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Rydberg Constant
In spectroscopy, the Rydberg constant, symbol R_\infty for heavy atoms or R_\text for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants according to his model of the atom. Before the 2019 revision of the SI, R_\infty and the electron spin ''g''-factor were the most accurately measured physical constants. The constant is expressed for either hydrogen as R_\text, or at the limit of infinite nuclear mass as R_\infty. In either case, the constant is used to express the limiting value of the highest wavenumber (inverse wavelength) of any photon that can be emitted from a hydrogen atom, or, alternatively, the wavenumber of the lowest-energy photon capable of ionizing a hydrogen at ...
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Spectroscopy
Spectroscopy is the field of study that measures and interprets electromagnetic spectra. In narrower contexts, spectroscopy is the precise study of color as generalized from visible light to all bands of the electromagnetic spectrum. Spectroscopy, primarily in the electromagnetic spectrum, is a fundamental exploratory tool in the fields of astronomy, chemistry, materials science, and physics, allowing the composition, physical structure and electronic structure of matter to be investigated at the atomic, molecular and macro scale, and over astronomical distances. Historically, spectroscopy originated as the study of the wavelength dependence of the absorption by gas phase matter of visible light dispersed by a prism. Current applications of spectroscopy include biomedical spectroscopy in the areas of tissue analysis and medical imaging. Matter waves and acoustic waves can also be considered forms of radiative energy, and recently gravitational waves have been associa ...
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Electron Mass
In particle physics, the electron mass (symbol: ) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy-equivalent of about or about . Terminology The term "rest mass" is sometimes used because in special relativity the mass of an object can be said to increase in a frame of reference that is moving relative to that object (or if the object is moving in a given frame of reference). Most practical measurements are carried out on moving electrons. If the electron is moving at a relativistic velocity, any measurement must use the correct expression for mass. Such correction becomes substantial for electrons accelerated by voltages of over . For example, the relativistic expression for the total energy, , of an electron moving at speed is E = \gamma m_\mathrm c^2 , where * is the speed of light; * is the Lorentz factor, \gamma = 1/\sq ...
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Center Of Mass
In physics, the center of mass of a distribution of mass in space (sometimes referred to as the barycenter or balance point) is the unique point at any given time where the weight function, weighted relative position (vector), position of the distributed mass sums to zero. For a rigid body containing its center of mass, this is the point to which a force may be applied to cause a linear acceleration without an angular acceleration. Calculations in mechanics are often simplified when formulated with respect to the center of mass. It is a hypothetical point where the entire mass of an object may be assumed to be concentrated to visualise its motion. In other words, the center of mass is the particle equivalent of a given object for application of Newton's laws of motion. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the Phys ...
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Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ...
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Hydrogen Spectral Series
The emission spectrum of atomic hydrogen has been divided into a number of ''spectral series'', with wavelengths given by the Rydberg formula. These observed spectral lines are due to the electron making transitions between two energy levels in an atom. The classification of the series by the Rydberg formula was important in the development of quantum mechanics. The spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen and calculating red shifts. Physics A hydrogen atom consists of an electron orbiting its nucleus. The electromagnetic force between the electron and the nuclear proton leads to a set of quantum states for the electron, each with its own energy. These states were visualized by the Bohr model of the hydrogen atom as being distinct orbits around the nucleus. Each energy level, or electron shell, or orbit, is designated by an integer, as shown in the figure. The Bohr model was later replaced by quantum mechanics in whi ...
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Angular Wavelength
In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same '' phase'' on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the ''spatial frequency''. Wavelength is commonly designated by the Greek letter lambda (''λ''). For a modulated wave, ''wavelength'' may refer to the carrier wavelength of the signal. The term ''wavelength'' may also apply to the repeating envelope of modulated waves or waves formed by interference of several sinusoids. Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to the frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequen ...
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Charles J
Charles is a masculine given name predominantly found in English and French speaking countries. It is from the French form ''Charles'' of the Proto-Germanic name (in runic alphabet) or ''*karilaz'' (in Latin alphabet), whose meaning was "free man". The Old English descendant of this word was '' Ċearl'' or ''Ċeorl'', as the name of King Cearl of Mercia, that disappeared after the Norman conquest of England. The name was notably borne by Charlemagne (Charles the Great), and was at the time Latinized as ''Karolus'' (as in ''Vita Karoli Magni''), later also as '' Carolus''. Etymology The name's etymology is a Common Germanic noun ''*karilaz'' meaning "free man", which survives in English as churl (James (wikt:Appendix:Proto-Indo-European/ǵerh₂-">ĝer-, where the ĝ is a palatal consonant, meaning "to rub; to be old; grain." An old man has been worn away and is now grey with age. In some Slavic languages, the name ''Drago (given name), Drago'' (and variants: ''Dragom ...
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Neutron
The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nuclear fission in 1938, the first self-sustaining nuclear reactor (Chicago Pile-1, 1942) and the first nuclear weapon (Trinity (nuclear test), Trinity, 1945). Neutrons are found, together with a similar number of protons in the atomic nucleus, nuclei of atoms. Atoms of a chemical element that differ only in neutron number are called isotopes. Free neutrons are produced copiously in nuclear fission and nuclear fusion, fusion. They are a primary contributor to the nucleosynthesis of chemical elements within stars through fission, fusion, and neutron capture processes. Neutron stars, formed from massive collapsing stars, consist of neutrons at the density of atomic nuclei but a total mass more than the Sun. Neutron properties and interactions ar ...
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Isotopic Shift
The isotopic shift (also called isotope shift) is the shift in various forms of spectroscopy that occurs when one nuclear isotope is replaced by another. NMR spectroscopy In NMR spectroscopy, isotopic effects on chemical shifts are typically small, far less than 1 ppm, the typical unit for measuring shifts. The NMR signals for and ("HD") are readily distinguished in terms of their chemical shifts. The asymmetry of the signal for the "protio" impurity in arises from the differing chemical shifts of and . Vibrational spectra Isotopic shifts are best known and most widely used in vibration spectroscopy, where the shifts are large, being proportional to the ratio of the square root of the isotopic masses. In the case of hydrogen, the "H-D shift" is (1/2)1/2 ≈ 1/1.41. Thus, the (totally symmetric) C−H and C−D vibrations for and occur at 2917 cm−1 and 2109 cm−1 respectively. This shift reflects the differing reduced mass for the affected bonds. Ato ...
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Proton
A proton is a stable subatomic particle, symbol , Hydron (chemistry), H+, or 1H+ with a positive electric charge of +1 ''e'' (elementary charge). Its mass is slightly less than the mass of a neutron and approximately times the mass of an electron (the proton-to-electron mass ratio). Protons and neutrons, each with a mass of approximately one Dalton (unit), dalton, are jointly referred to as ''nucleons'' (particles present in atomic nuclei). One or more protons are present in the Atomic nucleus, nucleus of every atom. They provide the attractive electrostatic central force which binds the atomic electrons. The number of protons in the nucleus is the defining property of an element, and is referred to as the atomic number (represented by the symbol ''Z''). Since each chemical element, element is identified by the number of protons in its nucleus, each element has its own atomic number, which determines the number of atomic electrons and consequently the chemical characteristi ...
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Reduced Mass
In physics, reduced mass is a measure of the effective inertial mass of a system with two or more particles when the particles are interacting with each other. Reduced mass allows the two-body problem to be solved as if it were a one-body problem. Note, however, that the mass determining the gravitational force is ''not'' reduced. In the computation, one mass ''can'' be replaced with the reduced mass, if this is compensated by replacing the other mass with the sum of both masses. The reduced mass is frequently denoted by \mu ( mu), although the standard gravitational parameter is also denoted by \mu (as are a number of other physical quantities). It has the dimensions of mass, and SI unit kg. Reduced mass is particularly useful in classical mechanics. Equation Given two bodies, one with mass ''m''1 and the other with mass ''m''2, the equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of mass \m ...
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Speed Of Light
The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time interval of second. The speed of light is invariant (physics), the same for all observers, no matter their relative velocity. It is the upper limit for the speed at which Information#Physics_and_determinacy, information, matter, or energy can travel through Space#Relativity, space. All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and sensitive measurements, their finite speed has noticeable effects. Much starlight viewed on Earth is from the distant past, allowing humans to study the history of the universe by viewing distant objects. When Data communication, comm ...
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