Why are some nuclei trapped by electrons

Cover story - be careful! Quantum physicist: Marveled, cheered - misunderstood

The Color of the Sun The quantum mechanics revolution began modestly. Its founder was not a juvenile hot spur, more of a reluctant revolutionary. In 1900 Max Planck was 42 years old and taught theoretical physics at the University of Berlin, an exotic subject at the time. Planck was concerned with the question of how colors are created in a hot body. If you heat a piece of iron, it glows red as the temperature rises, then white and finally blue. Planck was certain: There had to be a natural law for all bodies, regardless of their nature, that describes this behavior. Planck imagined that the particles in the bodies vibrate - similar to spiral springs - and absorb and emit radiation in the process. The oscillation frequency should correspond to the energy content of the particles. Physical considerations on the one hand and mathematical trial and error on the other hand finally led him to a formula that reproduced the measurement data surprisingly well. Everything fit together wonderfully - except for one small thing: Planck had to insert a constant into the formula, the meaning of which was completely unclear to him. This quantum of action (h = 6.626 · 10-34 joules · second) indicated that a radiation particle cannot absorb any amount of energy, but only individual “packets”, so-called quanta. “That was a purely formal assumption, and I didn't really think much about it, just that I wanted to bring about a positive result under all circumstances, no matter what the cost,” Planck said later. “It was an act of desperation.” When Planck had finished his lecture on December 14, 1900 at the Physics Institute on Berlin's Reichstagufer, the select audience must have looked rather perplexed. What should you think of that? Nature didn’t make any leaps. Planck himself tried for several years to incorporate his quantum of action into classical physics. In vain. The true nature of this tiny number remained unclear to him for a long time. Their fundamental importance was only discovered in the twenties by a group of young savages. Nevertheless, the day of his lecture is now considered to be the beginning of this physical revolution. Planck's quantum of action connects the energy of a body or gas with the wavelength of the emitted light: the higher the energy or temperature, the shorter the wavelength. This explains why a piece of iron first glows red (long wavelength) and finally blue (short wavelength) as the temperature rises. Quantum theory does not explain why the Planck constant has the value as it is measured today in the laboratory. It must be accepted as given by nature. But what if the Planck constant were larger or smaller? The effects on nature would be huge. Suppose the constant was half or twice as large. Then the sun, provided it still had a surface temperature of 5800 degrees, would no longer appear yellow. Rather, it would then emit most of the radiation at shorter or longer wavelengths than today. It would glow purple or infrared. In the second case we could not see our daytime stars at all, at least with the current condition of our eyes. But the evolution of living things would probably have taken a different course: Plants today might not be able to photosynthesize with red light as usual and would therefore not be green either. The eyes of living things would have developed differently and would be able to see UV or infrared radiation. Crystalline Spheres Planck had discovered the central magnitude of quantum mechanics, but the connection with the atomic world was only slowly becoming clear. Ernest Rutherford had shot helium atomic nuclei at wafer-thin gold foil and found that most of them flew through unhindered. Only a few were distracted, and occasionally they rebounded like ping-pong balls. Rutherford thought about this result for a long time until he had the explanation: he enthusiastically shouted to his assistant Hans Geiger: “I now know what an atom looks like!” He thought it was largely empty. In the center there should be a small nucleus surrounded by the electrons at large distances. This model from 1910 explained Rutherford's experiment, but it posed a crucial problem: According to the well-known laws of electrodynamics, an electrically charged particle emits radiation on a circular path. As a result, it loses energy and approaches the core on a deadly spiral path. It quickly became clear: if Rutherford were right, according to the laws of classical physics, all electrons would have to crash into their nuclei in a fraction of a second. There would be no stable atoms at all. Three years later, one of Rutherford's students radically solved the puzzle. Niels Bohr claimed that the electrons did not travel around the nucleus in any orbit like planets around the sun. Rather, they would be assigned paths that they can only leave under certain circumstances: If they absorb a light particle and gain energy in the process, they hop onto a path further away from the core, and if they release one and lose energy, they jump back again. As long as the electron stays on its orbit, it is in a stationary, unchangeable state. Bohr's theory was grotesque. For a long time he had to argue with Rutherford about the publication: "It seems to me that you are assuming that the electron knows in advance where it will stop," countered Bohr's teacher provocatively. In fact, it looked as if Bohr would reintroduce the crystalline spheres painstakingly removed from astronomy into atomic physics. Yet it could not be denied that his theory could explain the spectrum of luminous hydrogen gas. When Einstein heard about Bohr's work, he is said to have said: “This is one of the greatest discoveries.” But it should only have been the beginning. Borrowed energy It has long been known that electrons do not appear as spheres in some experiments, but that they clearly have the properties of waves. The French Prince Louis Victor de Broglie concluded from this in 1924 that electrons lead a double life. He suggested that the electron should be thought of as a standing wave that surrounds the atomic nucleus. This wave must be such that the circumference of the orbit always corresponds to an integral multiple of the wavelength. The Austrian Erwin Schrödinger took up this idea and worked it out mathematically. He achieved his breakthrough in 1926: in the Schrödinger equation named after him, the electron is a spatially extended wave that surrounds the atomic nucleus and oscillates similarly to a water-filled balloon that is hit. Only certain forms of oscillation are possible, with each form corresponding to a certain energy of the electron. When passing from one shape to another, the electron absorbs or emits a light quantum. That explained why an electron doesn't fall into the nucleus of an atom. Of course, it did not explain that electrons occasionally also appear as particles. In fact, the particle is actually hiding in the wave, so to speak. Their intensity indicates the likelihood of being in a certain location. This theory contradicts the classical physical law, according to which a particle is either in a certain place or not. This is exactly what distinguishes quantum mechanics from classical physics: In the realm of atoms, only probability statements are possible. Blurred paths Werner Heisenberg came across the most profound aspect of this atomic blurriness in 1927. At the age of 25, he had only recently become Germany's youngest professor at the University of Leipzig. He had developed a theory competing with Schrödinger to describe the atoms and the quantum leaps of the electrons. In doing so, he came across the strange fact that the position and momentum of an electron cannot be measured sharply at the same time. If the location is determined precisely, the impulse measurement becomes imprecise - and vice versa. Planck's quantum of action indicates the size of this uncertainty. Heisenberg's uncertainty principle says nothing about the skill of experimental physicists. It describes a fundamental peculiarity of the micro-world and is caused by the fact that particles also appear like "smeared" waves. "If there were ever an experiment that allowed momentum and location to be determined simultaneously and precisely, quantum mechanics would necessarily have to be wrong," claimed Heisenberg. To date, no one has succeeded in such an experiment. This vagueness has a huge impact on nature. It also applies to the time and energy couple. The shorter the process of measuring the energy of an electron, the more inaccurate the value becomes. This has an essential consequence: in classical physics, no particle can get energy out of nowhere. In quantum mechanics it is at least possible for an electron to borrow energy and return it within the time frame set by the uncertainty relation: the shorter the period of time, the greater the energy credit. With this additional energy it is possible for particles to jump over energy barriers that are actually too high for them - for example in the atomic nucleus. Inside the nucleus, the positively charged protons are bound to one another by the nuclear force on the one hand, and on the other they repel each other because of the electrical force and their charge of the same name. In general, nuclear power predominates. One can imagine that the protons roll around in a pot with too little energy to roll out of it. Now two protons and two neutrons can accidentally assemble in the nucleus to form a particularly stable helium nucleus that can escape from the pot. Outside the nucleus, this particle has an energy of four million electron volts. However, the energy barrier in the core is around 30 million electron volts. The particle borrowed the missing amount at short notice. Physicists speak of the tunnel effect because it looks as if the particle has dug a tunnel through the energy barrier. This also happens with radioactive decay, which would not exist without Heisenberg's uncertainty. The reverse process, the merging of two atomic nuclei, is also only possible through the tunnel effect. In the interior of the sun, for example, the temperature and thus the energy of the hydrogen nuclei is far too low for these positively charged particles to overcome the electrical repulsive force and unite. This is only made possible by the tunnel effect. Without quantum mechanical uncertainty, there would be no fire inside the sun. The tunnel effect is now used in technology, for example in the scanning tunneling microscope, with which individual atoms can be examined. An extremely fine metal tip is guided over a surface as close as possible. Usually the space between the tip and the surface forms an insurmountable hurdle for electrons. The tunnel effect, however, repeatedly enables particles to make the seemingly impossible jump. The closer the needle is to the surface, the greater the tunnel current. The surface shape can be determined from its thickness down to atomic resolution. Technically, the tunnel effect is also used in so-called Josephson contacts, in which two superconductors are separated by an insulator. Nevertheless, electrons migrating in pairs in superconductors manage to tunnel through this obstacle. This process can be influenced with magnetic fields. This enables the construction of SQUIDs (Superconducting Quantum Interference Devices) with which even the weakest magnetic fields - for example from brain waves - can be measured. Place cards in the atom Two years before Heisenberg's groundbreaking discovery, another amazing peculiarity of nature had become clear. Bohr had asked himself: If an atom is normally in the lowest energy state, then shouldn't all electrons also have the lowest energy level in this state? This is obviously not the case, because if all electrons in the atoms of all elements were in the same state, all atoms would also have almost the same appearance. Consequently there would not be an abundance of chemical compounds and no life either. The Austrian physicist Wolfgang Pauli came up with the idea in early 1925 that nature must have established a principle of exclusion. It should prescribe that all electrons in an atom have different energy states. Transferred to Bohr's model of the atom, this means that the shells were filled from the inside out with an increasing number of electrons. Pauli later applied his principle to the more abstract quantum mechanical atomic model by Schrödinger and Heisenberg. With Pauli's knowledge, the diversity of the elements could suddenly be explained. Because of the Pauli prohibition, the atoms in the outermost shell had different numbers of electrons, which are responsible for the chemical properties of an element. The Pauli principle has far-reaching consequences in solid-state physics. In a crystal, for example, the atoms are so close that their electrons get in each other's way. As a result, a collective exclusion principle applies to all electrons. That is, no two electrons in the body can be in the same physical state. This has the consequence that the energy levels of the electrons shift against each other. They are so close together that they form a broad band of energy. Strictly speaking, there are two bands. In the band of low energy - the so-called valence band - the electrons are trapped, while in the band of higher energy they can move in the body and conduct electricity. The distance between the two bands determines how easily the electrons can jump over from the valence band to the higher conduction band. This is the key property that distinguishes electrical conductors (tapes overlap), insulators (large spacing) and semiconductors (small spacing). This naturally imposed prohibition on the leveling of electrons cannot be explained in any more depth. It has to be taken for granted. Bohr was enthusiastic about this “complete madness”. Pauli, too, had no more to say than: “We mustn't want to put the atoms in the shackles of our prejudices.” The ban on exclusion is the key to understanding the diversity in nature Construction of the first transistor began and has now reached a high point in microelectronics.

Thomas Bührke

October 1, 2000

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