1.
System of measurement
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A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce, systems of measurement in modern use include the metric system, the imperial system, and United States customary units. The French Revolution gave rise to the system, and this has spread around the world. In most systems, length, mass, and time are base quantities, later science developments showed that either electric charge or electric current could be added to extend the set of base quantities by which many other metrological units could be easily defined. Other quantities, such as power and speed, are derived from the set, for example. Such arrangements were satisfactory in their own contexts, the preference for a more universal and consistent system only gradually spread with the growth of science. Changing a measurement system has substantial financial and cultural costs which must be offset against the advantages to be obtained using a more rational system. However pressure built up, including scientists and engineers for conversion to a more rational. The unifying characteristic is that there was some definition based on some standard, eventually cubits and strides gave way to customary units to met the needs of merchants and scientists. In the metric system and other recent systems, a basic unit is used for each base quantity. Often secondary units are derived from the units by multiplying by powers of ten. Thus the basic unit of length is the metre, a distance of 1.234 m is 1,234 millimetres. Metrication is complete or nearly complete in almost all countries, US customary units are heavily used in the United States and to some degree in Liberia. Traditional Burmese units of measurement are used in Burma, U. S. units are used in limited contexts in Canada due to the large volume of trade, there is also considerable use of Imperial weights and measures, despite de jure Canadian conversion to metric. In the United States, metric units are used almost universally in science, widely in the military, and partially in industry, but customary units predominate in household use. At retail stores, the liter is a used unit for volume, especially on bottles of beverages. Some other standard non-SI units are still in use, such as nautical miles and knots in aviation. Metric systems of units have evolved since the adoption of the first well-defined system in France in 1795, during this evolution the use of these systems has spread throughout the world, first to non-English-speaking countries, and then to English speaking countries
2.
Natural units
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In physics, natural units are physical units of measurement based only on universal physical constants. For example, the charge e is a natural unit of electric charge. It precludes the interpretation of an expression in terms of physical constants, such e and c. In this case, the reinsertion of the powers of e, c. Natural units are natural because the origin of their definition comes only from properties of nature, Planck units are often, without qualification, called natural units, although they constitute only one of several systems of natural units, albeit the best known such system. As with other systems of units, the units of a set of natural units will include definitions and values for length, mass, time, temperature. It is possible to disregard temperature as a physical quantity, since it states the energy per degree of freedom of a particle. Virtually every system of natural units normalizes Boltzmanns constant kB to 1, there are two common ways to relate charge to mass, length, and time, In Lorentz–Heaviside units, Coulombs law is F = q1q2/4πr2, and in Gaussian units, Coulombs law is F = q1q2/r2. Both possibilities are incorporated into different natural unit systems, where, α is the fine-structure constant,2 ≈0.007297, αG is the gravitational coupling constant,2 ≈ 6955175200000000000♠1. 752×10−45. Natural units are most commonly used by setting the units to one, for example, many natural unit systems include the equation c =1 in the unit-system definition, where c is the speed of light. If a velocity v is half the speed of light, then as v = c/2 and c =1, the equation v = 1/2 means the velocity v has the value one-half when measured in Planck units, or the velocity v is one-half the Planck unit of velocity. The equation c =1 can be plugged in anywhere else, for example, Einsteins equation E = mc2 can be rewritten in Planck units as E = m. This equation means The energy of a particle, measured in Planck units of energy, equals the mass of the particle, measured in Planck units of mass. For example, the special relativity equation E2 = p2c2 + m2c4 appears somewhat complicated, Physical interpretation, Natural unit systems automatically subsume dimensional analysis. For example, in Planck units, the units are defined by properties of quantum mechanics, not coincidentally, the Planck unit of length is approximately the distance at which quantum gravity effects become important. Likewise, atomic units are based on the mass and charge of an electron, no prototypes, A prototype is a physical object that defines a unit, such as the International Prototype Kilogram, a physical cylinder of metal whose mass is by definition exactly one kilogram. A prototype definition always has imperfect reproducibility between different places and between different times, and it is an advantage of natural systems that they use no prototypes. Less precise measurements, SI units are designed to be used in precision measurements, for example, the second is defined by an atomic transition frequency in cesium atoms, because this transition frequency can be precisely reproduced with atomic clock technology
3.
Atomic physics
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Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and this comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term atom includes ions. The term atomic physics can be associated with power and nuclear weapons, due to the synonymous use of atomic. Physicists distinguish between atomic physics — which deals with the atom as a system consisting of a nucleus and electrons — and nuclear physics, which considers atomic nuclei alone. As with many fields, strict delineation can be highly contrived and atomic physics is often considered in the wider context of atomic, molecular. Physics research groups are usually so classified, Atomic physics primarily considers atoms in isolation. Atomic models will consist of a nucleus that may be surrounded by one or more bound electrons. It is not concerned with the formation of molecules, nor does it examine atoms in a state as condensed matter. It is concerned with such as ionization and excitation by photons or collisions with atomic particles. This means that the atoms can be treated as if each were in isolation. By this consideration atomic physics provides the underlying theory in physics and atmospheric physics. Electrons form notional shells around the nucleus and these are normally in a ground state but can be excited by the absorption of energy from light, magnetic fields, or interaction with a colliding particle. Electrons that populate a shell are said to be in a bound state, the energy necessary to remove an electron from its shell is called the binding energy. Any quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy, the atom is said to have undergone the process of ionization. If the electron absorbs a quantity of less than the binding energy. After a certain time, the electron in a state will jump to a lower state. In a neutral atom, the system will emit a photon of the difference in energy, if an inner electron has absorbed more than the binding energy, then a more outer electron may undergo a transition to fill the inner orbital. The Auger effect allows one to multiply ionize an atom with a single photon, there are rather strict selection rules as to the electronic configurations that can be reached by excitation by light — however there are no such rules for excitation by collision processes
4.
Planck constant
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The Planck constant is a physical constant that is the quantum of action, central in quantum mechanics. The light quantum behaved in some respects as a neutral particle. It was eventually called the photon, the Planck–Einstein relation connects the particulate photon energy E with its associated wave frequency f, E = h f This energy is extremely small in terms of ordinarily perceived everyday objects. Since the frequency f, wavelength λ, and speed of c are related by f = c λ. This leads to another relationship involving the Planck constant, with p denoting the linear momentum of a particle, the de Broglie wavelength λ of the particle is given by λ = h p. In applications where it is natural to use the frequency it is often useful to absorb a factor of 2π into the Planck constant. The resulting constant is called the reduced Planck constant or Dirac constant and it is equal to the Planck constant divided by 2π, and is denoted ħ, ℏ = h 2 π. The energy of a photon with angular frequency ω, where ω = 2πf, is given by E = ℏ ω, while its linear momentum relates to p = ℏ k and this was confirmed by experiments soon afterwards. This holds throughout quantum theory, including electrodynamics and these two relations are the temporal and spatial component parts of the special relativistic expression using 4-Vectors. P μ = = ℏ K μ = ℏ Classical statistical mechanics requires the existence of h, eventually, following upon Plancks discovery, it was recognized that physical action cannot take on an arbitrary value. Instead, it must be multiple of a very small quantity. This is the old quantum theory developed by Bohr and Sommerfeld, in which particle trajectories exist but are hidden. Thus there is no value of the action as classically defined, related to this is the concept of energy quantization which existed in old quantum theory and also exists in altered form in modern quantum physics. Classical physics cannot explain either quantization of energy or the lack of a particle motion. In many cases, such as for light or for atoms, quantization of energy also implies that only certain energy levels are allowed. The Planck constant has dimensions of physical action, i. e. energy multiplied by time, or momentum multiplied by distance, in SI units, the Planck constant is expressed in joule-seconds or or. The value of the Planck constant is, h =6.626070040 ×10 −34 J⋅s =4.135667662 ×10 −15 eV⋅s. The value of the reduced Planck constant is, ℏ = h 2 π =1.054571800 ×10 −34 J⋅s =6.582119514 ×10 −16 eV⋅s
5.
Speed of light
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The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299792458 metres per second, it is exact because the unit of length, the metre, is defined from this constant, according to special relativity, c is the maximum speed at which all matter and hence information in the universe can travel. It is the speed at which all particles and changes of the associated fields travel in vacuum. Such particles and waves travel at c regardless of the motion of the source or the reference frame of the observer. In the theory of relativity, c interrelates space and time, the speed at which light propagates through transparent materials, such as glass or air, is less than c, similarly, the speed of radio waves in wire cables is slower than c. The ratio between c and the speed v at which light travels in a material is called the index n of the material. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, the light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light limits the theoretical maximum speed of computers. The speed of light can be used time of flight measurements to measure large distances to high precision. Ole Rømer first demonstrated in 1676 that light travels at a speed by studying the apparent motion of Jupiters moon Io. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, in 1905, Albert Einstein postulated that the speed of light c with respect to any inertial frame is a constant and is independent of the motion of the light source. He explored the consequences of that postulate by deriving the theory of relativity and in doing so showed that the parameter c had relevance outside of the context of light and electromagnetism. After centuries of increasingly precise measurements, in 1975 the speed of light was known to be 299792458 m/s with a measurement uncertainty of 4 parts per billion. In 1983, the metre was redefined in the International System of Units as the distance travelled by light in vacuum in 1/299792458 of a second, as a result, the numerical value of c in metres per second is now fixed exactly by the definition of the metre. The speed of light in vacuum is usually denoted by a lowercase c, historically, the symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant later shown to equal √2 times the speed of light in vacuum, in 1894, Paul Drude redefined c with its modern meaning. Einstein used V in his original German-language papers on special relativity in 1905, but in 1907 he switched to c, sometimes c is used for the speed of waves in any material medium, and c0 for the speed of light in vacuum. This article uses c exclusively for the speed of light in vacuum, since 1983, the metre has been defined in the International System of Units as the distance light travels in vacuum in 1⁄299792458 of a second
6.
Astronomical unit
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The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that varies as Earth orbits the Sun, from a maximum to a minimum. Originally conceived as the average of Earths aphelion and perihelion, it is now defined as exactly 149597870700 metres, the astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is also a component in the definition of another unit of astronomical length. A variety of symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A for the astronomical unit, in 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting that various symbols are presently in use for the astronomical unit, in the 2014 revision of the SI Brochure, the BIPM used the unit symbol au. In ISO 80000-3, the symbol of the unit is ua. Earths orbit around the Sun is an ellipse, the semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. The centre of the sun lies on this line segment. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, knowing Earths shift and a stars shift enabled the stars distance to be calculated. But all measurements are subject to some degree of error or uncertainty, improvements in precision have always been a key to improving astronomical understanding. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics, the expected positions and distances of objects at an established time are calculated from these laws, and assembled into a collection of data called an ephemeris. NASAs Jet Propulsion Laboratory provides one of several ephemeris computation services, in 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Equivalently, by definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass. As with all measurements, these rely on measuring the time taken for photons to be reflected from an object. However, for precision the calculations require adjustment for such as the motions of the probe. In addition, the measurement of the time itself must be translated to a scale that accounts for relativistic time dilation
7.
Arbitrary unit
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The reference measurement is typically defined by the local laboratories or dependent on individual measurement apparatus. Units of such kind are used in fields such as physiology to indicate substance concentration. When the reference measurement is defined and internationally agreed upon. One example of a publicly defined arbitrary unit is the WHO International Unit, abbreviations for arbitrary unit include, arb. unit, arb. u. AU, and a. u. Among these, AU and a. u. are common abbreviations for astronomical units, for this reason, Japanese Journal of Applied Physics, and probably other academic journals, recommend against using a. u. While arbitrary unit is not a recognized unit, IUPAC and IFCC recognize the need to deal with unknown units. The decision forbids using factors or denominators in conjunction with p. d. u
8.
SI units
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The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version
9.
Mass
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In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and this is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force, according to Newtons second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A bodys mass also determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. The standard International System of Units unit of mass is the kilogram, the kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and molecules. Outside the SI system, other units of mass include, the slug is an Imperial unit of mass, the pound is a unit of both mass and force, used mainly in the United States
10.
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
11.
Fine-structure constant
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It is related to the elementary charge e, which characterizes the strength of the coupling of an elementary charged particle with the electromagnetic field, by the formula 4πε0ħcα = e2. Being a dimensionless quantity, it has the numerical value of about 1⁄137 in all systems of units. Arnold Sommerfeld introduced the fine-structure constant in 1916, the definition reflects the relationship between α and the elementary charge e, which equals √4παε0ħc. In electrostatic cgs units, the unit of charge, the statcoulomb, is defined so that the Coulomb constant, ke, or the permittivity factor, 4πε0, is 1. Then the expression of the constant, as commonly found in older physics literature. In natural units, commonly used in high energy physics, where ε0 = c = ħ =1, the value of the fine-structure constant is α = e 24 π. As such, the constant is just another, albeit dimensionless, quantity determining the elementary charge. The 2014 CODATA recommended value of α is α = e 2 ℏ c =0.0072973525664 and this has a relative standard uncertainty of 0.32 parts per billion. For reasons of convenience, historically the value of the reciprocal of the constant is often specified. The 2014 CODATA recommended value is given by α −1 =137.035999139, the theory of QED predicts a relationship between the dimensionless magnetic moment of the electron and the fine-structure constant α.035999173. This measurement of α has a precision of 0.25 parts per billion and this value and uncertainty are about the same as the latest experimental results. The fine-structure constant, α, has several physical interpretations, α is, The square of the ratio of the elementary charge to the Planck charge α =2. The ratio of the velocity of the electron in the first circular orbit of the Bohr model of the atom to the speed of light in vacuum and this is Sommerfelds original physical interpretation. Then the square of α is the ratio between the Hartree energy and the electron rest energy, the theory does not predict its value. Therefore, α must be determined experimentally, in fact, α is one of the about 20 empirical parameters in the Standard Model of particle physics, whose value is not determined within the Standard Model. In the electroweak theory unifying the weak interaction with electromagnetism, α is absorbed into two other coupling constants associated with the gauge fields. In this theory, the interaction is treated as a mixture of interactions associated with the electroweak fields. The strength of the electromagnetic interaction varies with the strength of the energy field, the absorption value for normal-incident light on graphene in vacuum would then be given by πα/2 or 2. 24%, and the transmission by 1/2 or 97. 75%
12.
Proton mass
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A proton is a subatomic particle, symbol p or p+, with a positive electric charge of +1e elementary charge and mass slightly less than that of a neutron. Protons and neutrons, each with masses of one atomic mass unit, are collectively referred to as nucleons. One or more protons are present in the nucleus of every atom, the number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number. Since each element has a number of protons, each element has its own unique atomic number. The word proton is Greek for first, and this name was given to the nucleus by Ernest Rutherford in 1920. In previous years, Rutherford had discovered that the nucleus could be extracted from the nuclei of nitrogen by atomic collisions. Protons were therefore a candidate to be a particle, and hence a building block of nitrogen. In the modern Standard Model of particle physics, protons are hadrons, and like neutrons, although protons were originally considered fundamental or elementary particles, they are now known to be composed of three valence quarks, two up quarks and one down quark. The rest masses of quarks contribute only about 1% of a protons mass, the remainder of a protons mass is due to quantum chromodynamics binding energy, which includes the kinetic energy of the quarks and the energy of the gluon fields that bind the quarks together. At sufficiently low temperatures, free protons will bind to electrons, however, the character of such bound protons does not change, and they remain protons. A fast proton moving through matter will slow by interactions with electrons and nuclei, the result is a protonated atom, which is a chemical compound of hydrogen. In vacuum, when electrons are present, a sufficiently slow proton may pick up a single free electron, becoming a neutral hydrogen atom. Such free hydrogen atoms tend to react chemically with other types of atoms at sufficiently low energies. When free hydrogen atoms react with other, they form neutral hydrogen molecules. Protons are spin-½ fermions and are composed of three quarks, making them baryons. Protons have an exponentially decaying positive charge distribution with a mean square radius of about 0.8 fm. Protons and neutrons are both nucleons, which may be together by the nuclear force to form atomic nuclei. The nucleus of the most common isotope of the atom is a lone proton
13.
Boltzmann constant
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The Boltzmann constant, which is named after Ludwig Boltzmann, is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas. It is the gas constant R divided by the Avogadro constant NA, the Boltzmann constant has the dimension energy divided by temperature, the same as entropy. The accepted value in SI units is 6977138064851999999♠1. 38064852×10−23 J/K, the Boltzmann constant, k, is a bridge between macroscopic and microscopic physics. Introducing the Boltzmann constant transforms the gas law into an alternative form, p V = N k T. For n =1 mol, N is equal to the number of particles in one mole, given a thermodynamic system at an absolute temperature T, the average thermal energy carried by each microscopic degree of freedom in the system is on the order of magnitude of 1/2kT. In classical statistical mechanics, this average is predicted to hold exactly for homogeneous ideal gases, monatomic ideal gases possess three degrees of freedom per atom, corresponding to the three spatial directions, which means a thermal energy of 3/2kT per atom. This corresponds very well with experimental data, the thermal energy can be used to calculate the root-mean-square speed of the atoms, which turns out to be inversely proportional to the square root of the atomic mass. The root mean square speeds found at room temperature accurately reflect this, ranging from 7003137000000000000♠1370 m/s for helium, kinetic theory gives the average pressure p for an ideal gas as p =13 N V m v 2 ¯. Combination with the gas law p V = N k T shows that the average translational kinetic energy is 12 m v 2 ¯ =32 k T. Considering that the translational motion velocity vector v has three degrees of freedom gives the energy per degree of freedom equal to one third of that. Diatomic gases, for example, possess a total of six degrees of freedom per molecule that are related to atomic motion. Again, it is the energy-like quantity kT that takes central importance, consequences of this include the Arrhenius equation in chemical kinetics. This equation, which relates the details, or microstates. Such is its importance that it is inscribed on Boltzmanns tombstone, the constant of proportionality k serves to make the statistical mechanical entropy equal to the classical thermodynamic entropy of Clausius, Δ S = ∫ d Q T. One could choose instead a rescaled dimensionless entropy in terms such that S ′ = ln W, Δ S ′ = ∫ d Q k T. This is a natural form and this rescaled entropy exactly corresponds to Shannons subsequent information entropy. The characteristic energy kT is thus the required to increase the rescaled entropy by one nat. The iconic terse form of the equation S = k ln W on Boltzmanns tombstone is in due to Planck
14.
Length
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In geometric measurements, length is the most extended dimension of an object. In the International System of Quantities, length is any quantity with dimension distance, in other contexts length is the measured dimension of an object. For example, it is possible to cut a length of a wire which is shorter than wire thickness. Length may be distinguished from height, which is vertical extent, and width or breadth, length is a measure of one dimension, whereas area is a measure of two dimensions and volume is a measure of three dimensions. In most systems of measurement, the unit of length is a base unit, measurement has been important ever since humans settled from nomadic lifestyles and started using building materials, occupying land and trading with neighbours. As society has become more technologically oriented, much higher accuracies of measurement are required in a diverse set of fields. One of the oldest units of measurement used in the ancient world was the cubit which was the length of the arm from the tip of the finger to the elbow. This could then be subdivided into shorter units like the foot, hand or finger, the cubit could vary considerably due to the different sizes of people. After Albert Einsteins special relativity, length can no longer be thought of being constant in all reference frames. Thus a ruler that is one meter long in one frame of reference will not be one meter long in a frame that is travelling at a velocity relative to the first frame. This means length of an object is variable depending on the observer, in the physical sciences and engineering, when one speaks of units of length, the word length is synonymous with distance. There are several units that are used to measure length, in the International System of Units, the basic unit of length is the metre and is now defined in terms of the speed of light. The centimetre and the kilometre, derived from the metre, are commonly used units. In U. S. customary units, English or Imperial system of units, commonly used units of length are the inch, the foot, the yard, and the mile. Units used to denote distances in the vastness of space, as in astronomy, are longer than those typically used on Earth and include the astronomical unit, the light-year. Dimension Distance Orders of magnitude Reciprocal length Smoot Unit of length
15.
Energy
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In physics, energy is the property that must be transferred to an object in order to perform work on – or to heat – the object, and can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the transferred to an object by the mechanical work of moving it a distance of 1 metre against a force of 1 newton. Mass and energy are closely related, for example, with a sensitive enough scale, one could measure an increase in mass after heating an object. Living organisms require available energy to stay alive, such as the humans get from food. Civilisation gets the energy it needs from energy resources such as fuels, nuclear fuel. The processes of Earths climate and ecosystem are driven by the radiant energy Earth receives from the sun, the total energy of a system can be subdivided and classified in various ways. It may also be convenient to distinguish gravitational energy, thermal energy, several types of energy, electric energy. Many of these overlap, for instance, thermal energy usually consists partly of kinetic. Some types of energy are a mix of both potential and kinetic energy. An example is energy which is the sum of kinetic. Whenever physical scientists discover that a phenomenon appears to violate the law of energy conservation. Heat and work are special cases in that they are not properties of systems, in general we cannot measure how much heat or work are present in an object, but rather only how much energy is transferred among objects in certain ways during the occurrence of a given process. Heat and work are measured as positive or negative depending on which side of the transfer we view them from, the distinctions between different kinds of energy is not always clear-cut. In contrast to the definition, energeia was a qualitative philosophical concept, broad enough to include ideas such as happiness. The modern analog of this property, kinetic energy, differs from vis viva only by a factor of two, in 1807, Thomas Young was possibly the first to use the term energy instead of vis viva, in its modern sense. Gustave-Gaspard Coriolis described kinetic energy in 1829 in its modern sense, the law of conservation of energy was also first postulated in the early 19th century, and applies to any isolated system. It was argued for years whether heat was a physical substance, dubbed the caloric, or merely a physical quantity. In 1845 James Prescott Joule discovered the link between mechanical work and the generation of heat and these developments led to the theory of conservation of energy, formalized largely by William Thomson as the field of thermodynamics
16.
Time
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Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is often referred to as the dimension, along with the three spatial dimensions. Time has long been an important subject of study in religion, philosophy, and science, nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems. Two contrasting viewpoints on time divide prominent philosophers, one view is that time is part of the fundamental structure of the universe—a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is referred to as Newtonian time. This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, Time in physics is unambiguously operationally defined as what a clock reads. Time is one of the seven fundamental physical quantities in both the International System of Units and International System of Quantities, Time is used to define other quantities—such as velocity—so defining time in terms of such quantities would result in circularity of definition. The operational definition leaves aside the question there is something called time, apart from the counting activity just mentioned, that flows. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Furthermore, it may be there is a subjective component to time. Temporal measurement has occupied scientists and technologists, and was a motivation in navigation. Periodic events and periodic motion have long served as standards for units of time, examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is also of significant social importance, having economic value as well as value, due to an awareness of the limited time in each day. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day, increasingly, personal electronic devices display both calendars and clocks simultaneously. The number that marks the occurrence of an event as to hour or date is obtained by counting from a fiducial epoch—a central reference point. Artifacts from the Paleolithic suggest that the moon was used to time as early as 6,000 years ago. Lunar calendars were among the first to appear, either 12 or 13 lunar months, without intercalation to add days or months to some years, seasons quickly drift in a calendar based solely on twelve lunar months
17.
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
18.
Velocity
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The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of its speed and direction of motion, Velocity is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a vector quantity, both magnitude and direction are needed to define it. The scalar absolute value of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI system as metres per second or as the SI base unit of. For example,5 metres per second is a scalar, whereas 5 metres per second east is a vector, if there is a change in speed, direction or both, then the object has a changing velocity and is said to be undergoing an acceleration. To have a constant velocity, an object must have a constant speed in a constant direction, constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed. For example, a car moving at a constant 20 kilometres per hour in a path has a constant speed. Hence, the car is considered to be undergoing an acceleration, Speed describes only how fast an object is moving, whereas velocity gives both how fast and in what direction the object is moving. If a car is said to travel at 60 km/h, its speed has been specified, however, if the car is said to move at 60 km/h to the north, its velocity has now been specified. The big difference can be noticed when we consider movement around a circle and this is because the average velocity is calculated by only considering the displacement between the starting and the end points while the average speed considers only the total distance traveled. Velocity is defined as the rate of change of position with respect to time, average velocity can be calculated as, v ¯ = Δ x Δ t. The average velocity is less than or equal to the average speed of an object. This can be seen by realizing that while distance is always strictly increasing, from this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time is the displacement, x. In calculus terms, the integral of the velocity v is the displacement function x. In the figure, this corresponds to the area under the curve labeled s. Since the derivative of the position with respect to time gives the change in position divided by the change in time, although velocity is defined as the rate of change of position, it is often common to start with an expression for an objects acceleration. As seen by the three green tangent lines in the figure, an objects instantaneous acceleration at a point in time is the slope of the tangent to the curve of a v graph at that point. In other words, acceleration is defined as the derivative of velocity with respect to time, from there, we can obtain an expression for velocity as the area under an a acceleration vs. time graph
19.
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
20.
Temperature
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A temperature is an objective comparative measurement of hot or cold. It is measured by a thermometer, several scales and units exist for measuring temperature, the most common being Celsius, Fahrenheit, and, especially in science, Kelvin. Absolute zero is denoted as 0 K on the Kelvin scale, −273.15 °C on the Celsius scale, the kinetic theory offers a valuable but limited account of the behavior of the materials of macroscopic bodies, especially of fluids. Temperature is important in all fields of science including physics, geology, chemistry, atmospheric sciences, medicine. The Celsius scale is used for temperature measurements in most of the world. Because of the 100 degree interval, it is called a centigrade scale.15, the United States commonly uses the Fahrenheit scale, on which water freezes at 32°F and boils at 212°F at sea-level atmospheric pressure. Many scientific measurements use the Kelvin temperature scale, named in honor of the Scottish physicist who first defined it and it is a thermodynamic or absolute temperature scale. Its zero point, 0K, is defined to coincide with the coldest physically-possible temperature and its degrees are defined through thermodynamics. The temperature of zero occurs at 0K = −273. 15°C. For historical reasons, the triple point temperature of water is fixed at 273.16 units of the measurement increment, Temperature is one of the principal quantities in the study of thermodynamics. There is a variety of kinds of temperature scale and it may be convenient to classify them as empirically and theoretically based. Empirical temperature scales are historically older, while theoretically based scales arose in the middle of the nineteenth century, empirically based temperature scales rely directly on measurements of simple physical properties of materials. For example, the length of a column of mercury, confined in a capillary tube, is dependent largely on temperature. Such scales are only within convenient ranges of temperature. For example, above the point of mercury, a mercury-in-glass thermometer is impracticable. A material is of no use as a thermometer near one of its phase-change temperatures, in spite of these restrictions, most generally used practical thermometers are of the empirically based kind. Especially, it was used for calorimetry, which contributed greatly to the discovery of thermodynamics, nevertheless, empirical thermometry has serious drawbacks when judged as a basis for theoretical physics. Theoretically based temperature scales are based directly on theoretical arguments, especially those of thermodynamics, kinetic theory and they rely on theoretical properties of idealized devices and materials
21.
Pressure
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Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the relative to the ambient pressure. Various units are used to express pressure, Pressure may also be expressed in terms of standard atmospheric pressure, the atmosphere is equal to this pressure and the torr is defined as 1⁄760 of this. Manometric units such as the centimetre of water, millimetre of mercury, Pressure is the amount of force acting per unit area. The symbol for it is p or P, the IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. The usage of P vs p depends upon the field in one is working, on the nearby presence of other symbols for quantities such as power and momentum. Mathematically, p = F A where, p is the pressure, F is the normal force and it relates the vector surface element with the normal force acting on it. It is incorrect to say the pressure is directed in such or such direction, the pressure, as a scalar, has no direction. The force given by the relationship to the quantity has a direction. If we change the orientation of the element, the direction of the normal force changes accordingly. Pressure is distributed to solid boundaries or across arbitrary sections of normal to these boundaries or sections at every point. It is a parameter in thermodynamics, and it is conjugate to volume. The SI unit for pressure is the pascal, equal to one newton per square metre and this name for the unit was added in 1971, before that, pressure in SI was expressed simply in newtons per square metre. Other units of pressure, such as pounds per square inch, the CGS unit of pressure is the barye, equal to 1 dyn·cm−2 or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre, but using the names kilogram, gram, kilogram-force, or gram-force as units of force is expressly forbidden in SI. The technical atmosphere is 1 kgf/cm2, since a system under pressure has potential to perform work on its surroundings, pressure is a measure of potential energy stored per unit volume. It is therefore related to density and may be expressed in units such as joules per cubic metre. Similar pressures are given in kilopascals in most other fields, where the prefix is rarely used
22.
Electric field
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An electric field is a vector field that associates to each point in space the Coulomb force that would be experienced per unit of electric charge, by an infinitesimal test charge at that point. Electric fields are created by electric charges and can be induced by time-varying magnetic fields, the electric field combines with the magnetic field to form the electromagnetic field. The electric field, E, at a point is defined as the force, F. A particle of charge q would be subject to a force F = q E and its SI units are newtons per coulomb or, equivalently, volts per metre, which in terms of SI base units are kg⋅m⋅s−3⋅A−1. Electric fields are caused by electric charges or varying magnetic fields, in the special case of a steady state, the Maxwell-Faraday inductive effect disappears. The resulting two equations, taken together, are equivalent to Coulombs law, written as E =14 π ε0 ∫ d r ′ ρ r − r ′ | r − r ′ |3 for a charge density ρ. Notice that ε0, the permittivity of vacuum, must be substituted if charges are considered in non-empty media, the equations of electromagnetism are best described in a continuous description. A charge q located at r 0 can be described mathematically as a charge density ρ = q δ, conversely, a charge distribution can be approximated by many small point charges. Electric fields satisfy the principle, because Maxwells equations are linear. This principle is useful to calculate the field created by point charges. Q n are stationary in space at r 1, r 2, in that case, Coulombs law fully describes the field. If a system is static, such that magnetic fields are not time-varying, then by Faradays law, in this case, one can define an electric potential, that is, a function Φ such that E = − ∇ Φ. This is analogous to the gravitational potential, Coulombs law, which describes the interaction of electric charges, F = q = q E is similar to Newtons law of universal gravitation, F = m = m g. This suggests similarities between the electric field E and the gravitational field g, or their associated potentials, mass is sometimes called gravitational charge because of that similarity. Electrostatic and gravitational forces both are central, conservative and obey an inverse-square law, a uniform field is one in which the electric field is constant at every point. It can be approximated by placing two conducting plates parallel to other and maintaining a voltage between them, it is only an approximation because of boundary effects. Assuming infinite planes, the magnitude of the electric field E is, electrodynamic fields are E-fields which do change with time, for instance when charges are in motion. The electric field cannot be described independently of the field in that case
23.
Electric potential
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An electric potential is the amount of work needed to move a unit positive charge from a reference point to a specific point inside the field without producing any acceleration. Typically, the point is Earth or a point at Infinity. By dividing out the charge on the particle a remainder is obtained that is a property of the field itself. This value can be calculated in either a static or an electric field at a specific time in units of joules per coulomb. The electric potential at infinity is assumed to be zero, a generalized electric scalar potential is also used in electrodynamics when time-varying electromagnetic fields are present, but this can not be so simply calculated. The electric potential and the vector potential together form a four vector. Classical mechanics explores concepts such as force, energy, potential etc, force and potential energy are directly related. A net force acting on any object will cause it to accelerate, as it rolls downhill its potential energy decreases, being translated to motion, inertial energy. It is possible to define the potential of certain force fields so that the energy of an object in that field depends only on the position of the object with respect to the field. Two such force fields are the field and an electric field. Such fields must affect objects due to the properties of the object. Objects may possess a property known as charge and an electric field exerts a force on charged objects. If the charged object has a charge the force will be in the direction of the electric field vector at that point while if the charge is negative the force will be in the opposite direction. The magnitude of the force is given by the quantity of the charge multiplied by the magnitude of the field vector. The electric potential at a point r in an electric field E is given by the line integral where C is an arbitrary path connecting the point with zero potential to r. When the curl ∇ × E is zero, the integral above does not depend on the specific path C chosen. The concept of electric potential is linked with potential energy. A test charge q has a potential energy UE given by U E = q V
24.
Electric dipole moment
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In physics, the electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the systems overall polarity. The electric field strength of the dipole is proportional to the magnitude of dipole moment, the SI units for electric dipole moment are Coulomb-meter, however the most commonly used unit is the Debye. Theoretically, a dipole is defined by the first-order term of the multipole expansion. This is unrealistic, as real dipoles have separated charge, however, because the charge separation is very small compared to everyday lengths, the error introduced by treating real dipoles like they are theoretically perfect is usually negligible. The direction of dipole is defined from the negative charge towards the positive charge. Often in physics the dimensions of an object can be ignored and can be treated as a pointlike object. Point particles with electric charge are referred to as point charges, two point charges, one with charge +q and the other one with charge −q separated by a distance d, constitute an electric dipole. For this case, the dipole moment has a magnitude p = q d and is directed from the negative charge to the positive one. Some authors may split d in half and use s = d/2 since this quantity is the distance between either charge and the centre of the dipole, leading to a factor of two in the definition. The electric dipole moment vector p also points from the charge to the positive charge. An idealization of this system is the electrical point dipole consisting of two charges only infinitesimally separated, but with a finite p. This quantity is used in the definition of polarization density, an object with an electric dipole moment is subject to a torque τ when placed in an external electric field. The torque tends to align the dipole with the field, a dipole aligned parallel to an electric field has lower potential energy than a dipole making some angle with it. For a spatially uniform electric field E, the torque is given by, τ = p × E, where p is the moment. The field vector and the dipole vector define a plane, a dipole orientes co- or anti-parallel to the direction in which a non-uniform electric field is increasing will not experience a torque, only a force in the direction of its dipole moment. It can be shown that this force will always be parallel to the dipole moment regardless of co- or anti-parallel orientation of the dipole. For an array of point charges, the density becomes a sum of Dirac delta functions, ρ = ∑ i =1 N q i δ. Substitution into the integration formula provides, p = ∑ i =1 N q i ∫ V δ d 3 r 0 = ∑ i =1 N q i
25.
Magnetic field
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A magnetic field is the magnetic effect of electric currents and magnetic materials. The magnetic field at any point is specified by both a direction and a magnitude, as such it is represented by a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H, where H is measured in units of amperes per meter in the SI, B is measured in teslas and newtons per meter per ampere in the SI. B is most commonly defined in terms of the Lorentz force it exerts on moving electric charges, Magnetic fields can be produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. In quantum physics, the field is quantized and electromagnetic interactions result from the exchange of photons. Magnetic fields are used throughout modern technology, particularly in electrical engineering. The Earth produces its own field, which is important in navigation. Rotating magnetic fields are used in electric motors and generators. Magnetic forces give information about the carriers in a material through the Hall effect. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits, noting that the resulting field lines crossed at two points he named those points poles in analogy to Earths poles. He also clearly articulated the principle that magnets always have both a north and south pole, no matter how finely one slices them, almost three centuries later, William Gilbert of Colchester replicated Petrus Peregrinus work and was the first to state explicitly that Earth is a magnet. Published in 1600, Gilberts work, De Magnete, helped to establish magnetism as a science, in 1750, John Michell stated that magnetic poles attract and repel in accordance with an inverse square law. Charles-Augustin de Coulomb experimentally verified this in 1785 and stated explicitly that the north and south poles cannot be separated, building on this force between poles, Siméon Denis Poisson created the first successful model of the magnetic field, which he presented in 1824. In this model, a magnetic H-field is produced by magnetic poles, three discoveries challenged this foundation of magnetism, though. First, in 1819, Hans Christian Ørsted discovered that an electric current generates a magnetic field encircling it, then in 1820, André-Marie Ampère showed that parallel wires having currents in the same direction attract one another. Finally, Jean-Baptiste Biot and Félix Savart discovered the Biot–Savart law in 1820, extending these experiments, Ampère published his own successful model of magnetism in 1825. This has the benefit of explaining why magnetic charge can not be isolated. Also in this work, Ampère introduced the term electrodynamics to describe the relationship between electricity and magnetism, in 1831, Michael Faraday discovered electromagnetic induction when he found that a changing magnetic field generates an encircling electric field
26.
Magnetic dipole moment
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The magnetic moment of a magnet is a quantity that determines the torque it will experience in an external magnetic field. A loop of current, a bar magnet, an electron, a molecule. The magnetic moment may be considered to be a vector having a magnitude, the direction of the magnetic moment points from the south to north pole of the magnet. The magnetic field produced by the magnet is proportional to its magnetic moment, more precisely, the term magnetic moment normally refers to a systems magnetic dipole moment, which produces the first term in the multipole expansion of a general magnetic field. The dipole component of a magnetic field is symmetric about the direction of its magnetic dipole moment. The magnetic moment is defined as a vector relating the aligning torque on the object from an applied magnetic field to the field vector itself. The relationship is given by, τ = μ × B where τ is the acting on the dipole and B is the external magnetic field. This definition is based on how one would measure the magnetic moment, in principle, the unit for magnetic moment is not a base unit in the International System of Units. As the torque is measured in newton-meters and the field in teslas. This has equivalents in other units, N·m/T = A·m2 = J/T where A is amperes. In the CGS system, there are different sets of electromagnetism units, of which the main ones are ESU, Gaussian. The ratio of these two non-equivalent CGS units is equal to the speed of light in space, expressed in cm·s−1. All formulae in this article are correct in SI units, they may need to be changed for use in other unit systems. For example, in SI units, a loop of current with current I and area A has magnetic moment IA, the preferred classical explanation of a magnetic moment has changed over time. Before the 1930s, textbooks explained the moment using hypothetical magnetic point charges, since then, most have defined it in terms of Ampèrian currents. The sources of magnetic moments in materials can be represented by poles in analogy to electrostatics, consider a bar magnet which has magnetic poles of equal magnitude but opposite polarity. Each pole is the source of force which weakens with distance. Since magnetic poles always come in pairs, their forces partially cancel each other because while one pole pulls and this cancellation is greatest when the poles are close to each other i. e. when the bar magnet is short
27.
Electromagnetism
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Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as fields, magnetic fields. The other three fundamental interactions are the interaction, the weak interaction, and gravitation. The word electromagnetism is a form of two Greek terms, ἤλεκτρον, ēlektron, amber, and μαγνῆτις λίθος magnētis lithos, which means magnesian stone. The electromagnetic force plays a role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of forces between individual atoms and molecules in matter, and is a manifestation of the electromagnetic force. Electrons are bound by the force to atomic nuclei, and their orbital shapes. The electromagnetic force governs the processes involved in chemistry, which arise from interactions between the electrons of neighboring atoms, there are numerous mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric potential, although electromagnetism is considered one of the four fundamental forces, at high energy the weak force and electromagnetic force are unified as a single electroweak force. In the history of the universe, during the epoch the unified force broke into the two separate forces as the universe cooled. Originally, electricity and magnetism were considered to be two separate forces, Magnetic poles attract or repel one another in a manner similar to positive and negative charges and always exist as pairs, every north pole is yoked to a south pole. An electric current inside a wire creates a corresponding magnetic field outside the wire. Its direction depends on the direction of the current in the wire. A current is induced in a loop of wire when it is moved toward or away from a field, or a magnet is moved towards or away from it. While preparing for a lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation. As he was setting up his materials, he noticed a compass needle deflected away from north when the electric current from the battery he was using was switched on. At the time of discovery, Ørsted did not suggest any explanation of the phenomenon. However, three later he began more intensive investigations
28.
Tesla (unit)
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The tesla is a unit of measurement of the strength of a magnetic field. It is a unit of the International System of Units. One tesla is equal to one weber per square metre, the unit was announced during the General Conference on Weights and Measures in 1960 and is named in honour of Nikola Tesla, upon the proposal of the Slovenian electrical engineer France Avčin. The strongest fields encountered from permanent magnets are from Halbach spheres, the strongest field trapped in a laboratory superconductor as of June 2014 is 21 T. This may be appreciated by looking at the units for each, the unit of electric field in the MKS system of units is newtons per coulomb, N/C, while the magnetic field can be written as N/. The dividing factor between the two types of field is metres per second, which is velocity, in ferromagnets, the movement creating the magnetic field is the electron spin. In a current-carrying wire the movement is due to moving through the wire. One tesla is equivalent to,10,000 G, used in the CGS system, thus,10 kG =1 T, and 1 G = 10−4 T.1,000,000,000 γ, used in geophysics. Thus,1 γ =1 nT.42.6 MHz of the 1H nucleus frequency, thus, the magnetic field associated with NMR at 1 GHz is 23.5 T. One tesla is equal to 1 V·s/m2 and this can be shown by starting with the speed of light in vacuum, c = −1/2, and inserting the SI values and units for c, the vacuum permittivity ε0, and the vacuum permeability μ0. Cancellation of numbers and units then produces this relation, for those concerned with low-frequency electromagnetic radiation in the home, the following conversions are needed most,1000 nT =1 µT =10 mG,1,000,000 µT =1 T. For the relation to the units of the field, see the article on permeability
29.
Bohr model
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After the cubic model, the plum-pudding model, the Saturnian model, and the Rutherford model came the Rutherford–Bohr model or just Bohr model for short. The improvement to the Rutherford model is mostly a physical interpretation of it. The models key success lay in explaining the Rydberg formula for the emission lines of atomic hydrogen. While the Rydberg formula had been known experimentally, it did not gain a theoretical underpinning until the Bohr model was introduced. Not only did the Bohr model explain the reason for the structure of the Rydberg formula, the Bohr model is a relatively primitive model of the hydrogen atom, compared to the valence shell atom. A related model was proposed by Arthur Erich Haas in 1910. The quantum theory of the period between Plancks discovery of the quantum and the advent of a quantum mechanics is often referred to as the old quantum theory. In the early 20th century, experiments by Ernest Rutherford established that atoms consisted of a cloud of negatively charged electrons surrounding a small, dense. The laws of mechanics, predict that the electron will release electromagnetic radiation while orbiting a nucleus. Because the electron would lose energy, it would rapidly spiral inwards and this atom model is disastrous, because it predicts that all atoms are unstable. Also, as the electron spirals inward, the emission would rapidly increase in frequency as the orbit got smaller and faster and this would produce a continuous smear, in frequency, of electromagnetic radiation. However, late 19th century experiments with electric discharges have shown that atoms will emit light at certain discrete frequencies. To overcome this difficulty, Niels Bohr proposed, in 1913 and he suggested that electrons could only have certain classical motions, Electrons in atoms orbit the nucleus. The electrons can only orbit stably, without radiating, in certain orbits at a discrete set of distances from the nucleus. These orbits are associated with definite energies and are called energy shells or energy levels. In these orbits, the electrons acceleration does not result in radiation, the Bohr model of an atom was based upon Plancks quantum theory of radiation. The frequency of the radiation emitted at an orbit of period T is as it would be in classical mechanics, it is the reciprocal of the orbit period. The significance of the Bohr model is that the laws of classical mechanics apply to the motion of the electron about the nucleus only when restricted by a quantum rule, is called the principal quantum number, and ħ = h/2π
30.
Hydrogen atom
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A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the mass of the universe. In everyday life on Earth, isolated hydrogen atoms are extremely rare, instead, hydrogen tends to combine with other atoms in compounds, or with itself to form ordinary hydrogen gas, H2. Atomic hydrogen and hydrogen atom in ordinary English use have overlapping, yet distinct, for example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen. Attempts to develop an understanding of the hydrogen atom have been important to the history of quantum mechanics. The most abundant isotope, hydrogen-1, protium, or light hydrogen, contains no neutrons and is just a proton, protium is stable and makes up 99. 9885% of naturally occurring hydrogen by absolute number. Deuterium contains one neutron and one proton, deuterium is stable and makes up 0. 0115% of naturally occurring hydrogen and is used in industrial processes like nuclear reactors and Nuclear Magnetic Resonance. Tritium contains two neutrons and one proton and is not stable, decaying with a half-life of 12.32 years, because of the short half life, Tritium does not exist in nature except in trace amounts. Higher isotopes of hydrogen are only created in artificial accelerators and reactors and have half lives around the order of 10−22 seconds, the formulas below are valid for all three isotopes of hydrogen, but slightly different values of the Rydberg constant must be used for each hydrogen isotope. Hydrogen is not found without its electron in ordinary chemistry, as ionized hydrogen is highly chemically reactive. When ionized hydrogen is written as H+ as in the solvation of classical acids such as hydrochloric acid, in that case, the acid transfers the proton to H2O to form H3O+. Ionized hydrogen without its electron, or free protons, are common in the interstellar medium, experiments by Ernest Rutherford in 1909 showed the structure of the atom to be a dense, positive nucleus with a light, negative charge orbiting around it. This immediately caused problems on how such a system could be stable, classical electromagnetism had shown that any accelerating charge radiates energy described through the Larmor formula. If this were true, all atoms would instantly collapse, however seem to be stable. Furthermore, the spiral inward would release a smear of electromagnetic frequencies as the orbit got smaller, instead, atoms were observed to only emit discrete frequencies of radiation. The resolution would lie in the development of quantum mechanics, in 1913, Niels Bohr obtained the energy levels and spectral frequencies of the hydrogen atom after making a number of simple assumptions in order to correct the failed classical model. The assumptions included, Electrons can only be in certain, discrete circular orbits or stationary states, thereby having a set of possible radii
31.
Ground state
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The ground state of a quantum mechanical system is its lowest-energy state, the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with greater than the ground state. In the quantum theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate, many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state, according to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state, thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a crystal lattice, have a unique ground state. It is also possible for the highest excited state to have zero temperature for systems that exhibit negative temperature. In 1D, the state of the Schrödinger equation has no nodes. This can be proved considering the energy of a state with a node at x =0, i. e. ψ =0. Consider the average energy in this state ⟨ ψ | H | ψ ⟩ = ∫ d x where V is the potential, now consider a small interval around x =0, i. e. x ∈. Take a new wave function ψ ′ to be defined as ψ ′ = ψ, x < − ϵ and ψ ′ = − ψ, x > ϵ, if ϵ is small enough then this is always possible to do so that ψ ′ is continuous. Note that the energy density | d ψ ′ d x |2 < | d ψ d x |2 everywhere because of the normalization. For definiteness let us choose V ≥0, then it is clear that outside the interval x ∈ the potential energy density is smaller for the ψ ′ because | ψ ′ | < | ψ | there. Therefore, the energy is unchanged up to order ϵ2 if we deform the state with a node ψ into a state without a node ψ ′. We can therefore remove all nodes and reduce the energy, which implies that the wave function cannot have a node. The wave function of the state of a particle in a one-dimensional well is a half-period sine wave which goes to zero at the two edges of the well. The wave function of the state of a hydrogen atom is a spherically-symmetric distribution centred on the nucleus. The electron is most likely to be found at a distance from the equal to the Bohr radius
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Angular momentum
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In physics, angular momentum is the rotational analog of linear momentum. It is an important quantity in physics because it is a conserved quantity – the angular momentum of a system remains constant unless acted on by an external torque. The definition of momentum for a point particle is a pseudovector r×p. This definition can be applied to each point in continua like solids or fluids, unlike momentum, angular momentum does depend on where the origin is chosen, since the particles position is measured from it. The angular momentum of an object can also be connected to the angular velocity ω of the object via the moment of inertia I. However, while ω always points in the direction of the rotation axis, Angular momentum is additive, the total angular momentum of a system is the vector sum of the angular momenta. For continua or fields one uses integration, torque can be defined as the rate of change of angular momentum, analogous to force. Applications include the gyrocompass, control moment gyroscope, inertial systems, reaction wheels, flying discs or Frisbees. In general, conservation does limit the motion of a system. In quantum mechanics, angular momentum is an operator with quantized eigenvalues, Angular momentum is subject to the Heisenberg uncertainty principle, meaning only one component can be measured with definite precision, the other two cannot. Also, the spin of elementary particles does not correspond to literal spinning motion, Angular momentum is a vector quantity that represents the product of a bodys rotational inertia and rotational velocity about a particular axis. Angular momentum can be considered an analog of linear momentum. Thus, where momentum is proportional to mass m and linear speed v, p = m v, angular momentum is proportional to moment of inertia I. Unlike mass, which only on amount of matter, moment of inertia is also dependent on the position of the axis of rotation. Unlike linear speed, which occurs in a line, angular speed occurs about a center of rotation. Therefore, strictly speaking, L should be referred to as the angular momentum relative to that center and this simple analysis can also apply to non-circular motion if only the component of the motion which is perpendicular to the radius vector is considered. In that case, L = r m v ⊥, where v ⊥ = v sin θ is the component of the motion. It is this definition, × to which the moment of momentum refers
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Ionization energy
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The ionization energy is qualitatively defined as the amount of energy required to remove the most loosely bound electron, the valence electron, of an isolated gaseous atom to form a cation. Generally, the closer the electrons are to the nucleus of the atom, the units for ionization energy are different in physics and chemistry. In physics, the unit is the amount of required to remove a single electron from a single atom or molecule. Comparison of IEs of atoms in the periodic table reveals two patterns, IEs generally increase as one moves from left to right within a given period, IEs generally decrease as one moves down a given group. The nth ionization energy refers to the amount of required to remove an electron from the species with a charge of. However this term is now considered obsolete, type of orbital ionized as the atom having stable electronic configuration has less tendency to lose electrons and consequently has high ionization energy. Occupancy of the orbital matters as if the orbital is half or completely filled then it is harder to remove electrons Further, thus, the net energy may equals energy of attraction minus the repulsion energy. In aqueous solution perhaps the latent heat of the electron should be taken into account, generally, the th ionization energy is larger than the nth ionization energy. Electrons removed from more highly charged ions of a particular element experience greater forces of attraction, thus. Both of these factors increase the ionization energy. Some values for elements of the period are given in the following table. That electron is closer to the nucleus than the previous 3s electron. Ionization energy is also a trend within the periodic table organization. Moving left to right within a period, or upward within a group, as the nuclear charge of the nucleus increases across the period, the atomic radius decreases and the electron cloud becomes closer towards the nucleus. Atomic ionization energy can be predicted by an analysis using electrostatic potential, consider an electron of charge -e and an atomic nucleus with charge +Ze, where Z is the number of protons in the nucleus. According to the Bohr model, if the electron were to approach and bond with the atom, it would come to rest at a certain radius a. The energy required for the electron to climb out and leave the atom is, E = e V = Z e 2 a This analysis is incomplete, as it leaves the distance a as an unknown variable. It can be more rigorous by assigning to each electron of every chemical element a characteristic distance