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The Atomic Model of Niels Bohr

The first quantistic atomic model

If atomic physics seems self-evident today, at the beginning of the 20th century it had yet to be established. Richard Feynman, Nobel prize-winning physicist, during one of his famous physics lessons, said:

“If in a certain cataclysm, where all of the scientific knowledge is to be destroyed, but only one sentence is to be passed down to the next generation of creatures, what would be the best thing? The thing that contains the most information in the least number of words? It is the atomic hypothesis or the atomic fact or whatever you want to call it, that all things are made out of atoms, little particles that move around, are in perpetual motion, attract each other when they’re some distance apart but repel being squeezed into one another. In this single phrase, you see, there’s an enormous amount of information about the world if you only apply a little imagination and reflection”.

At the end of the 1800s, the English physicist Joseph Thomson was the first to suggest that one of the fundamental units of the atom was 1,000 times smaller than the atom itself: this subatomic particle is now known as the electron. Thomson discovered the electron through his explorations of the properties of so-called cathode rays, rays emitted by the negative electrode of an electrical apparatus. In particular, Thomson discovered that cathode rays could travel through the air much farther than atomic-sized particles had previously been thought. His experiments suggested not only that cathode rays were 1,000 times lighter than a hydrogen atom, but also that their mass was the same no matter which atom they came from. From this he concluded that cathode rays were composed of very light and negatively charged particles and that they were a universal building block of the atom. He called these particles “corpuscles” but later on, scientists preferred the name “electron”.

A few years after the discovery of the electron, Thomson proposed the “Plum Pudding Model” to try to explain the two properties of atoms known at the time: that electrons are negatively charged particles and that atoms don’t have a net electrical charge. According to this model, the atom was made up of a distribution of diffuse positive charges, a sort of “jelly” inside of which were inserted the negative charges, much like raisins in a plum pudding.

In 1909, Ernest Rutherford, a student of Thomson, demonstrated the nuclear nature of atoms. The experiment consisted of measuring the deflection of certain subatomic particles—alpha particles—when these were “shot” against a thin gold foil. By measuring the angle of deflection, Rutherford formulated an atomic model in which the main part of matter is concentrated in one chunk, the positively charged nucleus, very small considering atomic dimensions; the electrons rotate around the nucleus like the planets of our solar system rotate around the sun. The problem was that the electrons, orbiting in a circular trajectory are subjected to centrifugal acceleration so, being charged as per Maxwell’s laws, they should irradiate electromagnetic waves thus losing energy until they drop into the nucleus, creating an unstable atom.

Keeping in mind Rutherford’s discoveries, in 1913 the Danish physicist Neils Bohr began to consider what seemed to be a convincing idea. Perhaps the electrons were confined to specific orbits around the nucleus in which they could rotate without irradiating? In every atom there would exist a minimum orbit called the fundamental state, under which the electrons couldn’t descend; otherwise, given their negative charge, they’d be attracted by the positive charge of the nucleus, they would have fallen into it and all matter would explode. Electrons could, however, “jump” from one orbit to another and these jumps were accompanied by an absorption or an emission of light particles, in other words, the photons or light quanta that Einstein had theorized to explain the photoelectric effect.

The jump between two given orbits corresponded to the emission or absorption of a specific frequency of light. Bohr imagined an atomic model analogous to that of the planets orbiting the sun but assumed a stable atom. It was finally possible to calculate the emission spectrum of the hydrogen atom in a way that matched experimental data. It was observed, too, that even the simplest elements such as hydrogen, emit radiation, not in a continuous manner but discretely; in other words, they emit radiation only on specific wavelengths.

If Bohr’s theory resolved experimental problems, from a theoretical standpoint, a lot of work would still be necessary to justify it.




New Quantum Mechanics

The new quantum physics

 To explain the photoelectric effect, Albert Einstein postulated in 1905 that light must be composed of “Light Quanta”, particles that today we know as Photons. Louis de Broglie postulated in 1924 that even particles containing mass must show undulatory characteristics. More precisely, De Broglie theorized that a particle with a certain mass and speed would be equivalent to a wave with a frequency that could be found by dividing the product of the mass and speed of the particle by Planck’s constant. In 1927, only three years later, interference effects were observed using a beam of electrons and a thin metal plate. Thus, even atoms can act like light, giving rise to interference phenomena. These new results were an important building block giving substance to quantum theory.

Up to this point the study of subatomic physics had moved forward only through hypotheses and postulates: Planck theorized that energy exchange in emission phenomena and absorption of electromagnetic radiation occurred in a discrete and not continuous form. Einstein suggested that electromagnetic radiation was made up of light packets. Bohr thought that electrons spun around the nucleus only in circular orbits for which the value of the module of angular moment is a whole multiple of Planck’s constant. De Broglie postulated that a particle with a certain mass and velocity was equivalent to a wave with a frequency proportional to the product of m*v divided by Planck’s constant. But did a theory exist that could explain all this in a coherent way?

In 1925 the German physicist Werner Heisenberg publishes the first complete version of what will be called “Matrix Mechanics”, extending Bohr’s atomic model and justifying from a theoretical standpoint the existence of quantum leaps. Austrian physicist Erwin Schrödinger then published his theory based on an equation that is the basis of Wave Mechanics and that would indeed be called “Schrödinger’s Theory”.


How could these two methods, very different in their mathematic formalism and function, furnish the same answer to the thorny problems raised by quantum mechanics? In reality, matrix mechanics and wave mechanics were two faces of the same coin but it would take yet another genius to demonstrate it.

English physicist Paul Dirac demonstrated mathematically the equivalence between Heisenberg’s and Schrödinger’s formulas, showing that they were both different forms of the so-called transformation theory. Then matter is formed of waves or particles? Which is it? Niels Bohr, in 1927, tried to solve this dilemma with his Principle of Complementarity according to which a complete description of matter and light cannot refer only to its undulatory or particle nature but must necessarily include both. This brings us to the so-called wave-particle dualism. Wave-particle dualism is a principle of quantum physics by which physical objects like elementary particles can be described as both waves and particles.

However, this Principle raised other important questions: waves expand in space, they become stronger or weaker as they are superimposed and can also be in several places at once. Particles are only found in a certain place at a certain moment. Imagine something that can be described simultaneously as a projectile from a pistol, thus a particle, that can be found in a certain position in any instant, and a sound wave that is delocalized.

What does it mean to treat material objects as waves? It means that physical laws don’t tell us, for example, where an electron is but only the probability of finding it in one place and not another! From Quantum Mechanical laws comes the fact that precise limits of measurement exist and so, too, the knowledge of physical values such as the position and speed of a particle.

This impossibility of perfectly knowing the values of all physical aspects in play is called the Principle of Indetermination and was announced by Heisenberg and then confirmed by innumerable experiments. It was only recognized later as being a consequence of the laws of Quantum Mechanics and not an independent principle. This is a key concept of quantum physics and is a radical break from the laws of classical physics. In classical physics, it’s indeed possible to know the speed and position of specific object with arbitrary precision. But when the laws of nature are applied to the subatomic world as determined by quantum physics, they seem to respond completely differently, sometimes contradicting the laws of classical physics. The advent of quantum mechanics signaled a sea change in physics because it was able to offer a full picture of atomic and molecular physics. According to Fermi, these were the good years, an era of great discoveries that revolutionized physics and opened up new horizons.