What did Niels Bohr do right?

The Bohr model of the atom in today's physics

A hundred years ago, Niels Bohr designed his atomic model, which marked a decisive step towards modern quantum physics and which still inspires research today - for example with highly excited Rydberg atoms.

The atomic model by the Danish physicist Niels Bohr, which he published in the “Philosophical Journal” from July 1913, is today considered to be one of the decisive steps from atomic physics to quantum mechanics. At the beginning of the 20th century it was already known that atoms contain electrons whose negative electrical charge is balanced by an equally large positive charge. For a while, the atomic model of the British Nobel Prize winner in physics, Joseph John Thomson, was considered plausible: Atoms are spherical structures that are uniformly positively charged and in which the negative electrons are evenly distributed.

Niels Bohr

The New Zealand physicist Ernest Rutherford, also a Nobel Prize winner, found that atoms contain positively charged protons. The surprising thing about his results was that the protons in the atom are concentrated in an extremely small volume; the diameter of such an atomic nucleus is four to five orders of magnitude smaller than that of the entire atom. The negatively charged electrons had to circle around this positively charged atomic nucleus in some way. According to the laws of classical physics, the electrons are then subject to circular accelerations and accelerated charges emit radiation. In doing so, they would have to lose energy and circle ever closer to the atomic nucleus until they finally fall into it. This consequence of classical physics is in complete contradiction to the observed stability of the atoms.

Niels Bohr recognized the peculiarities of this stability problem very early on. He found an interesting approach with his British colleague John Nicholson. Nicholson had observed some of the sun's spectral lines and tried to reconcile the measured energies with his own atomic model. Despite some shortcomings in this model, Nicholson's great achievement lay in the realization that the orbital angular momentum of the electron orbits had to be quantized. The orbital angular momentum results from the speed and the mass of the electron, multiplied by its distance from the atomic nucleus around which it orbits. After the famous discovery of Max Planck, which ushered in the age of modern physics, energy and radiation can only occur in the smallest indivisible units, the quanta. Obviously, this connection also applied to the orbital motion of the electrons. So they could only walk on certain paths around the atomic nucleus.

The atomic model according to Bohr and Sommerfeld

Bohr took up this idea and developed his atomic model. He thought of the atom as a punctiform, positively charged nucleus around which the electrons circle like planets around their star. To get around the problem of instability, he introduced a new quantum rule: only those circular orbits should be allowed whose energy levels correspond to integer multiples of Planck's quantum of action. An electron can jump back and forth between these orbits when it absorbs or emits radiation. The energy of the radiation then corresponds exactly to the energy difference between the tracks. With this quantum rule, Bohr succeeded in calculating the energy levels in hydrogen, as shown in the spectral lines of the Lyman, Balmer and Paschen series. In these series, an electron passes over from a higher energy level to one of the three lowest energy levels in the hydrogen atom, emitting radiation.

Models of a hydrogen atom from then until now

The theorist Arnold Sommerfeld then expanded Bohr's atomic model to include elliptical orbits, so that the Bohr-Sommerfeld atomic model is also used. This model represents an important step between the early notions of atoms as impenetrable spheres and modern quantum physics. Atoms should now consist of several spheres - atomic nuclei and electrons - that are on classically described orbits, but at the same time meet quantum conditions .

However, this “semiclassical” model failed with more complex atoms, in which, in contrast to hydrogen, several electrons revolve around the atomic nucleus. The atomic physicists were only able to state the reason for this years later with the establishment of quantum mechanics: The microcosm does not obey classical mechanics, as Bohr still assumed; instead, completely new quantum physical laws and interactions play a role. The atomic radius, which Bohr calculated with his simple model for the ground state of the hydrogen atom, nevertheless agrees relatively well with the measured value. Even today, the so-called Bohr atomic radius is therefore used as a quantity in atomic physics. In quantum mechanics, electrons are no longer assigned fixed orbits, but cloud-shaped orbitals. Orbitals express the probability with which an electron is located anywhere around the atomic nucleus. The electron is no longer viewed as a point-like particle, but rather described by a wave function.

Research with highly excited atoms

The Bohr model of the atom has been overtaken by the developments in quantum physics, but in some cases it is still used as an illustration. Interestingly enough, a rule applies that Bohr had also introduced into quantum physics as the so-called correspondence principle. According to her, with strongly excited atoms, the behavior of quantum mechanical systems increasingly assimilates classical physical systems. The higher an atom is excited, the easier it can be described using semiclassical models such as Bohr's atomic model

Researchers are now able to generate highly excited atoms in which the electrons move on extremely wide paths around the atomic nucleus. In honor of the Swedish physicist Johannes Robert Rydberg, such atoms are also called Rydberg atoms. Rydberg states can be generated by irradiating atoms with light of an energy that is as precisely as possible. The light particles then lift the electron from its ground state to a very high orbit. This makes it much more sensitive to electromagnetic waves.

“The larger an atom, the more it interacts with electromagnetic waves such as light,” explains Tilman Pfau, who researches Rydberg atoms at the University of Stuttgart, among other things. The radius of an atom increases quadratically with the quantum number, i.e. the number of multiples of Planck's quantum of action. An atom excited with the principal quantum number of 100 is therefore 10,000 times larger than in the ground state. In such highly excited states, the locations of the electrons no longer look like an orbital, as is the case with the lower states. Instead, they resemble the semiclassical orbits of Bohr's atomic model.

Rydberg atoms

The researchers from Stuttgart are investigating the special behavior of such Rydberg atoms, which they have due to their enormous size. One of them is the so-called Rydberg blockade. Because of its size, a Rydberg atom has such an influence on its atomic environment that no second Rydberg atom can form in its vicinity.

In the meantime, some research groups have reached excitation levels of 300 to 500 for Rydberg atoms. However, these ultra-highly excited atoms are extremely sensitive to external influences because the electron is only very weakly bound in them. That is why they have to be shielded extremely well against heat radiation or electrical fields, for example.

But then the atoms have unique properties. "Rydberg atoms are excellent antennas for electromagnetic radiation," says Pfau. And with these antennas, researchers can do something that would otherwise not be possible: A Rydberg atom interacts with a single photon with a very high probability. This allows atoms and photons to be efficiently entangled with one another. When entangled, the particles form a special quantum-physical connection.

Rydberg atoms and quantum computers

Thanks to the phenomenon of entanglement, quantum computers and quantum cryptography are conceivable, which offer previously unknown possibilities for information processing and data transmission. Research on this is still in its infancy, but Rydberg atoms could play an important role here. “It is now possible to build special logic gates with optically manipulated Rydberg atoms,” says Pfau. Such logic gates are the basic building blocks for all possible arithmetic operations.

There are now a number of research groups around the world that work on these problems from different angles. At the Max Planck Institute for Quantum Optics in Garching, scientists are also working on Rydberg atoms. Immanuel Bloch's group has succeeded in arranging Rydberg atoms through targeted irradiation with laser light in such a way that a quasi-crystalline structure emerges. This could also be used for logic gates in a quantum computer. "We are particularly interested in how the interaction can be controlled in a targeted manner in order to generate new states of matter," explains Bloch. The technical possibilities that this basic research opens up are extensive. "We are therefore also researching the generation of many-particle states, because these are important for a powerful quantum computer," says Bloch.

The remarkable thing about the Rydberg atoms is that they build a bridge between the early beginnings of atomic physics and today's high technology based on quantum mechanics. Rydberg atoms are, so to speak, a particularly clear embodiment of the principle of correspondence, because they show the classical laws and the quantum laws equally.