The Particle Menace Part 1 The Solar System Model of the Atom

The Bohr-Sommerfeld model of the atom is described including the four quantum numbers used to identify electrons and explain the Zeeman effects and Pauli's exclusion principle. While this particle model is serviceable it is ontologically flawed. There is a pdf on the website with images and tables which may be helpful in following the podcast, plus a more detailed essay, a note on the Stern-Gerlach experiment, a booklist and a paper by Leibniz, 'Primary Truths'. 

Transcript

The Particle Menace Part 1: The Solar System Model of the Atom

Hello. This second series of six podcasts are about ontology or what is physically real. The previous six podcasts unravelled the claims of the Copenhagen interpretation of quantum mechanics as a genuine description of the world and showed it to be, insofar as it predicted results at the atomic level, instrumental but riddled with ontological anomalies. 

   The first three podcasts will cover atomic theory. What is the atom? A particle or a wave or something else? And the following three podcasts will cover the continuum. Is it space-time, a field, a vacuum, or something else? This first podcast looks in detail at the Bohr Sommerfeld Solar System Model of the Atom. To follow this podcast, please open the PDF in the additional materials section, which has images of the emission and absorption spectra of the hydrogen atom, a diagram of its energy levels, an image of the electromagnetic spectrum, a table explaining the quantum numbers, and a table of the standard model of elementary particles. 

   The solar system model of the atom consists of a nucleus composed of positively charged protons bound to a varying number of neutral neutrons. The varying number of neutrons for the same element produce isotopes. The nucleus is surrounded by shells of negatively charged electrons, which equal the number of protons, and so the finished atom has no charge. Dealing with each in turn and starting with the electron, it is characterized by four quantum numbers. Bohr arrived at the first number after an analysis of the Zeeman effect. See the emission and absorption spectra of the hydrogen atom. The next two were added by Arnold Sommerfeld, I believe, after noting the anomalous Zeeman effect, where further spectral lines occurred when the atom was introduced to a magnetic field. And then the more controversial fourth atomic number representing 'spin' was introduced to satisfy Pauli's exclusion principle. 

   The first quantum number n describes the possible energy levels of the electron. The electron moves between levels when the atom either absorbs or emits a photon. The remaining three numbers describe the movement, orientation, and the unknown variable spin of the electron at each energy level. All these descriptions are quantized in that they have definite values with nothing in between, meaning that the description for each quality is discontinuous. This is opposite to continuous wave phenomena. According to Pauli's exclusion principle, no two electrons can share an identical set of quantum numbers. This was initially a problem prior to the introduction of spin because the two electrons in the first energy level of a helium atom would have identical sets of three quantum numbers. Spin was introduced to avoid this, but was controversial from the outset. It is not the same as angular momentum or rotation in the same way as one thinks of a planet spinning on its axis. To this day its definition is far from clear. What is clear is that the model had to involve fresh ideas because classical mechanics could not explain, amongst other things, why the electron, when emitting radiation and losing energy, would not fall into the positively charged nucleus. Introducing this fourth number relating to an undescribable variable is supposed to solve this problem. 

   There are at least two specious arguments relating to this model that are worth noting. Firstly, the argument from spectral lines, that's the Zeeman effect and the anomalous Zeeman effect, and secondly, the argument for introducing spin based around the Stern-Gerlach experiment. Dealing with each in turn, the construction of the model relied on the results of spectroscopy and the unexpected irregular separation of the visible spectral lines. It was argued that classical electrodynamics would have predicted a continuous emission of radiation, and the reason for the results is that the electron is jumping between energy levels rather than progressing along a classical path of increasing or decreasing energy states. The fact that the visible line splits up further when a magnetic field is applied, that's the anomalous Zeeman effect, suggests further qualities of the electron, namely angular momentum and magnetic orientation, and these two qualities were combined in the Stern-Gerlach experiment to prove the fourth atomic number spin. 

   The more elegant approach was championed by Schördinger, where the electron is conceived as a standing wave with an integer number of waves, and as it absorbs a photon, the number of waves increases, that is, its frequency increases. The transition is continuous and may involve frequencies out with the visible section of the electromagnetic spectrum. The reverse would happen when the electron emits a photon. It may be in the emission spectrum that the standing wave has a transitory or still moment before it settles on a lower frequency. Similarly, in the absorption spectrum, the standing wave may undergo a frisson of high energy before settling on a higher frequency. 

   On the Stern-Gerlach experiment, a full explanation of the contradictions in this experiment and its failure to support the notion of spin is included in the additional material section of the website. The two main points to note, however, are firstly that this experiment was conducted in 1822 and predated the introduction of the concept of spin by about three years and was actually designed to disprove the quantized orientation of the electron. Secondly, the experiment involved an ensemble of silver atoms and the results applied to a single electron, which is 3,000 times smaller than an atom. So harnessing the results is really an ex post facto attempt to lend some credibility to the otherwise dubious variable of spin. 

   Turning to the proton, it is huge in comparison to the electron, but has the same amount of charge but in the opposite direction. The occult strong nuclear force holds the positively charged protons together, otherwise as similar charges repel each other, they would fly apart. And there is no good particle explanation other than spin as to why negatively charged electrons don't collapse into the protons. The neutron has no charge and has broadly the same mass as the proton. These particles are held together along with the protons by the strong nuclear force, which is attractive at short distances, limited to the boundaries of the nucleus, and repulsive at even shorter distances, and together form the nucleus of the atom. The combined mass is less than the sum of the mass of the individual particles, and this deficit is referred to as 'binding energy'. When there is insufficient binding energy, the nucleus becomes unstable or radioactive and decays by emitting energy in the form of alpha, beta, and gamma particles. 

   The alpha particle is the same as a helium nucleus, that is two protons and two neutrons. The beta particle is an electron created by the transition of one of the neutrons in the unstable element into a proton and electron. The gamma decay is the emission of a gamma-ray photon. There are a number of other types of decay involving positrons, neutrinos, and antineutrinos. The weak nuclear force is involved in the decay by facilitating the change of identity of the particles. For the purposes of the present argument, only these three functional subatomic particles will be considered, together with the three forces, strong and weak nuclear force forces and the electrostatic force. The meaning of 'functional' in this context means that they have serious and intrinsic roles to play in various other disciplines. 

   The scientists at CERN have broken these three subatomic particles down into quarks, bosons, leptons, fermions, and further subdivisions. I do not believe that these are functional in any interesting way. As an analogy, think of a car's constituent parts such as wheels, windscreen, engine, battery, and so on. A competent mechanic could assemble these named functional components to make a car. If, however, each functional component were smashed into tiny pieces and names given to each of them, what purpose would this serve? Possibly  some chemists and biologists have flirted with some of the claims of the particle physicists, and I may be wrong, but I do not believe that it has resulted in anything fruitful in these disciplines. This model, if viewed as a mathematical shorthand for solving practical problems, would be fine if it did not also claim to be ontologically sound. It is a case of mistaking the map for the territory, as Alfred North Whitehead cautioned. 

   If you want to find out more, please visit my website at quantumid.science, where you will find more in-depth downloadable essays, book lists, additional material, and original papers by some nineteenth and twentieth century physicists. The next podcast is titled The Wave Model of the Atom, which examines Schrödinger's more coherent approach to atomic structure.

© K.Strang 2025