1.
Outline of physical science
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Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a physical science, in natural science, hypotheses must be verified scientifically to be regarded as scientific theory. Validity, accuracy, and social mechanisms ensuring quality control, such as review and repeatability of findings, are amongst the criteria. Natural science can be broken into two branches, life science, for example biology and physical science. Each of these branches, and all of their sub-branches, are referred to as natural sciences, physics – natural and physical science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. More broadly, it is the analysis of nature, conducted in order to understand how the universe behaves. Branches of astronomy Chemistry – studies the composition, structure, properties, branches of chemistry Earth science – all-embracing term referring to the fields of science dealing with planet Earth. Earth science is the study of how the natural environment works and it includes the study of the atmosphere, hydrosphere, lithosphere, and biosphere. Branches of Earth science History of physical science – history of the branch of science that studies non-living systems. It in turn has many branches, each referred to as a physical science, however, the term physical creates an unintended, somewhat arbitrary distinction, since many branches of physical science also study biological phenomena. History of astrodynamics – history of the application of ballistics and celestial mechanics to the problems concerning the motion of rockets. History of astrometry – history of the branch of astronomy that involves precise measurements of the positions and movements of stars, History of cosmology – history of the discipline that deals with the nature of the Universe as a whole. History of physical cosmology – history of the study of the largest-scale structures, History of planetary science – history of the scientific study of planets, moons, and planetary systems, in particular those of the Solar System and the processes that form them. History of neurophysics – history of the branch of biophysics dealing with the nervous system, History of chemical physics – history of the branch of physics that studies chemical processes from the point of view of physics. History of computational physics – history of the study and implementation of algorithms to solve problems in physics for which a quantitative theory already exists. History of condensed matter physics – history of the study of the properties of condensed phases of matter. History of cryogenics – history of the cryogenics is the study of the production of low temperature. History of biomechanics – history of the study of the structure and function of biological systems such as humans, animals, plants, organs, History of fluid mechanics – history of the study of fluids and the forces on them
2.
Wave
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In physics, a wave is an oscillation accompanied by a transfer of energy that travels through a medium. Frequency refers to the addition of time, wave motion transfers energy from one point to another, which displace particles of the transmission medium–that is, with little or no associated mass transport. Waves consist, instead, of oscillations or vibrations, around almost fixed locations, there are two main types of waves. Mechanical waves propagate through a medium, and the substance of this medium is deformed, restoring forces then reverse the deformation. For example, sound waves propagate via air molecules colliding with their neighbors, when the molecules collide, they also bounce away from each other. This keeps the molecules from continuing to travel in the direction of the wave, the second main type, electromagnetic waves, do not require a medium. Instead, they consist of periodic oscillations of electrical and magnetic fields generated by charged particles. These types vary in wavelength, and include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, waves are described by a wave equation which sets out how the disturbance proceeds over time. The mathematical form of this varies depending on the type of wave. Further, the behavior of particles in quantum mechanics are described by waves, in addition, gravitational waves also travel through space, which are a result of a vibration or movement in gravitational fields. While mechanical waves can be transverse and longitudinal, all electromagnetic waves are transverse in free space. A single, all-encompassing definition for the wave is not straightforward. A vibration can be defined as a back-and-forth motion around a reference value, however, a vibration is not necessarily a wave. An attempt to define the necessary and sufficient characteristics that qualify a phenomenon as a results in a blurred line. The term wave is often understood as referring to a transport of spatial disturbances that are generally not accompanied by a motion of the medium occupying this space as a whole. In a wave, the energy of a vibration is moving away from the source in the form of a disturbance within the surrounding medium and it may appear that the description of waves is closely related to their physical origin for each specific instance of a wave process. For example, acoustics is distinguished from optics in that sound waves are related to a rather than an electromagnetic wave transfer caused by vibration. Concepts such as mass, momentum, inertia, or elasticity and this difference in origin introduces certain wave characteristics particular to the properties of the medium involved
3.
Frequency
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Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as frequency, which emphasizes the contrast to spatial frequency. The period is the duration of time of one cycle in a repeating event, for example, if a newborn babys heart beats at a frequency of 120 times a minute, its period—the time interval between beats—is half a second. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as vibrations, audio signals, radio waves. For cyclical processes, such as rotation, oscillations, or waves, in physics and engineering disciplines, such as optics, acoustics, and radio, frequency is usually denoted by a Latin letter f or by the Greek letter ν or ν. For a simple motion, the relation between the frequency and the period T is given by f =1 T. The SI unit of frequency is the hertz, named after the German physicist Heinrich Hertz, a previous name for this unit was cycles per second. The SI unit for period is the second, a traditional unit of measure used with rotating mechanical devices is revolutions per minute, abbreviated r/min or rpm. As a matter of convenience, longer and slower waves, such as ocean surface waves, short and fast waves, like audio and radio, are usually described by their frequency instead of period. Spatial frequency is analogous to temporal frequency, but the axis is replaced by one or more spatial displacement axes. Y = sin = sin d θ d x = k Wavenumber, in the case of more than one spatial dimension, wavenumber is a vector quantity. For periodic waves in nondispersive media, frequency has a relationship to the wavelength. Even in dispersive media, the frequency f of a wave is equal to the phase velocity v of the wave divided by the wavelength λ of the wave. In the special case of electromagnetic waves moving through a vacuum, then v = c, where c is the speed of light in a vacuum, and this expression becomes, f = c λ. When waves from a monochrome source travel from one medium to another, their remains the same—only their wavelength. For example, if 71 events occur within 15 seconds the frequency is, the latter method introduces a random error into the count of between zero and one count, so on average half a count. This is called gating error and causes an error in the calculated frequency of Δf = 1/, or a fractional error of Δf / f = 1/ where Tm is the timing interval. This error decreases with frequency, so it is a problem at low frequencies where the number of counts N is small, an older method of measuring the frequency of rotating or vibrating objects is to use a stroboscope
4.
Wave vector
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In physics, a wave vector is a vector which helps describe a wave. In the context of relativity the wave vector can also be defined as a four-vector. There are two definitions of wave vector, which differ by a factor of 2π in their magnitudes. One definition is preferred in physics and related fields, while the definition is preferred in crystallography. For this article, they will be called the physics definition, a perfect one-dimensional traveling wave follows the equation, ψ = A cos where, x is position, t is time, ψ is the disturbance describing the wave. This wave travels in the +x direction with speed ω / k, in crystallography, the same waves are described using slightly different equations. In one and three respectively, ψ = A cos ψ = A cos The differences are. They are related by 2 π ν = ω and this substitution is not important for this article, but reflects common practice in crystallography. The wavenumber k and wave vector k are defined in a different way, here, k = | k | =1 / λ, while in the physics definition above, k = | k | =2 π / λ. The direction of k is discussed below, the direction in which the wave vector points must be distinguished from the direction of wave propagation. The direction of propagation is the direction of a waves energy flow. For light waves, this is also the direction of the Poynting vector, on the other hand, the wave vector points in the direction of phase velocity. In other words, the vector points in the normal direction to the surfaces of constant phase. In a lossless isotropic medium such as air, any gas, any liquid, or some solids, if the medium is lossy, the wave vector in general points in directions other than that of wave propagation. The condition for wave vector to point in the direction in which the wave propagates is that the wave has to be homogeneous. In a homogeneous wave, the surfaces of constant phase are also surfaces of constant amplitude, in case of inhomogeneous waves, these two species of surfaces differ in orientation. Wave vector is perpendicular to surfaces of constant phase. In solid-state physics, the wavevector of an electron or hole in a crystal is the wavevector of its quantum-mechanical wavefunction, see Bloch wave for further details
5.
Reciprocal space
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In physics, the reciprocal lattice represents the Fourier transform of another lattice. In normal usage, this first lattice is usually a periodic spatial function in real-space and is known as the direct lattice. The reciprocal lattice plays a role in most analytic studies of periodic structures. In neutron and X-ray diffraction due to the Laue conditions the momentum difference between incoming and diffracted X-rays of a crystal is a lattice vector. The diffraction pattern of a crystal can be used to determine the reciprocal vectors of the lattice, using this process, one can infer the atomic arrangement of a crystal. The Brillouin zone is a Wigner-Seitz cell of the reciprocal lattice, assuming an ideal Bravais lattice R n = n 1 ⋅ a 1 + n 2 ⋅ a 2 where n 1, n 2 ∈ Z. Any quantity, e. g. the electronic density in a crystal can be written as a periodic function f = f Due to the periodicity it is useful to write it in Fourier expansions. Mathematically, we can describe the lattice as the set of all vectors G m that satisfy the above identity for all lattice point position vectors R. This reciprocal lattice is itself a Bravais lattice, and the reciprocal of the lattice is the original lattice. Using column vector representation of vectors, the formulae above can be rewritten using matrix inversion. This method appeals to the definition, and allows generalization to arbitrary dimensions, the cross product formula dominates introductory materials on crystallography. The above definition is called the physics definition, as the factor of 2 π comes naturally from the study of periodic structures. The crystallographers definition has the advantage that the definition of b 1 is just the reciprocal magnitude of a 1 in the direction of a 2 × a 3 and this can simplify certain mathematical manipulations, and expresses reciprocal lattice dimensions in units of spatial frequency. It is a matter of taste which definition of the lattice is used, each point in the reciprocal lattice corresponds to a set of lattice planes in the real space lattice. The direction of the lattice vector corresponds to the normal to the real space planes. The magnitude of the lattice vector is given in reciprocal length and is equal to the reciprocal of the interplanar spacing of the real space planes. Reciprocal lattices for the crystal system are as follows. The simple cubic Bravais lattice, with cubic primitive cell of side a, has for its reciprocal a simple cubic lattice with a primitive cell of side 2 π a
6.
X-ray crystallography
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By measuring the angles and intensities of these diffracted beams, a crystallographer can produce a three-dimensional picture of the density of electrons within the crystal. From this electron density, the positions of the atoms in the crystal can be determined, as well as their chemical bonds, their disorder. The method also revealed the structure and function of biological molecules, including vitamins, drugs, proteins. X-ray crystallography is still the method for characterizing the atomic structure of new materials. In a single-crystal X-ray diffraction measurement, a crystal is mounted on a goniometer, the goniometer is used to position the crystal at selected orientations. The crystal is illuminated with a finely focused monochromatic beam of X-rays, poor resolution or even errors may result if the crystals are too small, or not uniform enough in their internal makeup. X-ray crystallography is related to other methods for determining atomic structures. Similar diffraction patterns can be produced by scattering electrons or neutrons, for all above mentioned X-ray diffraction methods, the scattering is elastic, the scattered X-rays have the same wavelength as the incoming X-ray. By contrast, inelastic X-ray scattering methods are useful in studying excitations of the sample, Crystals, though long admired for their regularity and symmetry, were not investigated scientifically until the 17th century. Johannes Kepler hypothesized in his work Strena seu de Nive Sexangula that the symmetry of snowflake crystals was due to a regular packing of spherical water particles. The Danish scientist Nicolas Steno pioneered experimental investigations of crystal symmetry, hence, William Hallowes Miller in 1839 was able to give each face a unique label of three small integers, the Miller indices which remain in use today for identifying crystal faces. In the 19th century, a catalog of the possible symmetries of a crystal was worked out by Johan Hessel, Auguste Bravais, Evgraf Fedorov, Arthur Schönflies. Wilhelm Röntgen discovered X-rays in 1895, just as the studies of crystal symmetry were being concluded, physicists were initially uncertain of the nature of X-rays, but soon suspected that they were waves of electromagnetic radiation, in other words, another form of light. Single-slit experiments in the laboratory of Arnold Sommerfeld suggested that X-rays had a wavelength of about 1 angstrom, however, X-rays are composed of photons, and thus are not only waves of electromagnetic radiation but also exhibit particle-like properties. Albert Einstein introduced the concept in 1905, but it was not broadly accepted until 1922. Therefore, these properties of X-rays, such as their ionization of gases. Nevertheless, Braggs view was not broadly accepted and the observation of X-ray diffraction by Max von Laue in 1912 confirmed for most scientists that X-rays were a form of electromagnetic radiation, Crystals are regular arrays of atoms, and X-rays can be considered waves of electromagnetic radiation. Atoms scatter X-ray waves, primarily through the atoms electrons and this phenomenon is known as elastic scattering, and the electron is known as the scatterer
7.
Neutron diffraction
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Neutron diffraction or elastic neutron scattering is the application of neutron scattering to the determination of the atomic and/or magnetic structure of a material. A sample to be examined is placed in a beam of thermal or cold neutrons to obtain a pattern that provides information of the structure of the material. The technique requires a source of neutrons, neutrons are usually produced in a nuclear reactor or spallation source. At a research reactor, other components are needed, including a crystal monochromators as well as filters to select the desired neutron wavelength, some parts of the setup may also be movable. The technique is most commonly performed as powder diffraction, which requires a polycrystalline powder. Single crystal work is possible, but the crystals must be much larger than those that are used in single-crystal X-ray crystallography. It is common to use crystals that are about 1 mm3, summarizing, the main disadvantage to neutron diffraction is the requirement for a nuclear reactor. For single crystal work, the technique requires relatively large crystals, diffraction is one of these phenomena, it occurs when waves encounter obstacles whose size is comparable with the wavelength. If the wavelength of a particle is short enough, atoms or their nuclei can serve as diffraction obstacles. Such a beam can then be used to perform a diffraction experiment, impinging on a crystalline sample it will scatter under a limited number of well-defined angles according to the same Braggs law that describes X-ray diffraction. Neutrons and X-rays interact with matter differently, X-rays interact primarily with the electron cloud surrounding each atom. The contribution to the diffracted intensity is therefore larger for atoms with larger atomic number. It is also often the case that light atoms contribute strongly to the diffracted intensity even in the presence of large Z atoms, the scattering length varies from isotope to isotope rather than linearly with the atomic number. An element like vanadium is a scatterer of X-rays, but its nuclei hardly scatter neutrons. Non-magnetic neutron diffraction is directly sensitive to the positions of the nuclei of the atoms, unlike X-rays, neutrons scatter mostly from the nuclei of the atoms, which are tiny. Diffractograms therefore can show well defined diffraction peaks even at high angles. Many neutron sources are equipped with liquid cooling systems that allow data collection at temperatures down to 4.2 K. The superb high angle information means that the positions in the structure can be determined with high precision
8.
Elementary particle
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In particle physics, an elementary particle or fundamental particle is a particle whose substructure is unknown, thus, it is unknown whether it is composed of other particles. A particle containing two or more elementary particles is a composite particle, soon, subatomic constituents of the atom were identified. As the 1930s opened, the electron and the proton had been observed, along with the photon, via quantum theory, protons and neutrons were found to contain quarks—up quarks and down quarks—now considered elementary particles. And within a molecule, the three degrees of freedom can separate via wavefunction into three quasiparticles. Yet a free electron—which, not orbiting a nucleus, lacks orbital motion—appears unsplittable. Meanwhile, an elementary boson mediating gravitation—the graviton—remains hypothetical, all elementary particles are—depending on their spin—either bosons or fermions. These are differentiated via the theorem of quantum statistics. Particles of half-integer spin exhibit Fermi–Dirac statistics and are fermions, Particles of integer spin, in other words full-integer, exhibit Bose–Einstein statistics and are bosons. In the Standard Model, elementary particles are represented for predictive utility as point particles, though extremely successful, the Standard Model is limited to the microcosm by its omission of gravitation and has some parameters arbitrarily added but unexplained. According to the current models of big bang nucleosynthesis, the composition of visible matter of the universe should be about 75% hydrogen. Neutrons are made up of one up and two down quark, while protons are made of two up and one down quark. Since the other elementary particles are so light or so rare when compared to atomic nuclei. Therefore, one can conclude that most of the mass of the universe consists of protons and neutrons. Some estimates imply that there are roughly 1080 baryons in the observable universe, the number of protons in the observable universe is called the Eddington number. Other estimates imply that roughly 1097 elementary particles exist in the universe, mostly photons, gravitons. However, the Standard Model is widely considered to be a theory rather than a truly fundamental one. The 12 fundamental fermionic flavours are divided into three generations of four particles each, six of the particles are quarks. The remaining six are leptons, three of which are neutrinos, and the three of which have an electric charge of −1, the electron and its two cousins, the muon and the tau
9.
Quantum mechanics
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Quantum mechanics, including quantum field theory, is a branch of physics which is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, derives from quantum mechanics as an approximation valid only at large scales, early quantum theory was profoundly reconceived in the mid-1920s. The reconceived theory is formulated in various specially developed mathematical formalisms, in one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. In 1803, Thomas Young, an English polymath, performed the famous experiment that he later described in a paper titled On the nature of light. This experiment played a role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays, Plancks hypothesis that energy is radiated and absorbed in discrete quanta precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, ludwig Boltzmann independently arrived at this result by considerations of Maxwells equations. However, it was only at high frequencies and underestimated the radiance at low frequencies. Later, Planck corrected this model using Boltzmanns statistical interpretation of thermodynamics and proposed what is now called Plancks law, following Max Plancks solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, robert Andrews Millikan studied the photoelectric effect experimentally, and Albert Einstein developed a theory for it. In 1913, Peter Debye extended Niels Bohrs theory of structure, introducing elliptical orbits. This phase is known as old quantum theory, according to Planck, each energy element is proportional to its frequency, E = h ν, where h is Plancks constant. Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the reality of the radiation itself. In fact, he considered his quantum hypothesis a mathematical trick to get the right rather than a sizable discovery. He won the 1921 Nobel Prize in Physics for this work, lower energy/frequency means increased time and vice versa, photons of differing frequencies all deliver the same amount of action, but do so in varying time intervals. High frequency waves are damaging to human tissue because they deliver their action packets concentrated in time, the Copenhagen interpretation of Niels Bohr became widely accepted. In the mid-1920s, developments in mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the old quantum theory, out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons
10.
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
11.
Optical spectroscopy
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Spectroscopy /spɛkˈtrɒskəpi/ is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, later the concept was expanded greatly to include any interaction with radiative energy as a function of its wavelength or frequency. Spectroscopic data is represented by an emission spectrum, a plot of the response of interest as a function of wavelength or frequency. Spectroscopy and spectrography are terms used to refer to the measurement of radiation intensity as a function of wavelength and are used to describe experimental spectroscopic methods. Spectral measurement devices are referred to as spectrometers, spectrophotometers, spectrographs or spectral analyzers, daily observations of color can be related to spectroscopy. Neon lighting is an application of atomic spectroscopy. Neon and other noble gases have characteristic emission frequencies, neon lamps use collision of electrons with the gas to excite these emissions. Inks, dyes and paints include chemical compounds selected for their characteristics in order to generate specific colors. A commonly encountered molecular spectrum is that of nitrogen dioxide, gaseous nitrogen dioxide has a characteristic red absorption feature, and this gives air polluted with nitrogen dioxide a reddish-brown color. Rayleigh scattering is a spectroscopic scattering phenomenon that accounts for the color of the sky, Spectroscopy is used in physical and analytical chemistry because atoms and molecules have unique spectra. As a result, these spectra can be used to detect, identify and quantify information about the atoms, Spectroscopy is also used in astronomy and remote sensing on earth. The measured spectra are used to determine the composition and physical properties of astronomical objects. One of the concepts in spectroscopy is a resonance and its corresponding resonant frequency. Resonances were first characterized in mechanical systems such as pendulums, mechanical systems that vibrate or oscillate will experience large amplitude oscillations when they are driven at their resonant frequency. A plot of amplitude vs. excitation frequency will have a peak centered at the resonance frequency and this plot is one type of spectrum, with the peak often referred to as a spectral line, and most spectral lines have a similar appearance. In quantum mechanical systems, the resonance is a coupling of two quantum mechanical stationary states of one system, such as an atom, via an oscillatory source of energy such as a photon. The coupling of the two states is strongest when the energy of the matches the energy difference between the two states. The energy of a photon is related to its frequency by E = h ν where h is Plancks constant, spectra of atoms and molecules often consist of a series of spectral lines, each one representing a resonance between two different quantum states
12.
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
13.
Spectroscopy
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Spectroscopy /spɛkˈtrɒskəpi/ is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, later the concept was expanded greatly to include any interaction with radiative energy as a function of its wavelength or frequency. Spectroscopic data is represented by an emission spectrum, a plot of the response of interest as a function of wavelength or frequency. Spectroscopy and spectrography are terms used to refer to the measurement of radiation intensity as a function of wavelength and are used to describe experimental spectroscopic methods. Spectral measurement devices are referred to as spectrometers, spectrophotometers, spectrographs or spectral analyzers, daily observations of color can be related to spectroscopy. Neon lighting is an application of atomic spectroscopy. Neon and other noble gases have characteristic emission frequencies, neon lamps use collision of electrons with the gas to excite these emissions. Inks, dyes and paints include chemical compounds selected for their characteristics in order to generate specific colors. A commonly encountered molecular spectrum is that of nitrogen dioxide, gaseous nitrogen dioxide has a characteristic red absorption feature, and this gives air polluted with nitrogen dioxide a reddish-brown color. Rayleigh scattering is a spectroscopic scattering phenomenon that accounts for the color of the sky, Spectroscopy is used in physical and analytical chemistry because atoms and molecules have unique spectra. As a result, these spectra can be used to detect, identify and quantify information about the atoms, Spectroscopy is also used in astronomy and remote sensing on earth. The measured spectra are used to determine the composition and physical properties of astronomical objects. One of the concepts in spectroscopy is a resonance and its corresponding resonant frequency. Resonances were first characterized in mechanical systems such as pendulums, mechanical systems that vibrate or oscillate will experience large amplitude oscillations when they are driven at their resonant frequency. A plot of amplitude vs. excitation frequency will have a peak centered at the resonance frequency and this plot is one type of spectrum, with the peak often referred to as a spectral line, and most spectral lines have a similar appearance. In quantum mechanical systems, the resonance is a coupling of two quantum mechanical stationary states of one system, such as an atom, via an oscillatory source of energy such as a photon. The coupling of the two states is strongest when the energy of the matches the energy difference between the two states. The energy of a photon is related to its frequency by E = h ν where h is Plancks constant, spectra of atoms and molecules often consist of a series of spectral lines, each one representing a resonance between two different quantum states
14.
Wavelength
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In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the waves shape repeats, and thus the inverse of the spatial frequency. Wavelength is commonly designated by the Greek letter lambda, the concept can also be applied to periodic waves of non-sinusoidal shape. The term wavelength is also applied to modulated waves. Wavelength depends on the medium that a wave travels through, examples of wave-like phenomena are sound waves, light, water waves and periodic electrical signals in a conductor. A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric, water waves are variations in the height of a body of water. In a crystal lattice vibration, atomic positions vary, wavelength is a measure of the distance between repetitions of a shape feature such as peaks, valleys, or zero-crossings, not a measure of how far any given particle moves. For example, in waves over deep water a particle near the waters surface moves in a circle of the same diameter as the wave height. The range of wavelengths or frequencies for wave phenomena is called a spectrum, the name originated with the visible light spectrum but now can be applied to the entire electromagnetic spectrum as well as to a sound spectrum or vibration spectrum. In linear media, any pattern can be described in terms of the independent propagation of sinusoidal components. The wavelength λ of a sinusoidal waveform traveling at constant speed v is given by λ = v f, in a dispersive medium, the phase speed itself depends upon the frequency of the wave, making the relationship between wavelength and frequency nonlinear. In the case of electromagnetic radiation—such as light—in free space, the speed is the speed of light. Thus the wavelength of a 100 MHz electromagnetic wave is about, the wavelength of visible light ranges from deep red, roughly 700 nm, to violet, roughly 400 nm. For sound waves in air, the speed of sound is 343 m/s, the wavelengths of sound frequencies audible to the human ear are thus between approximately 17 m and 17 mm, respectively. Note that the wavelengths in audible sound are much longer than those in visible light, a standing wave is an undulatory motion that stays in one place. A sinusoidal standing wave includes stationary points of no motion, called nodes, the upper figure shows three standing waves in a box. The walls of the box are considered to require the wave to have nodes at the walls of the box determining which wavelengths are allowed, the stationary wave can be viewed as the sum of two traveling sinusoidal waves of oppositely directed velocities. Consequently, wavelength, period, and wave velocity are related just as for a traveling wave, for example, the speed of light can be determined from observation of standing waves in a metal box containing an ideal vacuum. In that case, the k, the magnitude of k, is still in the same relationship with wavelength as shown above
15.
Nu (letter)
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Nu /njuː/, is the 13th letter of the Greek alphabet. In the system of Greek numerals it has a value of 50 and it is derived from the ancient Phoenician alphabet nun. Its Latin equivalent is N, though the lowercase resembles the Roman lowercase v, the name of the letter is written νῦ in Ancient Greek and traditional Modern Greek polytonic orthography, while in Modern Greek it is written νι. The uppercase nu is not used, because it is identical to Latin N. The lower-case letter ν is used as a symbol for, Degree of freedom in statistics, the frequency of a wave in physics and other fields, sometimes also spatial frequency. Poissons ratio, the ratio of strains perpendicular with and parallel with an applied force, any of three kinds of neutrino in particle physics. One of the Greeks in mathematical finance, known as vega, the number of neutrons released per fission of an atom in nuclear physics. A DNA polymerase found in eukaryotes and implicated in translesion synthesis. Molecular vibrational mode, νx where x is the number of the vibration, the greatest fixed point of a function, as commonly used in the μ-calculus. Free names of a process, as used in the π-calculus, the maximum conditioning possible for an unconditioned stimulus in the Rescorla-Wagner model. The true anomaly, a parameter that defines the position of a body moving along an orbit. Greek Nu/Coptic Ni Mathematical Nu These characters are used only as mathematical symbols, stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style
16.
Hertz
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The hertz is the unit of frequency in the International System of Units and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide proof of the existence of electromagnetic waves. Hertz are commonly expressed in SI multiples kilohertz, megahertz, gigahertz, kilo means thousand, mega meaning million, giga meaning billion and tera for trillion. Some of the units most common uses are in the description of waves and musical tones, particularly those used in radio-. It is also used to describe the speeds at which computers, the hertz is equivalent to cycles per second, i. e. 1/second or s −1. In English, hertz is also used as the plural form, as an SI unit, Hz can be prefixed, commonly used multiples are kHz, MHz, GHz and THz. One hertz simply means one cycle per second,100 Hz means one hundred cycles per second, and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, the rate of aperiodic or stochastic events occur is expressed in reciprocal second or inverse second in general or, the specific case of radioactive decay, becquerels. Whereas 1 Hz is 1 cycle per second,1 Bq is 1 aperiodic radionuclide event per second, the conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second is ω =2 π f and f = ω2 π. This SI unit is named after Heinrich Hertz, as with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that degree Celsius conforms to this rule because the d is lowercase. — Based on The International System of Units, the hertz is named after the German physicist Heinrich Hertz, who made important scientific contributions to the study of electromagnetism. The name was established by the International Electrotechnical Commission in 1930, the term cycles per second was largely replaced by hertz by the 1970s. One hobby magazine, Electronics Illustrated, declared their intention to stick with the traditional kc. Mc. etc. units, sound is a traveling longitudinal wave which is an oscillation of pressure. Humans perceive frequency of waves as pitch. Each musical note corresponds to a frequency which can be measured in hertz. An infants ear is able to perceive frequencies ranging from 20 Hz to 20,000 Hz, the range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtoHz into the terahertz range and beyond. Electromagnetic radiation is described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz. Radio frequency radiation is measured in kilohertz, megahertz, or gigahertz
17.
Dimensional analysis
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Converting from one dimensional unit to another is often somewhat complex. Dimensional analysis, or more specifically the method, also known as the unit-factor method, is a widely used technique for such conversions using the rules of algebra. The concept of physical dimension was introduced by Joseph Fourier in 1822, Physical quantities that are measurable have the same dimension and can be directly compared to each other, even if they are originally expressed in differing units of measure. If physical quantities have different dimensions, they cannot be compared by similar units, hence, it is meaningless to ask whether a kilogram is greater than, equal to, or less than an hour. Any physically meaningful equation will have the dimensions on their left and right sides. Checking for dimensional homogeneity is an application of dimensional analysis. Dimensional analysis is routinely used as a check of the plausibility of derived equations and computations. It is generally used to categorize types of quantities and units based on their relationship to or dependence on other units. Many parameters and measurements in the sciences and engineering are expressed as a concrete number – a numerical quantity. Often a quantity is expressed in terms of other quantities, for example, speed is a combination of length and time. Compound relations with per are expressed with division, e. g.60 mi/1 h, other relations can involve multiplication, powers, or combinations thereof. A base unit is a unit that cannot be expressed as a combination of other units, for example, units for length and time are normally chosen as base units. Units for volume, however, can be factored into the units of length. Sometimes the names of units obscure that they are derived units, for example, an ampere is a unit of electric current, which is equivalent to electric charge per unit time and is measured in coulombs per second, so 1 A =1 C/s. Similarly, one newton is 1 kg⋅m/s2, percentages are dimensionless quantities, since they are ratios of two quantities with the same dimensions. In other words, the % sign can be read as 1/100, derivatives with respect to a quantity add the dimensions of the variable one is differentiating with respect to on the denominator. Thus, position has the dimension L, derivative of position with respect to time has dimension LT−1 – length from position, time from the derivative, the second derivative has dimension LT−2. In economics, one distinguishes between stocks and flows, a stock has units of units, while a flow is a derivative of a stock, in some contexts, dimensional quantities are expressed as dimensionless quantities or percentages by omitting some dimensions
18.
International System of 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
19.
Heinrich Kayser
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Heinrich Gustav Johannes Kayser ForMemRS was a German physicist and spectroscopist. Kayser was born at Bingen am Rhein, kaysers early work was concerned with the characteristics of acoustic waves. He discovered the occurrence of helium in the Earths atmosphere in 1868 during a solar eclipse when he detected a new line in the solar spectrum. In 1881 Kayser coined the word “adsorption”, together with Carl Runge, he examined the spectra of chemical elements. In 1905, he wrote a paper on electron theory, the kayser unit, associated with wavenumber, of the CGS system was named after him. Enke, Stuttgart 3rd ed.1900 Digital edition by the University and State Library Düsseldorf
20.
Radian
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The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement in radians of the angle that it subtends. The unit was formerly an SI supplementary unit, but this category was abolished in 1995, separately, the SI unit of solid angle measurement is the steradian. The radian is represented by the symbol rad, so for example, a value of 1.2 radians could be written as 1.2 rad,1.2 r,1. 2rad, or 1. 2c. Radian describes the angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Conversely, the length of the arc is equal to the radius multiplied by the magnitude of the angle in radians. As the ratio of two lengths, the radian is a number that needs no unit symbol, and in mathematical writing the symbol rad is almost always omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and it follows that the magnitude in radians of one complete revolution is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees, the concept of radian measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714. He described the radian in everything but name, and he recognized its naturalness as a unit of angular measure, the idea of measuring angles by the length of the arc was already in use by other mathematicians. For example, al-Kashi used so-called diameter parts as units where one part was 1/60 radian. The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson at Queens College, Belfast. He had used the term as early as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, in 1874, after a consultation with James Thomson, Muir adopted radian. As stated, one radian is equal to 180/π degrees, thus, to convert from radians to degrees, multiply by 180/π. The length of circumference of a circle is given by 2 π r, so, to convert from radians to gradians multiply by 200 / π, and to convert from gradians to radians multiply by π /200. This is because radians have a mathematical naturalness that leads to a more elegant formulation of a number of important results, most notably, results in analysis involving trigonometric functions are simple and elegant when the functions arguments are expressed in radians. Because of these and other properties, the trigonometric functions appear in solutions to problems that are not obviously related to the functions geometrical meanings
21.
Electromagnetic radiation
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In physics, electromagnetic radiation refers to the waves of the electromagnetic field, propagating through space carrying electromagnetic radiant energy. It includes radio waves, microwaves, infrared, light, ultraviolet, X-, classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through a vacuum. The oscillations of the two fields are perpendicular to other and perpendicular to the direction of energy and wave propagation. The wavefront of electromagnetic waves emitted from a point source is a sphere, the position of an electromagnetic wave within the electromagnetic spectrum can be characterized by either its frequency of oscillation or its wavelength. Electromagnetic waves are produced whenever charged particles are accelerated, and these waves can interact with other charged particles. EM waves carry energy, momentum and angular momentum away from their source particle, quanta of EM waves are called photons, whose rest mass is zero, but whose energy, or equivalent total mass, is not zero so they are still affected by gravity. Thus, EMR is sometimes referred to as the far field, in this language, the near field refers to EM fields near the charges and current that directly produced them, specifically, electromagnetic induction and electrostatic induction phenomena. In the quantum theory of electromagnetism, EMR consists of photons, quantum effects provide additional sources of EMR, such as the transition of electrons to lower energy levels in an atom and black-body radiation. The energy of a photon is quantized and is greater for photons of higher frequency. This relationship is given by Plancks equation E = hν, where E is the energy per photon, ν is the frequency of the photon, a single gamma ray photon, for example, might carry ~100,000 times the energy of a single photon of visible light. The effects of EMR upon chemical compounds and biological organisms depend both upon the power and its frequency. EMR of visible or lower frequencies is called non-ionizing radiation, because its photons do not individually have enough energy to ionize atoms or molecules, the effects of these radiations on chemical systems and living tissue are caused primarily by heating effects from the combined energy transfer of many photons. In contrast, high ultraviolet, X-rays and gamma rays are called ionizing radiation since individual photons of high frequency have enough energy to ionize molecules or break chemical bonds. These radiations have the ability to cause chemical reactions and damage living cells beyond that resulting from simple heating, Maxwell derived a wave form of the electric and magnetic equations, thus uncovering the wave-like nature of electric and magnetic fields and their symmetry. Because the speed of EM waves predicted by the wave equation coincided with the speed of light. Maxwell’s equations were confirmed by Heinrich Hertz through experiments with radio waves, according to Maxwells equations, a spatially varying electric field is always associated with a magnetic field that changes over time. Likewise, a varying magnetic field is associated with specific changes over time in the electric field. In an electromagnetic wave, the changes in the field are always accompanied by a wave in the magnetic field in one direction
22.
Photon
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A photon is an elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force. The photon has zero rest mass and is moving at the speed of light. Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a photon may be refracted by a lens and exhibit wave interference with itself. The quanta in a light wave cannot be spatially localized, some defined physical parameters of a photon are listed. The modern concept of the photon was developed gradually by Albert Einstein in the early 20th century to explain experimental observations that did not fit the classical model of light. The benefit of the model was that it accounted for the frequency dependence of lights energy. The photon model accounted for observations, including the properties of black-body radiation. In that model, light was described by Maxwells equations, in 1926 the optical physicist Frithiof Wolfers and the chemist Gilbert N. Lewis coined the name photon for these particles. After Arthur H. Compton won the Nobel Prize in 1927 for his studies, most scientists accepted that light quanta have an independent existence. In the Standard Model of particle physics, photons and other particles are described as a necessary consequence of physical laws having a certain symmetry at every point in spacetime. The intrinsic properties of particles, such as charge, mass and it has been applied to photochemistry, high-resolution microscopy, and measurements of molecular distances. Recently, photons have been studied as elements of quantum computers, in 1900, the German physicist Max Planck was studying black-body radiation and suggested that the energy carried by electromagnetic waves could only be released in packets of energy. In his 1901 article in Annalen der Physik he called these packets energy elements, the word quanta was used before 1900 to mean particles or amounts of different quantities, including electricity. In 1905, Albert Einstein suggested that waves could only exist as discrete wave-packets. He called such a wave-packet the light quantum, the name photon derives from the Greek word for light, φῶς. Arthur Compton used photon in 1928, referring to Gilbert N. Lewis, the name was suggested initially as a unit related to the illumination of the eye and the resulting sensation of light and was used later in a physiological context. Although Wolferss and Lewiss theories were contradicted by many experiments and never accepted, in physics, a photon is usually denoted by the symbol γ
23.
Permittivity
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In electromagnetism, permittivity or absolute permittivity is the measure of resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, the permittivity of a medium describes how much electric field is generated per unit charge in that medium. More electric flux exists in a medium with a low permittivity because of polarization effects, permittivity is directly related to electric susceptibility, which is a measure of how easily a dielectric polarizes in response to an electric field. Thus, permittivity relates to an ability to resist an electric field. In SI units, permittivity ε is measured in farads per meter and they are related to each other through ε = ε r ε0 = ε0 where εr is the relative permittivity of the material, and ε0 =8. 8541878176×10−12 F/m is the vacuum permittivity. 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, temperature, 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 real or 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 and it also appears in the Coulomb force constant, ke = 1/4πε0. The constants c0 and μ0 are defined in SI units to have exact values, shifting responsibility of experiment to the determination of the meter. The linear permittivity of a material is usually given relative to that of free space. In an anisotropic material, the relative permittivity may be a tensor, the actual permittivity is then calculated by multiplying the relative permittivity by ε0, ε = ε r ε0 = ε0, where χ is the electric susceptibility of the material. The susceptibility of a medium is related to its relative permittivity εr by χ = ε r −1, so in the case of a vacuum, χ =0. The susceptibility is related to the polarizability of individual particles in the medium by the Clausius-Mossotti relation. The electric displacement D is related to the polarization density P by D = ε0 E + P = ε0 E = ε r ε0 E. The permittivity ε and permeability µ of a medium together determine the velocity v = c/n of electromagnetic radiation through that medium. In general, a material cannot polarize instantaneously in response to an applied field and that is, the polarization is a convolution of the electric field at previous times with time-dependent susceptibility given by χ
24.
Permeability (electromagnetism)
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In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself. Hence, it is the degree of magnetization that a material obtains in response to a magnetic field. Magnetic permeability is typically represented by the Greek letter µ, the term was coined in September 1885 by Oliver Heaviside. The opposite of magnetic permeability is magnetic reluctance, in SI units, permeability is measured in henries per meter, or equivalently in newtons per ampere squared. The magnetic constant has the exact value and its relation to permeability is B = μ H, where the permeability, µ, is a scalar if the medium is isotropic or a second rank tensor for an anisotropic medium. In general, permeability is not a constant, as it can vary with the position in the medium, the frequency of the applied, humidity, temperature. In a nonlinear medium, the permeability can depend on the strength of the magnetic field, Permeability as a function of frequency can take on real or complex values. In ferromagnetic materials, the relationship between B and H exhibits both non-linearity and hysteresis, B is not a function of H, but depends also on the history of the material. For these materials it is useful to consider the incremental permeability defined as Δ B = μ Δ Δ H. Permeability is the inductance per unit length. In SI units, permeability is measured in henries per metre, the auxiliary magnetic field H has dimensions current per unit length and is measured in units of amperes per metre. The product µ H thus has dimensions inductance times current per unit area, but inductance is magnetic flux per unit current, so the product has dimensions magnetic flux per unit area, that is, magnetic flux density. This is the magnetic field B, which is measured in webers per square-metre, B is related to the Lorentz force on a moving charge q, F = q. A magnetic dipole is a circulation of electric current. The dipole moment has dimensions current times area, units ampere square-metre, the H field at a distance from a dipole has magnitude proportional to the dipole moment divided by distance cubed, which has dimensions current per unit length. Relative permeability, denoted by the symbol µr, is the ratio of the permeability of a medium to the permeability of free space µ0, μ r = μ μ0. In terms of relative permeability, the susceptibility is χ m = μ r −1. The number χm is a quantity, sometimes called volumetric or bulk susceptibility, to distinguish it from χp. Diamagnetism is the property of an object causes it to create a magnetic field in opposition of an externally applied magnetic field
25.
Refraction index
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In optics, the refractive index or index of refraction n of a material is a dimensionless number that describes how light propagates through that medium. It is defined as n = c v, where c is the speed of light in vacuum, for example, the refractive index of water is 1.333, meaning that light travels 1.333 times faster in a vacuum than it does in water. The refractive index determines how light is bent, or refracted. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the angle for total internal reflection. This implies that vacuum has a index of 1. The refractive index varies with the wavelength of light and this is called dispersion and causes the splitting of white light into its constituent colors in prisms and rainbows, and chromatic aberration in lenses. Light propagation in absorbing materials can be described using a refractive index. The imaginary part then handles the attenuation, while the real part accounts for refraction, the concept of refractive index is widely used within the full electromagnetic spectrum, from X-rays to radio waves. It can also be used with wave phenomena such as sound, in this case the speed of sound is used instead of that of light and a reference medium other than vacuum must be chosen. Thomas Young was presumably the person who first used, and invented, at the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers. The ratio had the disadvantage of different appearances, newton, who called it the proportion of the sines of incidence and refraction, wrote it as a ratio of two numbers, like 529 to 396. Hauksbee, who called it the ratio of refraction, wrote it as a ratio with a fixed numerator, hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1. Young did not use a symbol for the index of refraction, in the next years, others started using different symbols, n, m, and µ. For visible light most transparent media have refractive indices between 1 and 2, a few examples are given in the adjacent table. These values are measured at the yellow doublet D-line of sodium, with a wavelength of 589 nanometers, gases at atmospheric pressure have refractive indices close to 1 because of their low density. Almost all solids and liquids have refractive indices above 1.3, aerogel is a very low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, for infrared light refractive indices can be considerably higher
26.
Evanescent field
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A hallmark of an evanescent field is that there is no net energy flow in that region. Since the net flow of energy is given by the average Poynting vector. In many cases one cannot simply say that a field is or is not evanescent, for instance, in the above illustration energy is indeed transmitted in the horizontal direction. The field strength drops off exponentially away from the surface, leaving it concentrated in a very close to the interface. However there is no propagation of energy away from the surface and this is one illustration of the inexactness of the term. In most cases where they exist, evanescent fields are thought of and referred to as electric or magnetic fields. The term is applied to differentiate a field or solution from cases where one normally expects a propagating wave. Everyday electronic devices and electrical appliances are surrounded by large fields which have this property and their operation involves alternating voltages and alternating currents. The term evanescent is never heard in this ordinary context, rather, there may be concern with inadvertent production of a propagating electromagnetic wave and thus discussion of reducing radiation losses or interference. Or in some cases there would normally be an electromagnetic wave the term is invoked to describe the field when that wave is suppressed. For instance, the constant of a hollow metal waveguide is a strong function of frequency. Below a certain frequency the propagation constant becomes an imaginary number, a solution to the wave equation having an imaginary wavenumber does not propagate as a wave but falls off exponentially, so the field excited at that lower frequency is considered evanescent. It can also be said that propagation is disallowed for that frequency. One can describe the solution then as a mode or an evanescent mode. In quantum mechanics, the explanation is exactly analogous—the Schrödinger wave-function representing particle motion normal to the boundary cannot be discontinuous at the boundary. The evanescent wave from a fiber can be used in a gas sensor. In electrical engineering, evanescent waves are found in the region within one third of a wavelength of any radio antenna. During normal operation, an antenna emits electromagnetic fields into the surrounding region
27.
Dispersion relation
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In physical sciences and electrical engineering, dispersion relations describe the effect of dispersion in a medium on the properties of a wave traveling within that medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency, from this relation the phase velocity and group velocity of the wave have convenient expressions which then determine the refractive index of the medium. Dispersion may be caused either by geometric boundary conditions or by interaction of the waves with the transmitting medium, elementary particles, considered as matter waves, have a nontrivial dispersion relation even in the absence of geometric constraints and other media. In the presence of dispersion, wave velocity is no uniquely defined, giving rise to the distinction of phase velocity. Dispersion occurs when pure plane waves of different wavelengths have different propagation velocities, the speed of a plane wave, v, is a function of the waves wavelength λ, v = v. The waves speed, wavelength, and frequency, f, are related by the identity v = λ f, the function f expresses the dispersion relation of the given medium. Dispersion relations are more commonly expressed in terms of the angular frequency ω =2 π f, rewriting the relation above in these variables gives ω = v k. where we now view f as a function of k. The use of ω to describe the relation has become standard because both the phase velocity ω/k and the group velocity dω/dk have convenient representations via this function. Plane waves in vacuum are the simplest case of propagation, no geometric constraint. For electromagnetic waves in vacuum, the frequency is proportional to the wavenumber. This is a dispersion relation. In this case, the velocity and the group velocity are the same, v = ω k = d ω d k = c, they are given by c, the speed of light in vacuum. In the nonrelativistic limit, m c 2 is a constant and p 2 /2 m is the familiar kinetic energy expressed in terms of the momentum p = m v. According to the de Broglie relations, their kinetic energy E can be expressed as a frequency ω, accordingly, angular frequency and wavenumber are connected through a dispersion relation, which in the nonrelativistic limit reads ω = ℏ k 22 m. For particles, this translates to a knowledge of energy as a function of momentum, the name dispersion relation originally comes from optics. In this case, the waveform will spread over time, such that a pulse will become an extended pulse. In these materials, ∂ ω ∂ k is known as the velocity and corresponds to the speed at which the peak of the pulse propagates. The dispersion relation for water waves is often written as ω = g k
28.
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
29.
Matter wave
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Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter can exhibit wave-like behavior, for example, a beam of electrons can be diffracted just like a beam of light or a water wave. The concept that matter behaves like a wave is referred to as the de Broglie hypothesis due to having been proposed by Louis de Broglie in 1924. Matter waves are referred to as de Broglie waves, the de Broglie wavelength is the wavelength, λ, associated with a massive particle and is related to its momentum, p, through the Planck constant, h, λ = h p. The wave-like behavior of matter is crucial to the theory of atomic structure. In 1900, this division was exposed to doubt, when, investigating the theory of black body thermal radiation and it was thoroughly challenged in 1905. Extending Plancks investigation in several ways, including its connection with the photoelectric effect, light quanta are now called photons. In the modern convention, frequency is symbolized by f as is done in the rest of this article, einstein’s postulate was confirmed experimentally by Robert Millikan and Arthur Compton over the next two decades. De Broglie, in his 1924 PhD thesis, proposed that just as light has both wave-like and particle-like properties, electrons also have wave-like properties, the relationship is now known to hold for all types of matter, all matter exhibits properties of both particles and waves. In 1926, Erwin Schrödinger published an equation describing how a matter wave should evolve—the matter wave analogue of Maxwell’s equations—and used it to derive the energy spectrum of hydrogen, furthermore, neutral atoms and even molecules have been shown to be wave-like. In 1927 at Bell Labs, Clinton Davisson and Lester Germer fired slow-moving electrons at a nickel target. The angular dependence of the electron intensity was measured, and was determined to have the same diffraction pattern as those predicted by Bragg for x-rays. At the same time George Paget Thomson at the University of Aberdeen was independently firing electrons at very thin metal foils to demonstrate the same effect, before the acceptance of the de Broglie hypothesis, diffraction was a property that was thought to be exhibited only by waves. Therefore, the presence of any diffraction effects by matter demonstrated the wave-like nature of matter, when the de Broglie wavelength was inserted into the Bragg condition, the observed diffraction pattern was predicted, thereby experimentally confirming the de Broglie hypothesis for electrons. This was a result in the development of quantum mechanics. Just as the photoelectric effect demonstrated the particle nature of light, the Davisson–Germer experiment showed the wave-nature of matter, advances in laser cooling have allowed cooling of neutral atoms down to nanokelvin temperatures. At these temperatures, the thermal de Broglie wavelengths come into the micrometre range and this effect has been used to demonstrate atomic holography, and it may allow the construction of an atom probe imaging system with nanometer resolution. The description of phenomena is based on the wave properties of neutral atoms
30.
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
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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
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Kinetic energy
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In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes, the same amount of work is done by the body in decelerating from its current speed to a state of rest. In classical mechanics, the energy of a non-rotating object of mass m traveling at a speed v is 12 m v 2. In relativistic mechanics, this is an approximation only when v is much less than the speed of light. The standard unit of energy is the joule. The adjective kinetic has its roots in the Greek word κίνησις kinesis, the dichotomy between kinetic energy and potential energy can be traced back to Aristotles concepts of actuality and potentiality. The principle in classical mechanics that E ∝ mv2 was first developed by Gottfried Leibniz and Johann Bernoulli, Willem s Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, Émilie du Châtelet recognized the implications of the experiment and published an explanation. The terms kinetic energy and work in their present scientific meanings date back to the mid-19th century, early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled Du Calcul de lEffet des Machines outlining the mathematics of kinetic energy. William Thomson, later Lord Kelvin, is given the credit for coining the term kinetic energy c, energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, and rest energy. These can be categorized in two classes, potential energy and kinetic energy. Kinetic energy is the movement energy of an object, Kinetic energy can be transferred between objects and transformed into other kinds of energy. Kinetic energy may be best understood by examples that demonstrate how it is transformed to, for example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance, the chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms, for example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling, the energy is not destroyed, it has only been converted to another form by friction
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Group velocity
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The group velocity of a wave is the velocity with which the overall shape of the waves amplitudes—known as the modulation or envelope of the wave—propagates through space. For example, if a stone is thrown into the middle of a very still pond, the expanding ring of waves is the wave group, within which one can discern individual wavelets of differing wavelengths traveling at different speeds. The longer waves travel faster than the group as a whole, the shorter waves travel more slowly, and their amplitudes diminish as they emerge from the trailing boundary of the group. The group velocity vg is defined by the equation, v g ≡ ∂ ω ∂ k where ω is the angular frequency. The phase velocity is, vp = ω / k, the function ω, which gives ω as a function of k, is known as the dispersion relation. If ω is directly proportional to k, then the velocity is exactly equal to the phase velocity. A wave of any shape will travel undistorted at this velocity, if ω is a linear function of k, but not directly proportional, then the group velocity and phase velocity are different. The envelope of a packet will travel at the group velocity, while the individual peaks. If ω is not a function of k, the envelope of a wave packet will become distorted as it travels. Since a wave packet contains a range of different frequencies, the group velocity ∂ω/∂k will be different for different values of k, therefore, the envelope does not move at a single velocity, but its wavenumber components move at different velocities, distorting the envelope. If the wavepacket has a range of frequencies, and ω is approximately linear over that narrow range. For example, for deep water gravity waves, ω=√gk, and this underlies the Kelvin wake pattern for the bow wave of all ships and swimming objects. Regardless of how fast they are moving, as long as their velocity is constant, one derivation of the formula for group velocity is as follows. Consider a wave packet as a function of x and time t, α. Let A be its Fourier transform at time t=0, α = ∫ − ∞ ∞ d k A e i k x. By the superposition principle, the wavepacket at any time t is α = ∫ − ∞ ∞ d k A e i, assume that the wave packet α is almost monochromatic, so that A is sharply peaked around a central wavenumber k0. Then, linearization gives ω ≈ ω0 + ω0 ′ where ω0 = ω and ω0 ′ = ∂ ω ∂ k | k = k 0, then, after some algebra, α = e i ∫ − ∞ ∞ d k A e i. There are two factors in this expression, the first factor, e i, describes a perfect monochromatic wave with wavevector k0, with peaks and troughs moving at the phase velocity ω0 / k 0 within the envelope of the wavepacket
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Diffraction grating
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In optics, a diffraction grating is an optical component with a periodic structure, which splits and diffracts light into several beams travelling in different directions. The emerging coloration is a form of structural coloration, the directions of these beams depend on the spacing of the grating and the wavelength of the light so that the grating acts as the dispersive element. Because of this, gratings are used in monochromators and spectrometers. For practical applications, gratings generally have ridges or rulings on their surface rather than dark lines, such gratings can be either transmissive or reflective. Gratings which modulate the phase rather than the amplitude of the incident light are also produced, the principles of diffraction gratings were discovered by James Gregory, about a year after Newtons prism experiments, initially with items such as bird feathers. The first man-made diffraction grating was made around 1785 by Philadelphia inventor David Rittenhouse and this was similar to notable German physicist Joseph von Fraunhofers wire diffraction grating in 1821. Diffraction can create rainbow colors when illuminated by a wide spectrum light source, a grating has parallel lines, while a CD has a spiral of finely-spaced data tracks. Diffraction colors also appear when one looks at a point source through a translucent fine-pitch umbrella-fabric covering. Decorative patterned plastic films based on reflective grating patches are very inexpensive, the relationship between the grating spacing and the angles of the incident and diffracted beams of light is known as the grating equation. Gratings may be of the reflective or transmissive type, analogous to a mirror or lens, respectively. A grating has a mode, in which there is no diffraction. An idealised grating is considered here which is made up of a set of slits of spacing d, assuming a plane wave of monochromatic light of wavelength λ with normal incidence, each slit in the grating acts as a quasi point-source from which light propagates in all directions. After light interacts with the grating, the light is composed of the sum of interfering wave components emanating from each slit in the grating. At any given point in space through which diffracted light may pass, similarly, when the path difference is λ, the phases will add together and maxima will occur. Thus, when light is incident on the grating, the diffracted light will have maxima at angles θm given by. It is straightforward to show if a plane wave is incident at any arbitrary angle θi. When solved for the diffracted angle maxima, the equation is, please note that these equations assume that both sides of the grating are in contact with the same medium. The light that corresponds to direct transmission is called the zero order, the other maxima occur at angles which are represented by non-zero integers m
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Interferometry
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Interferometry is a family of techniques in which waves, usually electromagnetic waves, are superimposed causing the phenomenon of interference in order to extract information. Interferometers are widely used in science and industry for the measurement of small displacements, refractive index changes, in an interferometer, light from a single source is split into two beams that travel different optical paths, then combined again to produce interference. The resulting interference fringes give information about the difference in path length, waves which are not completely in phase nor completely out of phase will have an intermediate intensity pattern, which can be used to determine their relative phase difference. Most interferometers use light or some form of electromagnetic wave. Typically a single incoming beam of coherent light will be split into two beams by a beam splitter. Each of these beams travels a different route, called a path, the path difference, the difference in the distance traveled by each beam, creates a phase difference between them. It is this phase difference that creates the interference pattern between the initially identical waves. If a single beam has been split along two paths, then the difference is diagnostic of anything that changes the phase along the paths. This could be a change in the path length itself or a change in the refractive index along the path. As seen in Fig. 2a and 2b, the observer has a view of mirror M1 seen through the beam splitter. The fringes can be interpreted as the result of interference between light coming from the two virtual images S1 and S2 of the original source S, the characteristics of the interference pattern depend on the nature of the light source and the precise orientation of the mirrors and beam splitter. In Fig. 2a, the elements are oriented so that S1 and S2 are in line with the observer. Use of white light will result in a pattern of colored fringes, the central fringe representing equal path length may be light or dark depending on the number of phase inversions experienced by the two beams as they traverse the optical system. Interferometers and interferometric techniques may be categorized by a variety of criteria, In homodyne detection, the phase difference between the two beams results in a change in the intensity of the light on the detector. The resulting intensity of the light after mixing of two beams is measured, or the pattern of interference fringes is viewed or recorded. Most of the interferometers discussed in this article fall into this category, the heterodyne technique is used for shifting an input signal into a new frequency range as well as amplifying a weak input signal. A weak input signal of frequency f1 is mixed with a reference frequency f2 from a local oscillator. The nonlinear combination of the input signals creates two new signals, one at the sum f1 + f2 of the two frequencies, and the other at the difference f1 − f2 and these new frequencies are called heterodynes
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Johannes Rydberg
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The physical constant known as the Rydberg constant is named after him, as is the Rydberg unit. Excited atoms with very high values of the quantum number. Rydbergs anticipation that spectral studies could assist in an understanding of the atom. An important spectroscopic constant based on an atom of infinite mass is called the Rydberg in his honour. He was active at Lund University, Sweden, for all of his working life, the crater Rydberg on the Moon and asteroid 10506 Rydberg are named in his honour. There is a pub night held in Rydbergs honour every Wednesday at the Department of Physics at Lund University, Rydberg matter Rydberg state Rydberg atom Sutton, Mike. “Getting the numbers right – the lonely struggle of Rydberg. ”Martinson, Indrek, Curtis, L. J. Janne Rydberg – his life, oConnor, John J. Robertson, Edmund F. Johannes Rydberg, MacTutor History of Mathematics archive, University of St Andrews
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Hydrogen spectral series
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The emission spectrum of atomic hydrogen is 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 levels in the 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 atom as being distinct orbits around the nucleus. Each energy state, or orbit, is designated by an integer, 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 energy state is commonly designated as n′, and the higher energy state is designated as n. The energy of a photon corresponds to the energy difference between the two states. Because the energy of state is fixed, the energy difference between them is fixed, and 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, there are emission lines from hydrogen that fall outside of these series, such as the 21 cm line. These emission lines correspond to much rarer atomic events such as hyperfine transitions, the fine structure also results in single spectral lines appearing as two or more closely grouped thinner lines, due to relativistic corrections. 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, and the particular case of hydrogen spectral lines are given by Z=1. The series is named after its discoverer, Theodore Lyman, who discovered the lines from 1906–1914. All the wavelengths in the Lyman series are in the ultraviolet band, 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. Four of the Balmer lines are in the visible part of the spectrum, with wavelengths longer than 400 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
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Rydberg formula
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The Rydberg formula is used in atomic physics to describe the wavelengths of spectral lines of many chemical elements. It was formulated by the Swedish physicist Johannes Rydberg, and presented on 5 November 1888, in 1880, Rydberg worked on a formula describing the relation between the wavelengths in spectral lines of alkali metals. He noticed that lines came in series and he found that he could simplify his calculations by using the wavenumber as his unit of measurement and he plotted the wavenumbers of successive lines in each series against consecutive integers which represented the order of the lines in that particular series. Finding that the curves were similarly shaped, he sought a single function which could generate all of them. This did not work very well, Rydberg therefore rewrote Balmers formula in terms of wavenumbers, as n = n 0 −4 n 0 m 2. This suggested that the Balmer formula for hydrogen might be a case with m ′ =0 and C0 =4 n 0, where n 0 =1 h. The term Co was found to be a universal constant common to all elements and this constant is now known as the Rydberg constant, and m is known as the quantum defect. As stressed by Niels Bohr, expressing results in terms of wavenumber, the fundamental role of wavenumbers was also emphasized by the Rydberg-Ritz combination principle of 1908. The fundamental reason for this lies in quantum mechanics, lights wavenumber is proportional to frequency 1 λ = f c, and therefore also proportional to lights quantum energy E. Thus,1 λ = E h c. Rydbergs 1888 classical expression for the form of the series was not accompanied by a physical explanation. In Bohrs conception of the atom, the integer Rydberg n numbers represent electron orbitals at different integral distances from the atom. A frequency emitted in a transition from n1 to n2 therefore represents the energy emitted or absorbed when an electron makes a jump from orbital 1 to orbital 2. Later models found that the values for n1 and n2 corresponded to the quantum numbers of the two orbitals. The number of protons in the nucleus of this element, n 1 and n 2 are integers such that n 1 < n 2, corresponding to the principal quantum numbers of the orbitals occupied before. Examples would include He+, Li2+, Be3+ etc. where no other electrons exist in the atom and this is analogous to the Lyman-alpha line transition for hydrogen, and has the same frequency factor. Its frequency is thus the Lyman-alpha hydrogen frequency, increased by a factor of 2. This formula of f = c/λ = ⋅2 is historically known as Moseleys law, see the biography of Henry Moseley for the historical importance of this law, which was derived empirically at about the same time it was explained by the Bohr model of the atom. Rydberg–Ritz combination principle Balmer series Hydrogen line Sutton, Mike, getting the numbers right, The lonely struggle of the 19th century physicist/chemist Johannes Rydberg
