A spectrum is a condition, not limited to a specific set of values but can vary, without steps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism; as scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum. Spectrum has since been applied by analogy to topics outside optics. Thus, one might talk about the "spectrum of political opinion", or the "spectrum of activity" of a drug, or the "autism spectrum". In these uses, values within a spectrum may not be associated with quantifiable numbers or definitions; such uses imply a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion. Nonscientific uses of the term spectrum are sometimes misleading. For instance, a single left–right spectrum of political opinion does not capture the full range of people's political beliefs. Political scientists use a variety of biaxial and multiaxial systems to more characterize political opinion.
In most modern usages of spectrum there is a unifying theme between the extremes at either end. This was not always true in older usage. In Latin, spectrum means "image" or "apparition", including the meaning "spectre". Spectral evidence is testimony about what was done by spectres of persons not present physically, or hearsay evidence about what ghosts or apparitions of Satan said, it was used to convict a number of persons of witchcraft at Salem, Massachusetts in the late 17th century. The word "spectrum" was used to designate a ghostly optical afterimage by Goethe in his Theory of Colors and Schopenhauer in On Vision and Colors; the prefix "spectro-" is used to form words relating to spectra. For example, a spectrometer is a device used to record spectra and spectroscopy is the use of a spectrometer for chemical analysis. In the 17th century, the word spectrum was introduced into optics by Isaac Newton, referring to the range of colors observed when white light was dispersed through a prism.
Soon the term referred to a plot of light intensity or power as a function of frequency or wavelength known as a spectral density plot. The term spectrum was expanded to apply to other waves, such as sound waves that could be measured as a function of frequency, frequency spectrum and power spectrum of a signal; the term now applies to any signal that can be measured or decomposed along a continuous variable such as energy in electron spectroscopy or mass-to-charge ratio in mass spectrometry. Spectrum is used to refer to a graphical representation of the signal as a function of the dependent variable. Electromagnetic spectrum refers to the full range of all frequencies of electromagnetic radiation and to the characteristic distribution of electromagnetic radiation emitted or absorbed by that particular object. Devices used to measure an electromagnetic spectrum are called spectrometer; the visible spectrum is the part of the electromagnetic spectrum. The wavelength of visible light ranges from 390 to 700 nm.
The absorption spectrum of a chemical element or chemical compound is the spectrum of frequencies or wavelengths of incident radiation that are absorbed by the compound due to electron transitions from a lower to a higher energy state. The emission spectrum refers to the spectrum of radiation emitted by the compound due to electron transitions from a higher to a lower energy state. Light from many different sources contains various colors, each with its own brightness or intensity. A rainbow, or prism, sends these component colors in different directions, making them individually visible at different angles. A graph of the intensity plotted against the frequency is the frequency spectrum of the light; when all the visible frequencies are present the perceived color of the light is white, the spectrum is a flat line. Therefore, flat-line spectra in general are referred to as white, whether they represent light or another type of wave phenomenon. In radio and telecommunications, the frequency spectrum can be shared among many different broadcasters.
The radio spectrum is the part of the electromagnetic spectrum corresponding to frequencies lower below 300 GHz, which corresponds to wavelengths longer than about 1 mm. The microwave spectrum corresponds to frequencies between 300 MHz and 300 GHz and wavelengths between one meter and one millimeter; each broadcast radio and TV station transmits a wave on an assigned frequency range, called a channel. When many broadcasters are present, the radio spectrum consists of the sum of all the individual channels, each carrying separate information, spread across a wide frequency spectrum. Any particular radio receiver will detect a single function of amplitude vs. time. The radio uses a tuned circuit or tuner to select a single channel or frequency band and demodulate or decode the information from that broadcaster. If we made a graph of the strength of each channel vs. the frequency of the tuner, it would be the frequency spectrum of the antenna signal. In astronomical spectroscopy, the strength and position of absorption and emission lines, as well as the overall spectral energy distribution of the continuum, reveal many properties of astronomical objects.
Stellar classification is the categorisation of stars based on their characteristic electromagnetic spectra. The spectral flux density is used to represent the spectrum such as a star. In radiometry and colorimetry, the spectral power distribution of a light source is a measure o
In electromagnetism, absolute permittivity simply called permittivity denoted by the Greek letter ε, is the measure of capacitance, encountered when forming an electric field in a particular medium. More permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium; the SI unit for permittivity is farad per meter. The lowest possible permittivity is that of a vacuum. Vacuum permittivity, sometimes called the electric constant, is represented by ε0 and has a value of 8.85×10−12 F/m. The permittivity of a dielectric medium is represented by the ratio of its absolute permittivity to the electric constant; this dimensionless quantity is called the medium’s relative permittivity, sometimes called "permittivity". Relative permittivity is commonly referred to as the dielectric constant, a term, deprecated in physics and engineering as well as in chemistry.
Κ = ε r = ε ε 0 By definition, a perfect vacuum has a relative permittivity of 1. The difference in permittivity between a vacuum and air can be considered negligible, as κair = 1.0006. Relative permittivity is directly related to electric susceptibility, a measure of how a dielectric polarizes in response to an electric field, given by χ = κ − 1 otherwise written as ε = ε r ε 0 = ε 0 The standard SI unit for permittivity is Farad per meter. F m = C V ⋅ m = C 2 N ⋅ m 2 = A 2 ⋅ s 4 kg ⋅ m 3 = N V 2 In electromagnetism, the electric displacement field D represents how an electric field E influences the organization of electric charges in a given medium, including charge migration and electric dipole reorientation, its relation to permittivity in the simple case of linear, isotropic materials with "instantaneous" response to changes in electric field is D = ε E where the permittivity ε is a scalar. If the medium is anisotropic, the permittivity is a second rank tensor. In general, permittivity is not a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity and other parameters.
In a nonlinear medium, the permittivity can depend on the strength of the electric field. Permittivity as a function of frequency can take on complex values. In SI units, permittivity is measured in farads per meter; the displacement field D is measured in units of coulombs per square meter, while the electric field E is measured in volts per meter. D and E describe the interaction between charged objects. D is related to the charge densities associated with this interaction, while E is related to the forces and potential differences; the vacuum permittivity ε0 is the ratio D/E in free space. It appears in the Coulomb force constant, k e = 1 4 π ε 0 Its value is ε 0 = d e f 1 c 0 2 μ 0 = 1 35 950 207 149.472 7056 π F/m ≈ 8.854 187 8176 … × 10 − 12 F/m where c0 is the speed of light in free space, µ0 is the vacuum permeability. The constants c0 and μ0 are defined in SI units to have exact numerical values, shifting responsibility of experiment to the determination of the meter and the ampere; the linear permittivity of a homogeneous material is given relative to that of free space, as a relative permittivity εr (also called dielectric constant, although this term is deprecated and sometimes only refers to the static, zero-frequenc
Hydrogen spectral series
The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in an atom; the classification of the series by the Rydberg formula was important in the development of quantum mechanics. The spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen and calculating red shifts. A hydrogen atom consists of an electron orbiting its nucleus; the electromagnetic force between the electron and the nuclear proton leads to a set of quantum states for the electron, each with its own energy. These states were visualized by the Bohr model of the hydrogen atom as being distinct orbits around the nucleus; each energy state, or orbit, is designated by n as shown in the figure. The Bohr model was replaced by quantum mechanics in which the electron occupies an atomic orbital rather than an orbit, but the allowed energy levels of the hydrogen atom remained the same as in the earlier theory.
Spectral emission occurs when an electron transitions, or jumps, from a higher energy state to a lower energy state. To distinguish the two states, the lower energy state is designated as n′, the higher energy state is designated as n; the energy of an emitted photon corresponds to the energy difference between the two states. Because the energy of each state is fixed, the energy difference between them is fixed, the transition will always produce a photon with the same energy; the spectral lines are grouped into series according to n′. Lines are named sequentially starting from the longest wavelength/lowest frequency of the series, using Greek letters within each series. For example, the 2 → 1 line is called "Lyman-alpha", while the 7 → 3 line is called "Paschen-delta”. There are emission lines from hydrogen that fall outside such as the 21 cm line; these emission lines correspond to much rarer atomic events such as hyperfine transitions. The fine structure results in single spectral lines appearing as two or more grouped thinner lines, due to relativistic corrections.
In quantum mechanical theory, the discrete spectrum of atomic emission was based on the Schrödinger equation, devoted to the study of energy spectra of hydrogenlike atoms, whereas the time-dependent equivalent Heisenberg equation is convenient when studying an atom driven by an external electromagnetic wave. In the processes of absorption or emission of photons by an atom, the conservation laws hold for the whole isolated system, such as an atom plus a photon; therefore the motion of the electron in the process of photon absorption or emission is always accompanied by motion of the nucleus, because the mass of the nucleus is always finite, the energy spectra of hydrogen-like atoms must depend on the nuclear mass. And since hydrogen atoms have a nucleus of only one proton, the spectrum energy of an hydrogen atom depends only by the nucleus: in fact, the mass of one proton is ca 10 4 5 times the mass of an electron, which gives only the zero order of approximation and thus may be not taken into account.
The energy differences between levels in the Bohr model, hence the wavelengths of emitted/absorbed photons, is given by the Rydberg formula: 1 λ = R Z 2 where Z is the atomic number, i.e. the number of protons in the atomic nucleus of this element. Meaningful values are returned only when n is greater than n′. Note that this equation is valid for all hydrogen-like species, i.e. atoms having only a single electron, the particular case of hydrogen spectral lines are given by Z=1. In the Bohr model, the Lyman series includes the lines emitted by transitions of the electron from an outer orbit of quantum number n > 1 to the 1st orbit of quantum number n' = 1. The series is named after its discoverer, Theodore Lyman, who discovered the spectral lines from 1906–1914. All the wavelengths in the Lyman series are in the ultraviolet band; the Balmer series includes the lines due to transitions from an outer orbit n > 2 to the orbit n' = 2. Named after Johann Balmer, who discovered the Balmer formula, an empirical equation to predict the Balmer series, in 1885.
Balmer lines are referred to as "H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen. Four of the Balmer lines are in the technically "visible" part of the spectrum, with wavelengths longer than 400 nm and shorter than 700 nm. Parts of the Balmer series can be seen in the solar spectrum. H-alpha is an important line used in astronomy to detect the presence of hydrogen. Named after the German physicist Friedrich Paschen who first observed them in 1908; the Paschen lines all lie in the infrared band. This series overlaps with the next series, i.e. the shortest line in the Brackett series has a wavelength that falls among the Paschen series. All subsequent series overlap. Named after the American physicist Frederick Sumner Brackett who first observed the spectral lines in 1922. Experimentally discovered in 1924 by August Herman Pfund. Discovered in 1953 by American physicist Curtis J. Humphreys. Further series follow the same pattern as dictated by the Rydberg equation. Series are in
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists are interested in the root or ultimate causes of phenomena, frame their understanding in mathematical terms. Physicists work across a wide range of research fields, spanning all length scales: from sub-atomic and particle physics, through biological physics, to cosmological length scales encompassing the universe as a whole; the field includes two types of physicists: experimental physicists who specialize in the observation of physical phenomena and the analysis of experiments, theoretical physicists who specialize in mathematical modeling of physical systems to rationalize and predict natural phenomena. Physicists can apply their knowledge towards solving practical problems or to developing new technologies; the study and practice of physics is based on an intellectual ladder of discoveries and insights from ancient times to the present.
Many mathematical and physical ideas used today found their earliest expression in ancient Greek culture, for example in the work of Euclid, Thales of Miletus and Aristarchus. Roots emerged in ancient Asian culture and in the Islamic medieval period, for example the work of Alhazen in the 11th century; the modern scientific worldview and the bulk of physics education can be said to flow from the scientific revolution in Europe, starting with the work of Galileo Galilei and Johannes Kepler in the early 1600s. Newton's laws of motion and Newton's law of universal gravitation were formulated in the 17th century; the experimental discoveries of Faraday and the theory of Maxwell's equations of electromagnetism were developmental high points during the 19th century. Many physicists contributed to the development of quantum mechanics in the early-to-mid 20th century. New knowledge in the early 21st century includes a large increase in understanding physical cosmology; the broad and general study of nature, natural philosophy, was divided into several fields in the 19th century, when the concept of "science" received its modern shape.
Specific categories emerged, such as "biology" and "biologist", "physics" and "physicist", "chemistry" and "chemist", among other technical fields and titles. The term physicist was coined by William Whewell in his 1840 book The Philosophy of the Inductive Sciences. A standard undergraduate physics curriculum consists of classical mechanics and magnetism, non-relativistic quantum mechanics, statistical mechanics and thermodynamics, laboratory experience. Physics students need training in mathematics, in computer science. Any physics-oriented career position requires at least an undergraduate degree in physics or applied physics, while career options widen with a Master's degree like MSc, MPhil, MPhys or MSci. For research-oriented careers, students work toward a doctoral degree specializing in a particular field. Fields of specialization include experimental and theoretical astrophysics, atomic physics, biological physics, chemical physics, condensed matter physics, geophysics, gravitational physics, material science, medical physics, molecular physics, nuclear physics, radiophysics, electromagnetic field and microwave physics, particle physics, plasma physics.
The highest honor awarded to physicists is the Nobel Prize in Physics, awarded since 1901 by the Royal Swedish Academy of Sciences. National physics professional societies have many awards for professional recognition. In the case of the American Physical Society, as of 2017, there are 33 separate prizes and 38 separate awards in the field; the three major employers of career physicists are academic institutions and private industries, with the largest employer being the last. Physicists in academia or government labs tend to have titles such as Assistants, Professors, Sr./Jr. Scientist, or postdocs; as per the American Institute of Physics, some 20% of new physics Ph. D.s holds jobs in engineering development programs, while 14% turn to computer software and about 11% are in business/education. A majority of physicists employed apply their skills and training to interdisciplinary sectors. Job titles for graduate physicists include Agricultural Scientist, Air Traffic Controller, Computer Programmer, Electrical Engineer, Environmental Analyst, Medical Physicist, Oceanographer, Physics Teacher/Professor/Researcher, Research Scientist, Reactor Physicist, Engineering Physicist, Satellite Missions Analyst, Science Writer, Software Engineer, Systems Engineer, Microelectronics Engineer, Radar Developer, Technical Consultant, etc.
A majority of Physics terminal bachelor's degree holders are employed in the private sector. Other fields are academia and military service, nonprofit entities and teaching. Typical duties of physicists with master's and doctoral degrees working in their domain involve research and analysis, data preparation, instrumentation and development of industrial or medical equipment and software development, etc. Chartered Physicist is a chartered status and a professional qualification awarded by the Institute of Physics, it is denoted by the postnominals "CPhys". Achieving chartered status in any profession denotes to the wider community a high level of specialised subject knowledge and professional competence. According to the Institute of Physics, holders of the award of the Chartered Physicist demonst
Center of mass
In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are simplified when formulated with respect to the center of mass, it is a hypothetical point where entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, if the body has uniform density, it will be located at the centroid; the center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.
The center of mass is a useful reference point for calculations in mechanics that involve masses distributed in space, such as the linear and angular momentum of planetary bodies and rigid body dynamics. In orbital mechanics, the equations of motion of planets are formulated as point masses located at the centers of mass; the center of mass frame is an inertial frame in which the center of mass of a system is at rest with respect to the origin of the coordinate system. The concept of "center of mass" in the form of the center of gravity was first introduced by the great ancient Greek physicist and engineer Archimedes of Syracuse, he worked with simplified assumptions about gravity that amount to a uniform field, thus arriving at the mathematical properties of what we now call the center of mass. Archimedes showed that the torque exerted on a lever by weights resting at various points along the lever is the same as what it would be if all of the weights were moved to a single point—their center of mass.
In work on floating bodies he demonstrated that the orientation of a floating object is the one that makes its center of mass as low as possible. He developed mathematical techniques for finding the centers of mass of objects of uniform density of various well-defined shapes. Mathematicians who developed the theory of the center of mass include Pappus of Alexandria, Guido Ubaldi, Francesco Maurolico, Federico Commandino, Simon Stevin, Luca Valerio, Jean-Charles de la Faille, Paul Guldin, John Wallis, Louis Carré, Pierre Varignon, Alexis Clairaut. Newton's second law is reformulated with respect to the center of mass in Euler's first law; the center of mass is the unique point at the center of a distribution of mass in space that has the property that the weighted position vectors relative to this point sum to zero. In analogy to statistics, the center of mass is the mean location of a distribution of mass in space. In the case of a system of particles Pi, i = 1, …, n , each with mass mi that are located in space with coordinates ri, i = 1, …, n , the coordinates R of the center of mass satisfy the condition ∑ i = 1 n m i = 0.
Solving this equation for R yields the formula R = 1 M ∑ i = 1 n m i r i, where M is the sum of the masses of all of the particles. If the mass distribution is continuous with the density ρ within a solid Q the integral of the weighted position coordinates of the points in this volume relative to the center of mass R over the volume V is zero, ∭ Q ρ d V = 0. Solve this equation for the coordinates R to obtain R = 1 M ∭ Q ρ r d V, where M is the total mass in the volume. If a continuous mass distribution has uniform density, which means ρ is constant the center of mass is the same as the centroid of the volume; the coordinates R of the center of mass of a two-particle system, P1 and P2, with masses m1 and m2 is given by R = 1 m 1 + m 2. Let the percentage of the total mass divided between these two particles vary from 100% P1 and 0% P2 through 50% P1 and 50% P2 to 0% P1 and 100% P2 the center of mass R moves along the line from P1 to P2; the percentages of mass at each point can be viewed as projective coordinates of the point R on this line, are termed barycentric coordinates.
Another way of interpreting the process here is the mechanical balancing of moments about an arbitrary point. The numerator gives the total moment, balanced by an equivalent total force at the center of mass; this can be generalized
Speed of light
The speed of light in vacuum denoted c, is a universal physical constant important in many areas of physics. Its exact value is 299,792,458 metres per second, it is exact because by international agreement a metre is defined as the length of the path travelled by light in vacuum during a time interval of 1/299792458 second. According to special relativity, c is the maximum speed at which all conventional matter and hence all known forms of information in the universe can travel. Though this speed is most associated with light, it is in fact the speed at which all massless 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 inertial reference frame of the observer. In the special and general theories of relativity, c interrelates space and time, appears in the famous equation of mass–energy equivalence E = mc2; the speed at which light propagates through transparent materials, such as glass or air, is less than c.
The ratio between c and the speed v at which light travels in a material is called the refractive index n of the material. For example, for visible light the refractive index of glass is around 1.5, meaning that light in glass travels at c / 1.5 ≈ 200,000 km/s. For many practical purposes and other electromagnetic waves will appear to propagate instantaneously, but for long distances and sensitive measurements, their finite speed has noticeable effects. In communicating with distant space probes, it can take minutes to hours for a message to get from Earth to the spacecraft, or vice versa; 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, since information must be sent within the computer from chip to chip; the speed of light can be used with time of flight measurements to measure large distances to high precision. Ole Rømer first demonstrated in 1676 that light travels at a finite speed by studying the apparent motion of Jupiter's moon Io.
In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, therefore travelled at the speed c appearing in his theory of electromagnetism. 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 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; the speed of light in vacuum is denoted by a lowercase c, for "constant" or the Latin celeritas. In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch had used c for a different constant shown to equal √2 times the speed of light in vacuum.
The symbol V was used as an alternative symbol for the speed of light, introduced by James Clerk Maxwell in 1865. 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, which by had become the standard symbol for the speed of light. Sometimes c is used for the speed of waves in any material medium, c0 for the speed of light in vacuum; this subscripted notation, endorsed in official SI literature, has the same form as other related constants: namely, μ0 for the vacuum permeability or magnetic constant, ε0 for the vacuum permittivity or electric constant, Z0 for the impedance of free space. This article uses c 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; this definition fixes the speed of light in vacuum at 299,792,458 m/s. As a dimensional physical constant, the numerical value of c is different for different unit systems.
In branches of physics in which c appears such as in relativity, it is common to use systems of natural units of measurement or the geometrized unit system where c = 1. Using these units, c does not appear explicitly because multiplication or division by 1 does not affect the result; the speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer. This invariance of the speed of light was postulated by Einstein in 1905, after being motivated by Maxwell's theory of electromagnetism and the lack of evidence for the luminiferous aether, it is only possible to verify experimentally that the two-way speed of light is frame-independent, because it is impossible to measure the one-way speed of light without some convention as to how clocks at the source and at the detector should be synchronized. However