1.
Force
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In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass to change its velocity, force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity and it is measured in the SI unit of newtons and represented by the symbol F. The original form of Newtons second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. In an extended body, each part usually applies forces on the adjacent parts, such internal mechanical stresses cause no accelation of that body as the forces balance one another. Pressure, the distribution of small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate. Stress usually causes deformation of materials, or flow in fluids. In part this was due to an understanding of the sometimes non-obvious force of friction. A fundamental error was the belief that a force is required to maintain motion, most of the previous misunderstandings about motion and force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly three hundred years, the Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known, in order of decreasing strength, they are, strong, electromagnetic, weak, high-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotles view, the sphere contained four elements that come to rest at different natural places therein. Aristotle believed that objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground. He distinguished between the tendency of objects to find their natural place, which led to natural motion, and unnatural or forced motion
2.
Quantum field theory
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QFT treats particles as excited states of the underlying physical field, so these are called field quanta. In quantum field theory, quantum mechanical interactions among particles are described by interaction terms among the corresponding underlying quantum fields and these interactions are conveniently visualized by Feynman diagrams, which are a formal tool of relativistically covariant perturbation theory, serving to evaluate particle processes. The first achievement of quantum theory, namely quantum electrodynamics, is still the paradigmatic example of a successful quantum field theory. Ordinarily, quantum mechanics cannot give an account of photons which constitute the prime case of relativistic particles, since photons have rest mass zero, and correspondingly travel in the vacuum at the speed c, a non-relativistic theory such as ordinary QM cannot give even an approximate description. Photons are implicit in the emission and absorption processes which have to be postulated, for instance, the formalism of QFT is needed for an explicit description of photons. In fact most topics in the development of quantum theory were related to the interaction of radiation and matter. However, quantum mechanics as formulated by Dirac, Heisenberg, and Schrödinger in 1926–27 started from atomic spectra, as soon as the conceptual framework of quantum mechanics was developed, a small group of theoreticians tried to extend quantum methods to electromagnetic fields. A good example is the paper by Born, Jordan & Heisenberg. The basic idea was that in QFT the electromagnetic field should be represented by matrices in the way that position. The ideas of QM were thus extended to systems having a number of degrees of freedom. The inception of QFT is usually considered to be Diracs famous 1927 paper on The quantum theory of the emission and absorption of radiation, here Dirac coined the name quantum electrodynamics for the part of QFT that was developed first. Employing the theory of the harmonic oscillator, Dirac gave a theoretical description of how photons appear in the quantization of the electromagnetic radiation field. Later, Diracs procedure became a model for the quantization of fields as well. These first approaches to QFT were further developed during the three years. P. Jordan introduced creation and annihilation operators for fields obeying Fermi–Dirac statistics and these differ from the corresponding operators for Bose–Einstein statistics in that the former satisfy anti-commutation relations while the latter satisfy commutation relations. The methods of QFT could be applied to derive equations resulting from the treatment of particles, e. g. the Dirac equation, the Klein–Gordon equation. Schweber points out that the idea and procedure of second quantization goes back to Jordan, in a number of papers from 1927, some difficult problems concerning commutation relations, statistics, and Lorentz invariance were eventually solved. The first comprehensive account of a theory of quantum fields, in particular
3.
Electron
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The electron is a subatomic particle, symbol e− or β−, with a negative elementary electric charge. Electrons belong to the first generation of the lepton particle family, the electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the include a intrinsic angular momentum of a half-integer value, expressed in units of the reduced Planck constant. As it is a fermion, no two electrons can occupy the same state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of particles and waves, they can collide with other particles and can be diffracted like light. Since an electron has charge, it has an electric field. Electromagnetic fields produced from other sources will affect the motion of an electron according to the Lorentz force law, electrons radiate or absorb energy in the form of photons when they are accelerated. Laboratory instruments are capable of trapping individual electrons as well as electron plasma by the use of electromagnetic fields, special telescopes can detect electron plasma in outer space. Electrons are involved in applications such as electronics, welding, cathode ray tubes, electron microscopes, radiation therapy, lasers, gaseous ionization detectors. Interactions involving electrons with other particles are of interest in fields such as chemistry. The Coulomb force interaction between the positive protons within atomic nuclei and the negative electrons without, allows the composition of the two known as atoms, ionization or differences in the proportions of negative electrons versus positive nuclei changes the binding energy of an atomic system. The exchange or sharing of the electrons between two or more atoms is the cause of chemical bonding. In 1838, British natural philosopher Richard Laming first hypothesized the concept of a quantity of electric charge to explain the chemical properties of atoms. Irish physicist George Johnstone Stoney named this charge electron in 1891, electrons can also participate in nuclear reactions, such as nucleosynthesis in stars, where they are known as beta particles. Electrons can be created through beta decay of isotopes and in high-energy collisions. The antiparticle of the electron is called the positron, it is identical to the electron except that it carries electrical, when an electron collides with a positron, both particles can be totally annihilated, producing gamma ray photons. The ancient Greeks noticed that amber attracted small objects when rubbed with fur, along with lightning, this phenomenon is one of humanitys earliest recorded experiences with electricity. In his 1600 treatise De Magnete, the English scientist William Gilbert coined the New Latin term electricus, both electric and electricity are derived from the Latin ēlectrum, which came from the Greek word for amber, ἤλεκτρον
4.
Particle
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A particle is a minute fragment or quantity of matter. In the physical sciences, a particle is a small localized object to which can be ascribed several physical or chemical properties such as volume or mass. Particles can also be used to create models of even larger objects depending on their density. The term particle is rather general in meaning, and is refined as needed by various scientific fields, something that is composed of particles may be referred to as being particulate. However, the particulate is most frequently used to refer to pollutants in the Earths atmosphere. The concept of particles is particularly useful when modelling nature, as the treatment of many phenomena can be complex. It can be used to make simplifying assumptions concerning the processes involved, francis Sears and Mark Zemansky, in University Physics, give the example of calculating the landing location and speed of a baseball thrown in the air. The treatment of large numbers of particles is the realm of statistical physics, the term particle is usually applied differently to three classes of sizes. The term macroscopic particle, usually refers to particles much larger than atoms and these are usually abstracted as point-like particles, or even invisible. This is even though they have volumes, shapes, structures, examples of macroscopic particles would include powder, dust, sand, pieces of debris during a car accident, or even objects as big as the stars of a galaxy. Another type, microscopic particles usually refers to particles of sizes ranging from atoms to molecules, such as carbon dioxide, nanoparticles and these particles are studied in chemistry, as well as atomic and molecular physics. The smallest of particles are the particles, which refer to particles smaller than atoms. These particles are studied in particle physics, because of their extremely small size, the study of microscopic and subatomic particles fall in the realm of quantum mechanics. Particles can also be classified according to composition, composite particles refer to particles that have composition – that is particles which are made of other particles. For example, an atom is made of six protons, eight neutrons. By contrast, elementary particles refer to particles that are not made of other particles, according to our current understanding of the world, only a very small number of these exist, such as the leptons, quarks or gluons. However it is possible some of these might turn up to be composite particles after all. While composite particles can very often be considered point-like, elementary particles are truly punctual, both elementary and composite particles, are known to undergo particle decay
5.
Quark
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A quark is an elementary particle and a fundamental constituent of matter. Quarks combine to form composite particles called hadrons, the most stable of which are protons and neutrons, due to a phenomenon known as color confinement, quarks are never directly observed or found in isolation, they can be found only within hadrons, such as baryons and mesons. For this reason, much of what is known about quarks has been drawn from observations of the hadrons themselves, Quarks have various intrinsic properties, including electric charge, mass, color charge, and spin. There are six types of quarks, known as flavors, up, down, strange, charm, top, up and down quarks have the lowest masses of all quarks. The heavier quarks rapidly change into up and down quarks through a process of particle decay, the transformation from a higher mass state to a lower mass state. Because of this, up and down quarks are generally stable and the most common in the universe, whereas strange, charm, bottom, and top quarks can only be produced in high energy collisions. For every quark flavor there is a type of antiparticle, known as an antiquark. The quark model was proposed by physicists Murray Gell-Mann and George Zweig in 1964. Accelerator experiments have provided evidence for all six flavors, the top quark was the last to be discovered at Fermilab in 1995. The Standard Model is the theoretical framework describing all the known elementary particles. This model contains six flavors of quarks, named up, down, strange, charm, bottom, antiparticles of quarks are called antiquarks, and are denoted by a bar over the symbol for the corresponding quark, such as u for an up antiquark. As with antimatter in general, antiquarks have the mass, mean lifetime, and spin as their respective quarks. Quarks are spin- 1⁄2 particles, implying that they are fermions according to the spin-statistics theorem and they are subject to the Pauli exclusion principle, which states that no two identical fermions can simultaneously occupy the same quantum state. This is in contrast to bosons, any number of which can be in the same state, unlike leptons, quarks possess color charge, which causes them to engage in the strong interaction. The resulting attraction between different quarks causes the formation of composite particles known as hadrons, there are two families of hadrons, baryons, with three valence quarks, and mesons, with a valence quark and an antiquark. The most common baryons are the proton and the neutron, the blocks of the atomic nucleus. A great number of hadrons are known, most of them differentiated by their quark content, the existence of exotic hadrons with more valence quarks, such as tetraquarks and pentaquarks, has been conjectured but not proven. However, on 13 July 2015, the LHCb collaboration at CERN reported results consistent with pentaquark states, elementary fermions are grouped into three generations, each comprising two leptons and two quarks
6.
Momentum
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In classical mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object, quantified in kilogram-meters per second. It is dimensionally equivalent to impulse, the product of force and time, Newtons second law of motion states that the change in linear momentum of a body is equal to the net impulse acting on it. If the truck were lighter, or moving slowly, then it would have less momentum. Linear momentum is also a quantity, meaning that if a closed system is not affected by external forces. In classical mechanics, conservation of momentum is implied by Newtons laws. It also holds in special relativity and, with definitions, a linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory. It is ultimately an expression of one of the symmetries of space and time. Linear momentum depends on frame of reference, observers in different frames would find different values of linear momentum of a system. But each would observe that the value of linear momentum does not change with time, momentum has a direction as well as magnitude. Quantities that have both a magnitude and a direction are known as vector quantities, because momentum has a direction, it can be used to predict the resulting direction of objects after they collide, as well as their speeds. Below, the properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations, the momentum of a particle is traditionally represented by the letter p. It is the product of two quantities, the mass and velocity, p = m v, the units of momentum are the product of the units of mass and velocity. In SI units, if the mass is in kilograms and the velocity in meters per second then the momentum is in kilogram meters/second, in cgs units, if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters/second. Being a vector, momentum has magnitude and direction, for example, a 1 kg model airplane, traveling due north at 1 m/s in straight and level flight, has a momentum of 1 kg m/s due north measured from the ground. The momentum of a system of particles is the sum of their momenta, if two particles have masses m1 and m2, and velocities v1 and v2, the total momentum is p = p 1 + p 2 = m 1 v 1 + m 2 v 2. If all the particles are moving, the center of mass will generally be moving as well, if the center of mass is moving at velocity vcm, the momentum is, p = m v cm. This is known as Eulers first law, if a force F is applied to a particle for a time interval Δt, the momentum of the particle changes by an amount Δ p = F Δ t
7.
Point particle
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A point particle is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension, being zero-dimensional, a point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context. For example, from far away, an object of any shape will look. In the theory of gravity, physicists discuss a point mass, meaning a point particle with a nonzero mass. Likewise, in electromagnetism, physicists discuss a point charge, a point particle with a nonzero charge, sometimes, due to specific combinations of properties, extended objects behave as point-like even in their immediate vicinity. For example, the orbit of an electron in the hydrogen atom occupies a volume of ~10−30 m3. Elementary particles are called point particles, but this is in a different sense than discussed above. When a point particle has a property, such as mass or charge, concentrated at a single point in space. A common use for point mass lies in the analysis of the gravitational fields, when analyzing the gravitational forces in a system, it becomes impossible to account for every unit of mass individually. However, a spherically symmetric body affects external objects gravitationally as if all of its mass were concentrated at its center, to calculate such a point mass, an integration is carried out over the entire range of the random variable, on the probability density of the continuous part. After equating this integral to 1, the point mass can be found by further calculation, a point charge is an idealized model of a particle which has an electric charge. A point charge is a charge at a mathematical point with no dimensions. The fundamental equation of electrostatics is Coulombs law, which describes the force between two point charges. The electric field associated with a point charge increases to infinity as the distance from the point charge decreases towards zero making energy of point charge infinite. Earnshaws theorem states that a collection of point charges cannot be maintained in an equilibrium configuration solely by the interaction of the charges. In quantum mechanics, there is a distinction between a particle and a composite particle. An elementary particle, such as an electron, quark, or photon, is a particle with no structure, whereas a composite particle. However, neither elementary nor composite particles are spatially localized, because of the Heisenberg uncertainty principle, the particle wavepacket always occupies a nonzero volume
8.
Hypercharge
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The concept of hypercharge combines and unifies isospin and flavour into a single charge operator. Hypercharge in particle physics is a number relating the strong interactions of the SU model. Isospin is defined in the SU model while the SU model defines hypercharge, SU weight diagrams are 2-dimensional with the coordinates referring to two quantum numbers, Iz, which is the z-component of isospin and Y, which is the hypercharge. Mathematically, hypercharge is Y = S + C + B ′ + T + B, strong interactions conserve hypercharge, but weak interactions do not. The Gell-Mann–Nishijima formula relates isospin and electric charge Q = I3 +12 Y, isospin creates multiplets of particles whose average charge is related to the hypercharge by, Y =2 Q ¯. Since the hypercharge is the same for all members of a multiplet, the SU model has multiplets characterized by a quantum number J, which is the total angular momentum. Each multiplet consists of 2J +1 substates with equally spaced values of Jz, forming a symmetric arrangement seen in atomic spectra and isospin. This formalizes the observation that certain strong baryon decays were not observed, leading to the prediction of the mass, strangeness, the SU has supermultiplets containing SU multiplets. SU now needs 2 numbers to all its sub-states which are denoted by λ1. Specifies the number of points in the topmost side of the hexagon while specifies the number of points on the bottom side, the nucleon group have an average charge of +1/2, so they both have hypercharge Y =1. From the Gell-Mann–Nishijima formula we know that proton has isospin I3 = +1/2 and this also works for quarks, for the up quark, with a charge of +2/3, and an I3 of +1/2, we deduce a hypercharge of 1/3, due to its baryon number. For a strange quark, with charge −1/3, a number of 1/3 and strangeness of −1 we get a hypercharge Y = −2/3. That means that a strange quark makes a singlet of its own, while up, hypercharge was a concept developed in the 1960s, to organize groups of particles in the particle zoo and to develop ad hoc conservation laws based on their observed transformations. With the advent of the model, it is now obvious that, hypercharge Y is the following combination of the numbers of up, down, strange quarks, charm quarks, top quarks and bottom quarks. Weak hypercharge, however, remains of use in various theories of the electroweak interaction. Introduction to atomic and nuclear physics
9.
Energy level
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A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy and these discrete values are called energy levels. The energy spectrum of a system with discrete energy levels is said to be quantized. In chemistry and atomic physics, a shell, or a principal energy level. The closest shell to the nucleus is called the 1 shell, followed by the 2 shell, then the 3 shell, the shells correspond with the principal quantum numbers or are labeled alphabetically with letters used in the X-ray notation. Each shell can contain only a number of electrons, The first shell can hold up to two electrons, the second shell can hold up to eight electrons, the third shell can hold up to 18. The general formula is that the nth shell can in principle hold up to 2 electrons, since electrons are electrically attracted to the nucleus, an atoms electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a requirement, atoms may have two or even three incomplete outer shells. For an explanation of why electrons exist in these shells see electron configuration, if the potential energy is set to zero at infinite distance from the atomic nucleus or molecule, the usual convention, then bound electron states have negative potential energy. If an atom, ion, or molecule is at the lowest possible level, it. If it is at an energy level, it is said to be excited. If more than one quantum state is at the same energy. They are then called degenerate energy levels, quantized energy levels result from the relation between a particles energy and its wavelength. For a confined particle such as an electron in an atom, only stationary states with energies corresponding to integral numbers of wavelengths can exist, for other states the waves interfere destructively, resulting in zero probability density. Elementary examples that show mathematically how energy levels come about are the particle in a box, the first evidence of quantization in atoms was the observation of spectral lines in light from the sun in the early 1800s by Joseph von Fraunhofer and William Hyde Wollaston. The notion of levels was proposed in 1913 by Danish physicist Niels Bohr in the Bohr theory of the atom. The modern quantum mechanical theory giving an explanation of these levels in terms of the Schrödinger equation was advanced by Erwin Schrödinger and Werner Heisenberg in 1926. When the electron is bound to the atom in any closer value of n, assume there is one electron in a given atomic orbital in a hydrogen-like atom
10.
Standard Model
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The Standard Model of particle physics is a theory concerning the electromagnetic, weak, and strong interactions, as well as classifying all the elementary particles known. It was developed throughout the half of the 20th century. The current formulation was finalized in the mid-1970s upon experimental confirmation of the existence of quarks, since then, discoveries of the top quark, the tau neutrino, and the Higgs boson have given further credence to the Standard Model. Because of its success in explaining a wide variety of experimental results and it does not incorporate the full theory of gravitation as described by general relativity, or account for the accelerating expansion of the Universe. The model does not contain any viable dark matter particle that all of the required properties deduced from observational cosmology. It also does not incorporate neutrino oscillations, the development of the Standard Model was driven by theoretical and experimental particle physicists alike. For theorists, the Standard Model is a paradigm of a field theory. The first step towards the Standard Model was Sheldon Glashows discovery in 1961 of a way to combine the electromagnetic, in 1967 Steven Weinberg and Abdus Salam incorporated the Higgs mechanism into Glashows electroweak interaction, giving it its modern form. The Higgs mechanism is believed to rise to the masses of all the elementary particles in the Standard Model. This includes the masses of the W and Z bosons, the W± and Z0 bosons were discovered experimentally in 1983, and the ratio of their masses was found to be as the Standard Model predicted. The theory of the interaction, to which many contributed, acquired its modern form around 1973–74. At present, matter and energy are best understood in terms of the kinematics, to date, physics has reduced the laws governing the behavior and interaction of all known forms of matter and energy to a small set of fundamental laws and theories. The Standard Model includes members of classes of elementary particles. All particles can be summarized as follows, The Standard Model includes 12 elementary particles of spin known as fermions. According to the theorem, fermions respect the Pauli exclusion principle. Each fermion has a corresponding antiparticle, the fermions of the Standard Model are classified according to how they interact. There are six quarks, and six leptons, pairs from each classification are grouped together to form a generation, with corresponding particles exhibiting similar physical behavior. The defining property of the quarks is that they carry color charge, a phenomenon called color confinement results in quarks being very strongly bound to one another, forming color-neutral composite particles containing either a quark and an antiquark or three quarks
11.
Electric charge
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Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of charges, positive and negative. Like charges repel and unlike attract, an absence of net charge is referred to as neutral. An object is charged if it has an excess of electrons. The SI derived unit of charge is the coulomb. In electrical engineering, it is common to use the ampere-hour. The symbol Q often denotes charge, early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that dont require consideration of quantum effects. The electric charge is a conserved property of some subatomic particles. Electrically charged matter is influenced by, and produces, electromagnetic fields, the interaction between a moving charge and an electromagnetic field is the source of the electromagnetic force, which is one of the four fundamental forces. 602×10−19 coulombs. The proton has a charge of +e, and the electron has a charge of −e, the study of charged particles, and how their interactions are mediated by photons, is called quantum electrodynamics. Charge is the property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter. Electric charge is a property of many subatomic particles. The charges of free-standing particles are integer multiples of the charge e. Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge, robert Millikans oil drop experiment demonstrated this fact directly, and measured the elementary charge. By convention, the charge of an electron is −1, while that of a proton is +1, charged particles whose charges have the same sign repel one another, and particles whose charges have different signs attract. The charge of an antiparticle equals that of the corresponding particle, quarks have fractional charges of either −1/3 or +2/3, but free-standing quarks have never been observed. The electric charge of an object is the sum of the electric charges of the particles that make it up. An ion is an atom that has lost one or more electrons, giving it a net charge, or that has gained one or more electrons
12.
Lepton
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A lepton is an elementary, half-integer spin particle that does not undergo strong interactions. Two main classes of leptons exist, charged leptons, and neutral leptons, the best known of all leptons is the electron. There are six types of leptons, known as flavours, forming three generations, electrons have the least mass of all the charged leptons. The heavier muons and taus will rapidly change into electrons and neutrinos through a process of particle decay, thus electrons are stable and the most common charged lepton in the universe, whereas muons and taus can only be produced in high energy collisions. Leptons have various properties, including electric charge, spin. Unlike quarks however, leptons are not subject to the strong interaction, for every lepton flavor there is a corresponding type of antiparticle, known as an antilepton, that differs from the lepton only in that some of its properties have equal magnitude but opposite sign. However, according to theories, neutrinos may be their own antiparticle. The first charged lepton, the electron, was theorized in the century by several scientists and was discovered in 1897 by J. J. Thomson. The next lepton to be observed was the muon, discovered by Carl D. Anderson in 1936, after investigation, it was realized that the muon did not have the expected properties of a meson, but rather behaved like an electron, only with higher mass. It took until 1947 for the concept of leptons as a family of particle to be proposed, the first neutrino, the electron neutrino, was proposed by Wolfgang Pauli in 1930 to explain certain characteristics of beta decay. It was first observed in the Cowan–Reines neutrino experiment conducted by Clyde Cowan, the muon neutrino was discovered in 1962 by Leon M. The tau neutrino remained elusive until July 2000, when the DONUT collaboration from Fermilab announced its discovery, Leptons are an important part of the Standard Model. Electrons are one of the components of atoms, alongside protons and neutrons, exotic atoms with muons and taus instead of electrons can also be synthesized, as well as lepton–antilepton particles such as positronium. The name lepton comes from the Greek λεπτός leptós, fine, small, thin, Lepton was first used by physicist Léon Rosenfeld in 1948, Following a suggestion of Prof. C. Møller, I adopt—as a pendant to nucleon—the denomination lepton to denote a particle of small mass, the etymology incorrectly implies that all the leptons are of small mass. However, the mass of the tau is nearly twice that of the proton, the first lepton identified was the electron, discovered by J. J. Thomson and his team of British physicists in 1897, then in 1930 Wolfgang Pauli postulated the electron neutrino to preserve conservation of energy, conservation of momentum, and conservation of angular momentum in beta decay. Pauli theorized that a particle was carrying away the difference between the energy, momentum, and angular momentum of the initial and observed final particles