta. After Thomson discovered that the negative electric fluid consisted of distinct particles, he (and most others) still proceeded on the assumption that positive charge consisted of a fluid … and that the atom was thus a positive liquid drop (either large or small) with charges moving around it or around in it.

    2) The 1904 paper by Thomson describes something that looks more like the Nagaoka model, except the electron circle is inside the positive charge droplet instead of outside of it, than what you drew. There is another publication by Thomson, after the Geiger and Marsden experiment, in Proc. Cambridge Philos. Soc. 15 (1910) 465, that I think describes the classic plum pudding model.

    3) It is not an overstatement to say the Bohr’s model “won”, because it has persisted despite being completely wrong on key details like the angular momentum of the ground state and the need for discontinuous jumps in space to change energy levels. It should be noted that Bohr’s two conditions are also completely inconsistent with actual quantum mechanics, and that Heisenberg’s invention was driven by the utter failure of the Bohr model to explain anything other than the basic spectrum of the Hydrogen atom (and even then it could not explain the line intensities).

  3. dr. dave: Thanks!

    CCPhysicist: Regarding your points:

    1. I found it interesting that the German models seemed to focus more on developing a ‘fundamental’ theory of matter that could, in essence, explain the periodic table, while the English models focused more on atomic stability and the Rydberg formula. Evidently different scientific ‘cultures’ found different aspects of atomic structure to be most important.

    2. From what I’ve seen, the 1904 paper is the ‘official’ plum pudding paper, though it isn’t quite what most people imagine it to be. People usually describe the model in a way that assumes a ‘static’ collection of electrons, though Thomson himself never described it in such a way. My picture is closer to the popular conception of the model than the actual model described by Thomson. I’ll have to look into his 1910 paper to see how things developed.

    3. For me, the groundbreaking aspect of Bohr’s model was that it ‘pointed’ the investigations of physicists in the proper direction and made the physicists realize that new physics was required. It seems to be persistent because it forms a nice conceptual ‘transition’ from classical thinking to quantum thinking, even though, as you said, it is in many ways just as wrong as the models that came before it.

  4. CCPhysicist says:

    The 1910 paper is a response to the Geiger-Marsden data. I have not read the 1904 paper, and no longer recall if there were any differences. By the way, there is a really interesting static equilibrium problem on the distribution of charges on a conducting plate, where they go from all being on the edge to forming an interior ring when you cross a critical number.

    As you can tell, my 3rd point was an afterthought. When I teach about Bohr (maybe not in a Poets class, but I might try that in my summer class) I make the point that the greatest value of his model was that (a) it was good enough that it stimulated lots of experiments to test its other predictions, but (b) those predictions were entirely wrong and stayed wrong even after Sommerfeld worked his mathematical physics butt off to put in relativity and elliptical orbits, and (c) it was an utter disaster for Helium. This drove experiment [the single most important thing any theory can do] and created enough theoretical frustration that Heisenberg and others looked in a completely different direction.

    The value of wrong theories is often understated. We don’t teach them very much, and biologists don’t teach them at all. I should blog about that.

    I also tell them that the linear flow from Bohr to de Broglie to Schroedinger is bogus, because Heisenberg got to QM first without using waves or orbits or any of those earlier ideas at all.

  5. “I have not read the 1904 paper, and no longer recall if there were any differences.”

    If you want a copy, I can send you the pdf! Be prepared, though, for lots of tedious calculations! 🙂

    “This drove experiment [the single most important thing any theory can do]”

    Even being a theorist myself, I stress to students in both my class and my research group that all of our work isn’t worth much if we can’t tie it to experiment in the end…

    “By the way, there is a really interesting static equilibrium problem on the distribution of charges on a conducting plate…”

    That does sound rather interesting!

  6. i have a problem about the inconsitance of flows of old atomic model most of people they seems to undustarnd it but me i just find them rumbling i the same page of flaws.what i want is this may u pleace explain to me in more detailed about inconsistance of fllaws of old atomic model.

  7. I.M. says:

    Thanks a lot for posting this comprehensive review!

    While there are many sites that claim to “explain” the different models, few are as thorough.

  8. edna makena says:

    this helped me a lot. thanx!

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  11. John Cowan says:

    Physicists would be wary of teaching “wrong models” too if there were a large multinational group of people committed to the truth of, say, post-Aristotelian impetus physics as a matter of religion, and who were convinced that if their children ever heard an unbiased report on Newton’s physics (never mind Einstein’s or Heisenberg’s or Wheeler’s) they would go straight to Hell, do not pass Go, do not collect $200.

    In any case, elementary biology does contain a discussion of Lamarckian inheritance, perhaps because it’s part of the folk theory of inheritance.

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  13. Science geek says:

    this is an easy way to find how atoms are different and how they can be defined different ways. I really liked the magnet one I never thought it would be that way.

  14. Franklin Hu says:

    There are continuing attempts to redefine the atomic model by cranks and crackpot hobby scientists like myself. It is interesting that none of the models mentioned ever attempted to come up with a solid structured approach to an atomic model. See:

    This model does account for the ionization and spectral data. This is part of my broader theories

  15. Blake Stacey says:

    I just found out about another mostly-forgotten figure from the early days of quantum physics: Jun Ishiwara.

  16. Jimbob anonamous says:

    This was a big help thanx

  17. For anyone who might be interested, I wrote a paper for the 24th Regional Conference on the History and Philosophy of Science (2008) on essentially the same topic – I read many of the original papers discussed above as part of my research, and discuss them in some detail here:

    Click to access Atomic_Modeling.pdf

  18. Another “failed” model is described in my 1966 U.S patent (3276148) “Model for Atomic Forms”
    Also Leonardo’s Atom! on YouTube:

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  20. Sturton says:

    Apparently Thompson first proposed a variant of the ‘plum pudding’ model in 1898. Can anyone explain how it differed from the 1904 revision, as explained here.

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  27. Raghu says:

    Thanks for the nice and very informative article. I have collected some points for my QM lecture. Any chance you can also include the 1910 contribution by Arthur Haas? Thanks.

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  29. Gunnar Øyro says:

    Thanks for your fine article! I would like to point attention to a paper about Hantaro Nagaoka (that you are writing about above): (Nagaoka’s atomic model and hyperfine interactionsBy Takashi T. INAMURA). Here the author writes that Nagaoka stated that the electrons did not have to live in the same plane. This means that the often quoted name for the model (the “Saturnian model”) is misleading. So it looks like his model was at that time, as close one could get to the “correct” theory, and I think we should give Nagaoka more credit than he is ususally given. Textbooks often neglect his contribution, although Rutherford perfectly well knew about the Nagaoka model (but, also failed to give proper credit). Cheers Gunnar Øyro



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