Have you completed the course unit Das Elektron and are looking for further material? Then we recommend the following learning units:

### The Millikan experiment (oil droplet experiment)40 min.

#### ChemistryGeneral Chemistryatomic structure

The Millikan oil droplet experiment is discussed in depth.

## The electron on the scales

© Sven Sturm / MPI for Nuclear Physics

A balance for absolute lightweights: In this Penning trap, physicists determine the mass of an electron by forcing it together with a carbon-12 nucleus on a screwed circular path. The orbital frequency of the carbon ion is included in a calculation that ultimately provides an extremely precise value for the electron mass.

© Sven Sturm / MPI for Nuclear Physics

How do you weigh an electron? In a Penning trap (left), a magnetic field (black arrow) forces a carbon-12 nucleus with a single electron to run on a screwed circuit (right). Simply imagine this as a circular path (green). The precise mass of the carbon-12 nucleus with one electron can be determined from the rotational frequency. From the mass of the fivefold charged carbon ion and the gyration of the electron spin (black line, right), a quantum mechanical relationship then gives the electron mass.

Electrons are the quantum cement of our world. Without electrons there would be no chemistry and light could not interact with matter. If electrons were just a little heavier or lighter than they are, the world would look radically different. But how do you weigh a particle that is so tiny that it has until now been considered point-shaped? This feat has now been achieved through a cooperation involving physicists from the Max Planck Institute for Nuclear Physics in Heidelberg. It “weighed” the mass of the electron 13 times more precisely than previously known. Since the electron mass is contained in fundamental natural constants, this is important for basic physics.

“Normally you have to research precision physics for ten or twenty years to improve a fundamental value by an order of magnitude,” says Klaus Blaum. The director at the Max Planck Institute for Nuclear Physics in Heidelberg is happy to report on the “enormous reaction” that the latest result provokes at scientific conferences. In just a few years, a research collaboration led by the Heidelberg team managed to determine the value of the mass of an electron more precisely by a factor of 13. Project manager Sven Sturm illustrates the extremely high sensitivity of the “scales” used for this purpose: “Converted to an Airbus A-380, we could determine whether a mosquito was on board as a stowaway by weighing alone.”

It is important that physicists now know the mass of the electron exactly to eleven places behind the decimal point, because electrons are involved practically everywhere. Even to read this text, electrons in the eyes have to convert light into nerve impulses. These ultra-tiny particles, which, according to current knowledge, have no size, represent a tremendous power in nature. Among other things, the value of fundamental natural constants is related to their mass. This includes, for example, the so-called fine structure constant: This constant determines the shape and properties of atoms and molecules. “It basically describes everything we see,” says Blaum, “because it plays a central role in the interaction between light and matter.” If nature had given the electrons just a slightly different mass, the atoms would look completely different. Such a world would be very strange.

### The electron is weighed with a carbon nucleus

The mass of the electron is also included as a central variable in the so-called standard model of physics. This model describes three of the four basic forces known today in physics. Even though it works impressively well, it is still clear today that its validity is limited. However, it is not clear where these limits of the Standard Model lie. Precise knowledge of the electron mass can therefore be of decisive help in the search for previously unknown physical relationships.

To determine the extremely small mass of the electron, the physicists working with Klaus Blaum and Sven Sturm developed a sophisticated experiment. Basically, you need a reference for comparison when weighing. "When you step on the scales in the morning, it's a spring with the old mechanical models," explains Blaum. Beam scales have a counterweight for reference. With the electron, the physicists were faced with the problem that all elementary particles that could usefully be used as reference weights are much heavier. “The proton or the neutron, for example, is two thousand times heavier,” explains Blaum, “that would be like weighing a rabbit with an elephant as a counterweight.” In their experiment, the physicists therefore decided on a trick. Although they brought together two extremely unequal masses, they did not even try to weigh the rabbit electron directly with the help of an atomic elephant.

Sven Sturm set up the experiment as Blaums doctoral student at the University of Mainz. “The main challenge was developing the measurement method,” he says. As a postdoctoral fellow, he then heads the team that carried out the precise measurement of the electron mass. The physicists paired a single electron with a bare nucleus of the much heavier carbon (C) -12 isotope. This carbon isotope has been carefully selected because it defines what is known as the atomic mass unit. Thus, by definition, the exact mass of C-12 is known, and using it as a reference eliminates an important source of error. "The control of systematic errors is very important," emphasizes Sturm.

### The carbon ion completes a racing course in a Penning trap

To prepare the C-12 nucleus with the single electron, the physicists shot five of the six electrons away from the carbon atom. They sent the remaining five-fold charged carbon ion - the carbon nucleus with a single electron - on a racing circuit that, in a simplified way, can be imagined as circular. A so-called Penning trap, with its extremely uniform magnetic field, forces the carbon ion onto this circular path.

“With precision measurements, one always strives to make the measured variable precisely countable”, explains Blaum the ulterior motive: “In a Formula 1 race on a circuit, spectators can count how often a racing car speeds by and use the length of the track to count them Estimate speed. ”It works in a similar way in the Penning trap, in which case the physicists were able to measure even the smallest fractions of entire cycles.

In the second step, which was now necessary to determine the electron mass, quantum mechanics helps. Electrons have a “spin”, and this makes them a tiny magnet. In the strong magnetic field of a Penning trap, this spin performs a precession motion like a tiny top. This is extremely fast, but the physicists were able to capture it precisely using tricks. The decisive factor here is: the orbital frequency of the carbon ion in the trap and the wobbling frequency of the electron precession are in an exact relationship. In this way, like a gear train, quantum mechanics firmly links the mass of the carbon ion with the mass of the electron, which can then be measured.

### Only a theoretical contribution made it possible to measure the electron mass

However, there was a not-so-well-known "cogwheel" in this gear train. In physics, it is known as the g-factor or the gyromagnetic factor. "The close cooperation with Christoph Keitel's theory department at our institute was crucial here," explains Blaum. Based on previous results from the same collaboration, the Heidelberg theorists headed by group leader Zoltan Harman were able to calculate the g-factor more precisely than ever before and thus achieve the highest level of precision in determining the electron mass to date.

Precision experiments of this kind benefit from collaborations with scientists who bring different levels of expertise. Physicists from the GSI Helmholtz Center for Heavy Ion Research in Darmstadt and the Johannes Gutenberg University Mainz made important contributions. The result is an extremely precise number: the electron weighs one 1836.15267377th of the proton mass. If you want to convert your mass into kilograms, you get an unimaginable 10-30 kilograms, i.e. thirty zeros after the decimal point. The electron is truly a lightweight and yet it plays an important role in nature.

## Quantum mechanical treatment Edit source]

In order to describe the hydrogen atom correctly, one must go to the QM description:

Stationary SG:

The two-body problem is decoupled through the introduction of center of gravity and relative coordinates:

The movement of the center of gravity corresponds to that of a free particle and can be determined by the product approach be separated.

The remaining equation can due to the radial symmetry through a product approach into a DGL for be convicted.

This can after splitting off the asymptotic behavior can be solved by the Laguerre polynomials and finally leads to the hydrogen forbitals.

### Stationary solutions Edit source]

- are the generalized Laguerre polynomials of degree .

The hydrogen levels are twofold degenerate (in l and m), although due to the radial symmetry only a degeneracy in the m quantum number would have been expected. Except for the reduced mass, they are precisely given by Bohr's energy levels.

the **l-degeneracy of the hydrogen spectrum** is characteristic of the Coulomb potential. The only other radially symmetric potential that exhibits this property is the 3d harmonic oscillator. To put it clearly, the deterioration is already evident in the classic Kepler problem noticeable because the elliptical solution trajectories are not yet fully characterized by the given energy and angular momentum. As an additional conservation variable there is the Runge-Lenz vector, which contains information about the eccentricity of the elliptical orbit.

Due to the shielding effects of electrons on deeper shells, multi-electron atoms no longer have a simple Coulomb potential; the l-degeneracy of their energy levels is therefore canceled even without relativistic corrections.

### Visualization of the orbitals [edit | Edit source]

## The free electron in physics and technology

Authors: **Fractions**, E., **Ewest**, H., **Frerichs**, R., **Gerlach**, W., **Glaziers**, A., **Kossel**, W., **Ramsauer**, C., **Rothe**, H., **Rukop**, H., **Ruska**, E., **Schottky**, W., **Steenbeck**, M.

Editor: **Guild master**, M., **Goldschmidt**, R., **Neuberg C. Parnas, J. Ruhland, W.** (Ed.)

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## Electrons in solids - ribbon model

Now many atoms join together like this in one **Solid body** is the case, a corresponding number of molecular orbitals are formed. Each molecular orbital in turn has its own specific energy value. Since these energy values are all within a limited range around the energy of the original atomic orbital, their intervals are very small - so small that the energy values are practically continuous. This means that the individual molecular orbitals become one **Energy band** smear.

The expression & ldquoBand & ldquo for the energy states extended over the entire crystal therefore has nothing to do with the spatial form, but refers to the (almost) continuous energy values - it is not about a & ldquoBand & ldquo that winds through the crystal. To a certain extent, the energy band envelops all atoms.

However, there may still be energy gaps between the bands that cannot be filled.

Because the gaps between the individual energy levels within a band are very small, the electrons can easily jump from one level to the next. But even in the band, two electrons cannot have exactly the same energy. So if all energy states in a band are occupied, the electrons cannot & quot; their & ldquo leave & ldquo state - unless they leave the band and jump into another band. Whether this is possible depends on how big the energy difference to the next higher band is. Since the energy bands in the crystal take the place of the orbitals in the atom, they are through so-called **Energy gap** separated from each other - comparable to the energetic distances between the orbitals in the atom. There are no energy levels in these energy gaps - just as there are no possible energy levels for electrons between the orbitals in the atoms.

The size of the energy gaps and the occupation of the bands is what distinguishes metals, insulators and semiconductors from one another. at **Metals** is the (energetically considered) highest band that still contains electrons, is not completely filled - the electrons still find free energy levels within this band and can move in the band and transport a current.

The uppermost band occupied by electrons is called the valence band, the one in which conduction is possible because there are still free spaces is called the conduction band. In the case of metals, the uppermost band is therefore at the same time the valence and conduction band. One speaks generally of the conduction band.

Changing the energy state means changing speed. If an electrical voltage is applied to a metal, it can supply the electrons with energy by raising them to a higher energy level - or to put it in the classic way: by setting them in motion.

at **Isolators** (like diamond) the highest band containing electrons is completely filled - the electrons do not find any free energy levels in the band and are therefore immobile. (This tape is called **Valence band**.) In order to set them in motion, they would have to receive so much energy that they could reach the next highest empty band. (This is the conduction band.) The energy gap between the valence and conduction band is too large, and the supply of electrical energy from a voltage source is not enough to lift the electrons into the conduction band. Therefore no electricity can flow.

at **Semiconductors** (like silicon) the valence band is also completely filled, but with them the energy gap to the conduction band is so small that it is easily possible to supply the electrons in the valence band with the energy that lifts them into the conduction band. Even at room temperature, some electrons move from the valence band to the conduction band.

## The electron on the scales

09.02.2014

Max Planck Institute for Physics, Heidelberg

Electrons are the quantum cement of our world. Without electrons there would be no chemistry and light could not interact with matter. If electrons were just a little heavier or lighter than they are, the world would look radically different. But how do you weigh a particle that is so tiny that it has until now been considered point-shaped? This feat has now been achieved through a cooperation involving physicists from the Max Planck Institute for Nuclear Physics in Heidelberg. It “weighed” the mass of the electron 13 times more precisely than previously known. Since the electron mass is contained in fundamental natural constants, this is important for basic physics.

“Normally you have to research precision physics for ten or twenty years to improve a fundamental value by an order of magnitude,” says Klaus Blaum. The director at the Max Planck Institute for Nuclear Physics in Heidelberg is happy to report on the “enormous reaction” that the latest result provokes at scientific conferences. In just a few years, a research collaboration led by the Heidelberg team managed to determine the value of the mass of an electron more precisely by a factor of 13. The project manager Sven Sturm illustrates the extremely high sensitivity of the “scales” used for this: “Converted to an Airbus A-380, we could determine whether a mosquito is on board as a stowaway by weighing alone.”

It is important that physicists now know the mass of the electron exactly to eleven places behind the decimal point, because electrons are involved practically everywhere. Even to read this text, electrons in the eyes have to convert light into nerve impulses. These ultra-tiny particles, which, according to current knowledge, have no size, represent a tremendous power in nature. Among other things, the value of fundamental natural constants is related to their mass. This includes, for example, the so-called fine structure constant: This constant determines the shape and properties of atoms and molecules. “It basically describes everything we see,” says Blaum, “because it plays a central role in the interaction between light and matter.” If nature had given the electrons just a slightly different mass, the atoms would look completely different. Such a world would be very strange.

**The electron is weighed with a carbon nucleus**

The mass of the electron is also included as a key variable in the so-called standard model of physics. This model describes three of the four basic forces known today in physics. Even though it works impressively well, it is still clear today that its validity is limited. However, it is not clear where these limits of the Standard Model lie. Precise knowledge of the electron mass can therefore be of decisive help in the search for previously unknown physical relationships.

To determine the extremely small mass of the electron, the physicists working with Klaus Blaum and Sven Sturm carried out a sophisticated experiment. It represents a further development of a project started by the working group of Prof. Günter Werth at the Institute of Physics at the University of Mainz. Basically, you need a reference for comparison when weighing. "When you step on the scales in the morning, it's a spring with the old mechanical models," explains Blaum. Beam scales have a counterweight for reference. With the electron, the physicists were faced with the problem that all elementary particles that could usefully be used as reference weights are much heavier. “The proton or the neutron, for example, is two thousand times heavier,” explains Blaum, “that would be like weighing a rabbit with an elephant as a counterweight.” In their experiment, the physicists therefore decided on a trick. Although they brought two extremely unequal masses together, they did not even try to weigh the rabbit electron directly with the help of an atomic elephant.

“The main challenge was to improve the measurement method,” says Sven Sturm. As a postdoctoral fellow, he leads the team that carried out the precise measurement of the electron mass. The physicists paired a single electron with a bare nucleus of the much heavier carbon (C) -12 isotope. This carbon isotope has been carefully selected because it defines what is known as the atomic mass unit. Thus, by definition, the exact mass of C-12 is known, and using it as a reference eliminates an important source of error. “The control of systematic errors is very important,” emphasizes Sturm.

**The carbon ion completes a racing course in a Penning trap**

To prepare the C-12 nucleus with the single electron, the physicists shot five of the six electrons away from the carbon atom. They sent the remaining five-fold charged carbon ion - the carbon nucleus with a single electron - on a racing circuit that, in a simplified way, can be imagined as circular. A so-called Penning trap, with its extremely uniform magnetic field, forces the carbon ion onto this circular path.

“With precision measurements, one always strives to make the measured variable precisely countable”, explains Blaum the ulterior motive: “In a Formula 1 race on a circuit, spectators can count how often a racing car speeds by and use the length of the track to count them Estimate speed. ”It works in a similar way in the Penning trap, in which case the physicists were able to measure even the smallest fractions of entire cycles.

In the second step, which was now necessary to determine the electron mass, quantum mechanics helps. Electrons have a "spin", and this makes them a tiny magnet. In the strong magnetic field of a Penning trap, this spin performs a precession motion like a tiny top. This is extremely fast, but the physicists were able to capture it precisely using tricks. The decisive factor here is: The orbital frequency of the carbon ion in the trap and the wobbling frequency of the electron precession are in an exact relationship. In this way, like a gear train, quantum mechanics firmly links the mass of the carbon ion with the mass of the electron, which can then be measured.

**Only a theoretical contribution made it possible to measure the electron mass**

However, there was a not-so-well-known "cogwheel" in this gear train. In physics, it is known as the g-factor or the gyromagnetic factor. "The close cooperation with Christoph Keitel's theory department at our institute was decisive here," explains Blaum. Based on previous results from the same collaboration, the Heidelberg theorists working with Jacek Zatorski were able to calculate the g-factor more precisely than ever before and thus achieve the highest level of precision in determining the electron mass to date.

Precision experiments of this kind benefit from collaborations with scientists who bring different levels of expertise. Physicists from the GSI Helmholtz Center for Heavy Ion Research in Darmstadt and the Johannes Gutenberg University Mainz made important contributions. The result is an extremely precise number: the electron weighs one 1836.15267377th of the proton mass. If you want to convert your mass into kilograms, you get an unimaginable 10-30 kilograms, i.e. thirty zeros after the decimal point. The electron is truly a lightweight and yet it plays an important role in nature.

(RW / PH / BF)

Max Planck Institute for Physics, Heidelberg

**publication**

Sven Sturm, Florian Köhler, Jacek Zatorski, Anke Wagner, Zoltán Harman, Günter Werth, Wolfgang Quint, Christoph H. Keitel and Klaus Blaum

"High-precision measurement of the atomic mass of the electron" *Nature*, February 20, 2014

doi: 10.1038 / nature1302601

## Particle Physics: The Enigmatic Electron

Load.What is an electron This question played a central role in the development of quantum theory in the early 20th century and continues to push physics to its limits today. There are several irreconcilable answers, all of which seem correct. Even a century after the Danish physicist Niels Bohr imagined the electron as the satellite of the proton [1], our picture of the electron is still developing and expanding.

In 1927 Bohr provided his answer to the question and with it his beloved concept of complementarity: Under some circumstances electrons can best be described as particles, with a clear location, others like waves, with a clear momentum [2]. Both representations are valid and meaningful, even if, according to Heisenberg's uncertainty principle, they are mutually exclusive: location and momentum cannot be known exactly at the same time. Each image only records certain properties of the electron, but none of them fully characterize it.

Load.#### This article is included in Spectrum & # 8211 Die Woche 25 KW 2013

Modern quantum theory reinforces Bohr's idea that what you see depends on how you look at it. Electrons are both incredibly simple and incredibly complex. They are understood down to the last detail and yet remain mysterious. Electrons form the solid foundation in the worldview of physicists, and at the same time represent a kind of toy that they want to split up and manipulate.

### Simple and complex

In most practical applications, the electron appears as a structureless particle with an intrinsic angular momentum or spin. Just two numbers & # 8211 the mass of the electron and its electrical charge & # 8211 are sufficient to describe its behavior with the help of mathematical equations. Based on this "practical electron model", physicists developed modern microelectronics. It also forms the working basis for chemistry, including biochemistry. But to a high-energy positron (anti-electron), an electron appears to be much more multifaceted. Collisions of electrons and positrons, as they took place at the Large Electron-Positron Collider (LEP) at CERN, produce a flood of quarks, gluons, muons, tau-leptons, photons and neutrinos. In order to understand the complexity of an electron, all the exotic means of modern physics have to be used.

Between these two observations & # 8211 the electron appears as a simple point particle and, on the other hand, apparently contains the entire world & # 8211 there is a huge conflict. However, through a concept that I call quantum censorship, the two views can be reconciled: The properties of the objects change depending on the energy with which they are examined. This quantum censorship was already implicit in Bohr's atomic model and, in a general form, forms a central pillar of modern quantum theory.

In his 1913 published model of the hydrogen atom [1] Bohr imagined that the electron orbits the proton like a tiny planet around the sun. But such mechanical models of the atom have serious problems, as the physicist James Clerk Maxwell had already pointed out, and Bohr was also aware of this. They predict a multitude of hydrogen atoms, with different orbital shapes and sizes, when in reality all hydrogen atoms are identical. The models also produce unstable atoms. Because moving electrons would have to emit energy and thus approach the central proton on spiral paths. But they clearly don't do that.

Bohr made these difficulties out of the way by making some bold assumptions. To avoid instability, he restricted the electrons to a number of discrete or quantized energy states within the atom. He realized that the level with the lowest energy or the ground state has a finite size and holds the electron and proton apart. Today we trace Bohr's postulates back to the fact that the correct quantum mechanical description of electrons is based on wave functions that describe the oscillation patterns of standing waves. The equations for electrons in atoms are similar to those for vibrations in musical instruments that produce different tones.

The same ideas can also be applied to complex, bound systems, such as atoms with many electrons and larger nuclei. If only a little energy is fed in, a system in its basic state tends to remain there too & # 8211 and not reveal any information about its internal structure. Only when it is stimulated into a higher state does its complexity emerge. This is the essence of quantum censorship. Below a certain energy threshold, atoms therefore appear to us as the "hard, massive, impenetrable" particles that Isaac Newton once assumed. Its components can be separated using this.

Likewise, electrons do not reveal anything about their inner workings at low energies, despite their multifaceted nature in the LEP accelerator. The electron structure is only revealed if enough energy is provided to generate electron-positron pairs & # 8211 that is at least one megaelectron volt, which corresponds to the above-ground temperature of 10 10 Kelvin. The concrete electron is therefore not a mere approximation of reality, in the usual sense of uncertainty, but an exact description that applies under restricted (albeit very generous) conditions.

Load.Now that we have seen its importance, we should appreciate the intellectual splendor of the concrete electron. Each of its properties is closely interwoven with profound symmetries of physical laws: the mass and spin of a particle with the special theory of relativity and the electrical charge with the "gauge symmetry" of electromagnetism. The behavior of the concrete electron under symmetry operations determines its physical behavior. The electron is thus the epitome of symmetry: its physical properties are inextricably linked with its mathematical form.

### Precise and mysterious

In principle, electrons can have both magnetic and electrical dipole fields, the axes of which are determined by the spin of the electron. But the status of these fields could hardly be more different. The strength of the magnetic field offers perhaps the most precise and uniquely successful balance between theory and experiment in all of natural science, while the magnitude of the electric field has never been measured. He even puzzles theorists.

Detecting the magnetic field strength of the electron & # 8211 in the form of a gyromagnetic ratio or "g-factor" & # 8211 was a central subject of physics in the 20th century. The relativistic wave equation for electrons, which the physicist Paul Dirac formulated in 1928 [3], had its first success. Demnach sollte g = 2 sein, was mit Ergebnissen aus der Atomspektroskopie übereinstimmte. Nach dem Krieg hatte sich die Präzisionsspektroskopie weiterentwickelt, und man zeigte mit Hilfe von Atomstrahlen, dass g um ein Tausendstel von diesem Wert abweicht. Diese Differenz konnten Theoretiker erst erklären, nachdem sie die mathematischen Schwierigkeiten in der Quantenfeldtheorie ausreichend gemeistert hatten und Korrekturen für die Dirac-Gleichung berechnen konnten, um Quantenfluktuationen zu berücksichtigen.

Der kreative Dialog zwischen Experiment und Theorie setzt sich auch heute noch fort, wobei die verbesserte Genauigkeit auf beiden Seiten immer gründlichere Vergleiche erlaubt. Die experimentelle Grenze hat sich zu großartigen Untersuchungen einzelner Elektronen in elektrischen und magnetischen Fallen verschoben. Theoretische Berechnungen werden zunehmend komplexer und schließen inzwischen auch die Fluktuationen der Fluktuationen in den Fluktuationen ein. Der Wert für g ist auf zwölf signifikante Stellen bekannt [4].

Eine unausgereifte, aber reizvolle "Erklärung" für den Ursprung des Magnetfelds beim Elektron könnte sein, dass die Quantenunschärfe bezüglich des Orts die Ladung des Elektrons über ein Volumen verschmiert, das sich wegen des Elektronspins dreht. Das Elektron ist also gewissermaßen eine rotierende, geladene Kugel, und diese erzeugt nach den Grundregeln des Elektromagnetismus ein magnetisches Dipolfeld. Die Größe dieser Kugel schätzen Physiker auf rund 2,4 x 10 -12 Meter. Alle Versuche, die Position eines Elektrons genauer als dies zu ermitteln, würde der Unschärferelation zufolge so viel Energie erfordern, dass zusätzliche Elektronen und Antielektronen entstehen und die Identität des ursprünglichen Elektrons verschleiern.

Ein elektrischer Dipol, sollte er denn existieren, würde weit gehend ähnliche Korrekturen bewirken. Doch bislang bleibt ein solches Feld unentdeckt. Physiker investierten viel Mühe in die experimentelle Suche und setzten alle Tricks und Fallen ein, die damals das magnetische Moment aufdeckten. Bisher existiert nur eine obere Schranke für das elektrische Dipolmoment [5]. Diese ist beträchtliche 17 Größenordnungen kleiner als man erwarten würde – harmlos, angesichts effektiven Größe des Elektrons.

## Elektron

**Elektron**, zur Familie der Leptonen gehörendes elementares Fermion (Elementarteilchen). Das Elektron hat eine Masse von 511 keV / c 2 , entsprechend 9,1096 · 10 -31 kg (5,4859 · 10 -4 amu), eine Ladung entsprechend der Elementarladung von 1,60219 · 10 -19 C und trägt als Fermion einen Spin von 1 / 2 . Das Elektron unterliegt der starken und elektroschwachen Wechselwirkung. Der Name leitet sich aus dem griechischen Wort für Bernstein ab. J.J. Thomson entdeckte das Elektron in den Jahren 1897-1899 im Rahmen seiner Versuche zur Bestimmung des Ladungs-Masse-Verhältnisses *e* / *m* für Kathodenstrahlen.

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Andreas Kohlmann, Heidelberg [AK2] (A) (29)

Dr. Barbara Kopff, Heidelberg [BK2] (A) (26)

Dr. Bernd Krause, Karlsruhe [BK1] (A) (19)

Ralph Kühnle, Heidelberg [RK1] (A) (05)

Dr. Andreas Markwitz, Dresden [AM1] (A) (21)

Holger Mathiszik, Bensheim [HM3] (A) (29)

Mathias Mertens, Mainz [MM1] (A) (15)

Dr. Dirk Metzger, Mannheim [DM] (A) (07)

Dr. Rudi Michalak, Warwick, UK [RM1] (A) (23)

Helmut Milde, Dresden [HM1] (A) (09 Essay Akustik)

Guenter Milde, Dresden [GM1] (A) (12)

Maritha Milde, Dresden [MM2] (A) (12)

Dr. Christopher Monroe, Boulder, USA [CM] (A) (Essay Atom- und Ionenfallen)

Dr. Andreas Müller, Kiel [AM2] (A) (33 Essay Alltagsphysik)

Dr. Nikolaus Nestle, Regensburg [NN] (A) (05)

Dr. Thomas Otto, Genf [TO] (A) (06 Essay Analytische Mechanik)

Prof. Dr. Harry Paul, Berlin [HP] (A) (13)

Cand. Phys. Christof Pflumm, Karlsruhe [CP] (A) (06, 08)

Prof. Dr. Ulrich Platt, Heidelberg [UP] (A) (Essay Atmosphäre)

Dr. Oliver Probst, Monterrey, Mexico [OP] (A) (30)

Dr. Roland Andreas Puntigam, München [RAP] (A) (14 Essay Allgemeine Relativitätstheorie)

Dr. Gunnar Radons, Mannheim [GR1] (A) (01, 02, 32)

Prof. Dr. Günter Radons, Stuttgart [GR2] (A) (11)

Oliver Rattunde, Freiburg [OR2] (A) (16 Essay Clusterphysik)

Dr. Karl-Henning Rehren, Göttingen [KHR] (A) (Essay Algebraische Quantenfeldtheorie)

Ingrid Reiser, Manhattan, USA [IR] (A) (16)

Dr. Uwe Renner, Leipzig [UR] (A) (10)

Dr. Ursula Resch-Esser, Berlin [URE] (A) (21)

Prof. Dr. Hermann Rietschel, Karlsruhe [HR1] (A, B) (23)

Dr. Peter Oliver Roll, Mainz [OR1] (A, B) (04, 15 Essay Distributionen)

Hans-Jörg Rutsch, Heidelberg [HJR] (A) (29)

Dr. Margit Sarstedt, Newcastle upon Tyne, UK [MS2] (A) (25)

Rolf Sauermost, Waldkirch [RS1] (A) (02)

Prof. Dr. Arthur Scharmann, Gießen (B) (06, 20)

Dr. Arne Schirrmacher, München [AS5] (A) (02)

Christina Schmitt, Freiburg [CS] (A) (16)

Cand. Phys. Jörg Schuler, Karlsruhe [JS1] (A) (06, 08)

Dr. Joachim Schüller, Mainz [JS2] (A) (10 Essay Analytische Mechanik)

Prof. Dr. Heinz-Georg Schuster, Kiel [HGS] (A, B) (11 Essay Chaos)

Richard Schwalbach, Mainz [RS2] (A) (17)

Prof. Dr. Klaus Stierstadt, München [KS] (A, B) (07, 20)

Cornelius Suchy, Brussels [CS2] (A) (20)

William J. Thompson, Chapel Hill, USA [WJT] (A) (Essay Computer in der Physik)

Dr. Thomas Volkmann, Köln [TV] (A) (20)

Dipl.-Geophys. Rolf vom Stein, Köln [RVS] (A) (29)

Patrick Voss-de Haan, Mainz [PVDH] (A) (17)

Thomas Wagner, Heidelberg [TW2] (A) (29 Essay Atmosphäre)

Manfred Weber, Frankfurt [MW1] (A) (28)

Markus Wenke, Heidelberg [MW3] (A) (15)

Prof. Dr. David Wineland, Boulder, USA [DW] (A) (Essay Atom- und Ionenfallen)

Dr. Harald Wirth, Saint Genis-Pouilly, F [HW1] (A) (20)Steffen Wolf, Freiburg [SW] (A) (16)

Dr. Michael Zillgitt, Frankfurt [MZ] (A) (02)

Prof. Dr. Helmut Zimmermann, Jena [HZ] (A) (32)

Dr. Kai Zuber, Dortmund [KZ] (A) (19)

Dr. Ulrich Kilian (responsible)

Christine Weber

Priv.-Doz. Dr. Dieter Hoffmann, Berlin

In eckigen Klammern steht das Autorenkürzel, die Zahl in der runden Klammer ist die Fachgebietsnummer eine Liste der Fachgebiete findet sich im Vorwort.

Markus Aspelmeyer, München [MA1] (A) (20)

Dr. Katja Bammel, Cagliari, I [KB2] (A) (13)

Doz. Dr. Hans-Georg Bartel, Berlin [HGB] (A) (02)

Steffen Bauer, Karlsruhe [SB2] (A) (20, 22)

Dr. Günther Beikert, Viernheim [GB1] (A) (04, 10, 25)

Prof. Dr. Hans Berckhemer, Frankfurt [HB1] (A, B) (29)

Dr. Werner Biberacher, Garching [WB] (B) (20)

Prof. Tamás S. Biró, Budapest [TB2] (A) (15)

Prof. Dr. Helmut Bokemeyer, Darmstadt [HB2] (A, B) (18)

Dr. Ulf Borgeest, Hamburg [UB2] (A) (Essay Quasare)

Dr. Thomas Bührke, Leimen [TB] (A) (32)

Jochen Büttner, Berlin [JB] (A) (02)

Dr. Matthias Delbrück, Dossenheim [MD] (A) (12, 24, 29)

Karl Eberl, Stuttgart [KE] (A) (Essay Molekularstrahlepitaxie)

Dr. Dietrich Einzel, Garching [DE] (A) (20)

Dr. Wolfgang Eisenberg, Leipzig [WE] (A) (15)

Dr. Frank Eisenhaber, Wien [FE] (A) (27)

Dr. Roger Erb, Kassel [RE1] (A) (33 Essay Optische Erscheinungen der Atmosphäre)

Dr. Christian Eurich, Bremen [CE] (A) (Essay Neuronale Netze)

Dr. Angelika Fallert-Müller, Groß-Zimmern [AFM] (A) (16, 26)

Stephan Fichtner, Heidelberg [SF] (A) (31)

Dr. Thomas Filk, Freiburg [TF3] (A) (10, 15 Essay Perkolationstheorie)

Natalie Fischer, Walldorf [NF] (A) (32)

Dr. Harald Fuchs, Münster [HF] (A) (Essay Rastersondenmikroskopie)

Dr. Thomas Fuhrmann, Mannheim [TF1] (A) (14)

Christian Fulda, Hannover [CF] (A) (07)

Dr. Harald Genz, Darmstadt [HG1] (A) (18)

Michael Gerding, Kühlungsborn [MG2] (A) (13)

Prof. Dr. Gerd Graßhoff, Bern [GG] (A) (02)

Andrea Greiner, Heidelberg [AG1] (A) (06)

Uwe Grigoleit, Weinheim [UG] (A) (13)

Prof. Dr. Michael Grodzicki, Salzburg [MG1] (B) (01, 16)

Gunther Hadwich, München [GH] (A) (20)

Dr. Andreas Heilmann, Halle [AH1] (A) (20, 21)

Carsten Heinisch, Kaiserslautern [CH] (A) (03)

Dr. Christoph Heinze, Hamburg [CH3] (A) (29)

Dr. Marc Hemberger, Heidelberg [MH2] (A) (19)

Florian Herold, München [FH] (A) (20)

Dr. Hermann Hinsch, Heidelberg [HH2] (A) (22)

Priv.-Doz. Dr. Dieter Hoffmann, Berlin [DH2] (A, B) (02)

Dr. Georg Hoffmann, Gif-sur-Yvette, FR [GH1] (A) (29)

Dr. Gert Jacobi, Hamburg [GJ] (B) (09)

Renate Jerecic, Heidelberg [RJ] (A) (28)

Dr. Catherine Journet, Stuttgart [CJ] (A) (Essay Nanoröhrchen)

Prof. Dr. Josef Kallrath, Ludwigshafen, [JK] (A) (04 Essay Numerische Methoden in der Physik)

Priv.-Doz. Dr. Claus Kiefer, Freiburg [CK] (A) (14, 15 Essay Quantengravitation)

Richard Kilian, Wiesbaden [RK3] (22)

Dr. Ulrich Kilian, Heidelberg [UK] (A) (19)

Dr. Uwe Klemradt, München [UK1] (A) (20, Essay Phasenübergänge und kritische Phänomene)

Dr. Achim Knoll, Karlsruhe [AK1] (A) (20)

Dr. Alexei Kojevnikov, College Park, USA [AK3] (A) (02)

Dr. Berndt Koslowski, Ulm [BK] (A) (Essay Ober- und Grenzflächenphysik)

Dr. Bernd Krause, München [BK1] (A) (19)

Dr. Jens Kreisel, Grenoble [JK2] (A) (20)

Dr. Gero Kube, Mainz [GK] (A) (18)

Ralph Kühnle, Heidelberg [RK1] (A) (05)

Volker Lauff, Magdeburg [VL] (A) (04)

Priv.-Doz. Dr. Axel Lorke, München [AL] (A) (20)

Dr. Andreas Markwitz, Lower Hutt, NZ [AM1] (A) (21)

Holger Mathiszik, Celle [HM3] (A) (29)

Dr. Dirk Metzger, Mannheim [DM] (A) (07)

Prof. Dr. Karl von Meyenn, München [KVM] (A) (02)

Dr. Rudi Michalak, Augsburg [RM1] (A) (23)

Helmut Milde, Dresden [HM1] (A) (09)

Günter Milde, Dresden [GM1] (A) (12)

Marita Milde, Dresden [MM2] (A) (12)

Dr. Andreas Müller, Kiel [AM2] (A) (33)

Dr. Nikolaus Nestle, Leipzig [NN] (A, B) (05, 20 Essays Molekularstrahlepitaxie, Ober- und Grenzflächenphysik und Rastersondenmikroskopie)

Dr. Thomas Otto, Genf [TO] (A) (06)

Dr. Ulrich Parlitz, Göttingen [UP1] (A) (11)

Christof Pflumm, Karlsruhe [CP] (A) (06, 08)

Dr. Oliver Probst, Monterrey, Mexico [OP] (A) (30)

Dr. Roland Andreas Puntigam, München [RAP] (A) (14)

Dr. Andrea Quintel, Stuttgart [AQ] (A) (Essay Nanoröhrchen)

Dr. Gunnar Radons, Mannheim [GR1] (A) (01, 02, 32)

Dr. Max Rauner, Weinheim [MR3] (A) (15 Essay Quanteninformatik)

Robert Raussendorf, München [RR1] (A) (19)

Ingrid Reiser, Manhattan, USA [IR] (A) (16)

Dr. Uwe Renner, Leipzig [UR] (A) (10)

Dr. Ursula Resch-Esser, Berlin [URE] (A) (21)

Dr. Peter Oliver Roll, Ingelheim [OR1] (A, B) (15 Essay Quantenmechanik und ihre Interpretationen)

Prof. Dr. Siegmar Roth, Stuttgart [SR] (A) (Essay Nanoröhrchen)

Hans-Jörg Rutsch, Walldorf [HJR] (A) (29)

Dr. Margit Sarstedt, Leuven, B [MS2] (A) (25)

Rolf Sauermost, Waldkirch [RS1] (A) (02)

Matthias Schemmel, Berlin [MS4] (A) (02)

Michael Schmid, Stuttgart [MS5] (A) (Essay Nanoröhrchen)

Dr. Martin Schön, Konstanz [MS] (A) (14)

Jörg Schuler, Taunusstein [JS1] (A) (06, 08)

Dr. Joachim Schüller, Dossenheim [JS2] (A) (10)

Richard Schwalbach, Mainz [RS2] (A) (17)

Prof. Dr. Paul Steinhardt, Princeton, USA [PS] (A) (Essay Quasikristalle und Quasi-Elementarzellen)

Prof. Dr. Klaus Stierstadt, München [KS] (B)

Dr. Siegmund Stintzing, München [SS1] (A) (22)

Cornelius Suchy, Brussels [CS2] (A) (20)

Dr. Volker Theileis, München [VT] (A) (20)

Prof. Dr. Gerald 't Hooft, Utrecht, NL [GT2] (A) (Essay Renormierung)

Dr. Annette Vogt, Berlin [AV] (A) (02)

Dr. Thomas Volkmann, Köln [TV] (A) (20)

Rolf vom Stein, Köln [RVS] (A) (29)

Patrick Voss-de Haan, Mainz [PVDH] (A) (17)

Dr. Thomas Wagner, Heidelberg [TW2] (A) (29)

Dr. Hildegard Wasmuth-Fries, Ludwigshafen [HWF] (A) (26)

Manfred Weber, Frankfurt [MW1] (A) (28)

Priv.-Doz. Dr. Burghard Weiss, Lübeck [BW2] (A) (02)

Prof. Dr. Klaus Winter, Berlin [KW] (A) (Essay Neutrinophysik)

Dr. Achim Wixforth, München [AW1] (A) (20)

Dr. Steffen Wolf, Berkeley, USA [SW] (A) (16)

Priv.-Doz. Dr. Jochen Wosnitza, Karlsruhe [JW] (A) (23 Essay Organische Supraleiter)

Priv.-Doz. Dr. Jörg Zegenhagen, Stuttgart [JZ3] (A) (21 Essay Oberflächenrekonstruktionen)

Dr. Kai Zuber, Dortmund [KZ] (A) (19)

Dr. Werner Zwerger, München [WZ] (A) (20)

Dr. Ulrich Kilian (responsible)

Christine Weber

Priv.-Doz. Dr. Dieter Hoffmann, Berlin

In eckigen Klammern steht das Autorenkürzel, die Zahl in der runden Klammer ist die Fachgebietsnummer eine Liste der Fachgebiete findet sich im Vorwort.

Prof. Dr. Klaus Andres, Garching [KA] (A) (10)

Markus Aspelmeyer, München [MA1] (A) (20)

Dr. Katja Bammel, Cagliari, I [KB2] (A) (13)

Doz. Dr. Hans-Georg Bartel, Berlin [HGB] (A) (02)

Steffen Bauer, Karlsruhe [SB2] (A) (20, 22)

Dr. Günther Beikert, Viernheim [GB1] (A) (04, 10, 25)

Prof. Dr. Hans Berckhemer, Frankfurt [HB1] (A, B) (29 Essay Seismologie)

Dr. Werner Biberacher, Garching [WB] (B) (20)

Prof. Tamás S. Biró, Budapest [TB2] (A) (15)

Prof. Dr. Helmut Bokemeyer, Darmstadt [HB2] (A, B) (18)

Dr. Thomas Bührke, Leimen [TB] (A) (32)

Jochen Büttner, Berlin [JB] (A) (02)

Dr. Matthias Delbrück, Dossenheim [MD] (A) (12, 24, 29)

Prof. Dr. Martin Dressel, Stuttgart (A) (Essay Spindichtewellen)

Dr. Michael Eckert, München [ME] (A) (02)

Dr. Dietrich Einzel, Garching (A) (Essay Supraleitung und Suprafluidität)

Dr. Wolfgang Eisenberg, Leipzig [WE] (A) (15)

Dr. Frank Eisenhaber, Wien [FE] (A) (27)

Dr. Roger Erb, Kassel [RE1] (A) (33)

Dr. Angelika Fallert-Müller, Groß-Zimmern [AFM] (A) (16, 26)

Stephan Fichtner, Heidelberg [SF] (A) (31)

Dr. Thomas Filk, Freiburg [TF3] (A) (10, 15)

Natalie Fischer, Walldorf [NF] (A) (32)

Dr. Thomas Fuhrmann, Mannheim [TF1] (A) (14)

Christian Fulda, Hannover [CF] (A) (07)

Frank Gabler, Frankfurt [FG1] (A) (22)

Dr. Harald Genz, Darmstadt [HG1] (A) (18)

Prof. Dr. Henning Genz, Karlsruhe [HG2] (A) (Essays Symmetrie und Vakuum)

Dr. Michael Gerding, Potsdam [MG2] (A) (13)

Andrea Greiner, Heidelberg [AG1] (A) (06)

Uwe Grigoleit, Weinheim [UG] (A) (13)

Gunther Hadwich, München [GH] (A) (20)

Dr. Andreas Heilmann, Halle [AH1] (A) (20, 21)

Carsten Heinisch, Kaiserslautern [CH] (A) (03)

Dr. Marc Hemberger, Heidelberg [MH2] (A) (19)

Dr. Sascha Hilgenfeldt, Cambridge, USA (A) (Essay Sonolumineszenz)

Dr. Hermann Hinsch, Heidelberg [HH2] (A) (22)

Priv.-Doz. Dr. Dieter Hoffmann, Berlin [DH2] (A, B) (02)

Dr. Gert Jacobi, Hamburg [GJ] (B) (09)

Renate Jerecic, Heidelberg [RJ] (A) (28)

Prof. Dr. Josef Kallrath, Ludwigshafen [JK] (A) (04)

Priv.-Doz. Dr. Claus Kiefer, Freiburg [CK] (A) (14, 15)

Richard Kilian, Wiesbaden [RK3] (22)

Dr. Ulrich Kilian, Heidelberg [UK] (A) (19)

Thomas Kluge, Jülich [TK] (A) (20)

Dr. Achim Knoll, Karlsruhe [AK1] (A) (20)

Dr. Alexei Kojevnikov, College Park, USA [AK3] (A) (02)

Dr. Bernd Krause, München [BK1] (A) (19)

Dr. Gero Kube, Mainz [GK] (A) (18)

Ralph Kühnle, Heidelberg [RK1] (A) (05)

Volker Lauff, Magdeburg [VL] (A) (04)

Dr. Anton Lerf, Garching [AL1] (A) (23)

Dr. Detlef Lohse, Twente, NL (A) (Essay Sonolumineszenz)

Priv.-Doz. Dr. Axel Lorke, München [AL] (A) (20)

Prof. Dr. Jan Louis, Halle (A) (Essay Stringtheorie)

Dr. Andreas Markwitz, Lower Hutt, NZ [AM1] (A) (21)

Holger Mathiszik, Celle [HM3] (A) (29)

Dr. Dirk Metzger, Mannheim [DM] (A) (07)

Dr. Rudi Michalak, Dresden [RM1] (A) (23 Essay Tieftemperaturphysik)

Günter Milde, Dresden [GM1] (A) (12)

Helmut Milde, Dresden [HM1] (A) (09)

Marita Milde, Dresden [MM2] (A) (12)

Prof. Dr. Andreas Müller, Trier [AM2] (A) (33)

Prof. Dr. Karl Otto Münnich, Heidelberg (A) (Essay Umweltphysik)

Dr. Nikolaus Nestle, Leipzig [NN] (A, B) (05, 20)

Dr. Thomas Otto, Genf [TO] (A) (06)

Priv.-Doz. Dr. Ulrich Parlitz, Göttingen [UP1] (A) (11)

Christof Pflumm, Karlsruhe [CP] (A) (06, 08)

Dr. Oliver Probst, Monterrey, Mexico [OP] (A) (30)

Dr. Roland Andreas Puntigam, München [RAP] (A) (14)

Dr. Gunnar Radons, Mannheim [GR1] (A) (01, 02, 32)

Dr. Max Rauner, Weinheim [MR3] (A) (15)

Robert Raussendorf, München [RR1] (A) (19)

Ingrid Reiser, Manhattan, USA [IR] (A) (16)

Dr. Uwe Renner, Leipzig [UR] (A) (10)

Dr. Ursula Resch-Esser, Berlin [URE] (A) (21)

Dr. Peter Oliver Roll, Ingelheim [OR1] (A, B) (15)

Hans-Jörg Rutsch, Walldorf [HJR] (A) (29)

Rolf Sauermost, Waldkirch [RS1] (A) (02)

Matthias Schemmel, Berlin [MS4] (A) (02)

Prof. Dr. Erhard Scholz, Wuppertal [ES] (A) (02)

Dr. Martin Schön, Konstanz [MS] (A) (14 Essay Spezielle Relativitätstheorie)

Dr. Erwin Schuberth, Garching [ES4] (A) (23)

Jörg Schuler, Taunusstein [JS1] (A) (06, 08)

Dr. Joachim Schüller, Dossenheim [JS2] (A) (10)

Richard Schwalbach, Mainz [RS2] (A) (17)

Prof. Dr. Klaus Stierstadt, München [KS] (B)

Dr. Siegmund Stintzing, München [SS1] (A) (22)

Dr. Berthold Suchan, Gießen [BS] (A) (Essay Wissenschaftsphilosophie)

Cornelius Suchy, Brussels [CS2] (A) (20)

Dr. Volker Theileis, München [VT] (A) (20)

Prof. Dr. Stefan Theisen, München (A) (Essay Stringtheorie)

Dr. Annette Vogt, Berlin [AV] (A) (02)

Dr. Thomas Volkmann, Köln [TV] (A) (20)

Rolf vom Stein, Köln [RVS] (A) (29)

Dr. Patrick Voss-de Haan, Mainz [PVDH] (A) (17)

Dr. Thomas Wagner, Heidelberg [TW2] (A) (29)

Manfred Weber, Frankfurt [MW1] (A) (28)

Dr. Martin Werner, Hamburg [MW] (A) (29)

Dr. Achim Wixforth, München [AW1] (A) (20)

Dr. Steffen Wolf, Berkeley, USA [SW] (A) (16)

Dr. Stefan L. Wolff, München [SW1] (A) (02)

Priv.-Doz. Dr. Jochen Wosnitza, Karlsruhe [JW] (A) (23)

Dr. Kai Zuber, Dortmund [KZ] (A) (19)

Dr. Werner Zwerger, München [WZ] (A) (20)

### Artikel zum Thema

Laden.Das Elektron war das erste entdeckte Elementarteilchen.

1895 zeigte Jean Perrin bei der Analyse der elektrischen Ladung der sogenannten Kathodenstrahlen, dass sie eine negative Ladung trugen.

Joseph John Thomson gelang es, die spezifische Ladung der Partikel zu bestimmen. 1906 gewann Thomson den Nobelpreis für Physik.

Millikan nutzte Thomsons Arbeit, um das Öltropfenexperiment durchzuführen. In diesem Experiment konnte er die Last und die Masse messen

Die Produktion freier Elektronen hat zur Entwicklung der Elektronik geführt.