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Urey-Bigeleisen-Mayer Equation
In stable isotope geochemistry, the Urey-Bigeleisen-Mayer equation, also known as the Bigeleisen-Mayer equation or the Urey model, is a model describing the approximate equilibrium isotope fractionation in an isotope exchange reaction. While the equation itself can be written in numerous forms, it is generally presented as a ratio of partition functions of the isotopic molecules involved in a given reaction. The Urey-Bigeleisen-Mayer equation is widely applied in the fields of quantum chemistry and geochemistry and is often modified or paired with other quantum chemical modelling methods (such as density functional theory) to improve accuracy and precision and reduce the computational cost of calculations. The equation was first introduced by Harold Urey and, independently, by Jacob Bigeleisen and Maria Goeppert Mayer in 1947. Description Since its original descriptions, the Urey-Bigeleisen-Mayer equation has taken many forms. Given an isotopic exchange reaction A+B^*=A^*+B, s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stable Isotope Geochemistry
Isotope geochemistry is an aspect of geology based upon the study of natural variations in the relative abundances of isotopes of various elements. Variations in isotopic abundance are measured by isotope ratio mass spectrometry, and can reveal information about the ages and origins of rock, air or water bodies, or processes of mixing between them. Stable isotope geochemistry is largely concerned with isotopic variations arising from mass-dependent isotope fractionation, whereas radiogenic isotope geochemistry is concerned with the products of natural radioactivity. Stable isotope geochemistry For most stable isotopes, the magnitude of fractionation from kinetic and equilibrium fractionation is very small; for this reason, enrichments are typically reported in "per mil" (‰, parts per thousand). These enrichments (δ) represent the ratio of heavy isotope to light isotope in the sample over the ratio of a standard. That is, :\delta \ce = \left( \frac -1 \right) \times 1000 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecular Vibration
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 1013 Hz to approximately 1014 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm−1 and wavelengths of approximately 30 to 3 µm. For a diatomic molecule A−B, the vibrational frequency in s−1 is given by \nu = \frac \sqrt , where k is the force constant in dyne/cm or erg/cm2 and μ is the reduced mass given by \frac = \frac+\frac. The vibrational wavenumber in cm−1 is \tilde \;= \frac \sqrt, where c is the speed of light in cm/s. Vibrations of polyatomic molecules are described in terms of normal modes, which are independent of each other, but each normal mode involves simultaneous vibrations of different parts of the molecule. In general, a non-linear molecule with ''N'' atoms has 3''N'' – 6 normal modes of vibration, but a ''linear'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Columbia University
Columbia University (also known as Columbia, and officially as Columbia University in the City of New York) is a private research university in New York City. Established in 1754 as King's College on the grounds of Trinity Church in Manhattan, Columbia is the oldest institution of higher education in New York and the fifth-oldest institution of higher learning in the United States. It is one of nine colonial colleges founded prior to the Declaration of Independence. It is a member of the Ivy League. Columbia is ranked among the top universities in the world. Columbia was established by royal charter under George II of Great Britain. It was renamed Columbia College in 1784 following the American Revolution, and in 1787 was placed under a private board of trustees headed by former students Alexander Hamilton and John Jay. In 1896, the campus was moved to its current location in Morningside Heights and renamed Columbia University. Columbia scientists and scholars have ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deuterium
Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium atom, called a deuteron, contains one proton and one neutron, whereas the far more common protium has no neutrons in the nucleus. Deuterium has a natural abundance in Earth's oceans of about one atom of deuterium among all atoms of hydrogen (see heavy water). Thus deuterium accounts for approximately 0.0156% by number (0.0312% by mass) of all the naturally occurring hydrogen in the oceans, while protium accounts for more than 99.98%. The abundance of deuterium changes slightly from one kind of natural water to another (see Vienna Standard Mean Ocean Water). (Tritium is yet another hydrogen isotope, with two neutrons, that is far more rare and is radioactive.) The name ''deuterium'' is derived from the Greek , meaning "second", to denot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Phosphorus-32
Phosphorus-32 (32P) is a radioactive isotope of phosphorus. The nucleus of phosphorus-32 contains 15 protons and 17 neutrons, one more neutron than the most common isotope of phosphorus, phosphorus-31. Phosphorus-32 only exists in small quantities on Earth as it has a short half-life of 14 days and so decays rapidly. Phosphorus is found in many organic molecules and so phosphorus-32 has many applications in medicine, biochemistry, and molecular biology where it can be used to trace phosphorylated molecules (for example, in elucidating metabolic pathways) and radioactively label DNA. Decay Phosphorus-32 has a short half-life of 14.268 days and decays into sulfur-32 by beta decay as shown in this nuclear equation: : 1.709 MeV of energy is released during the decay. The kinetic energy of the electron varies with an average of approximately 0.5 MeV and the remainder of the energy is carried by the nearly undetectable electron antineutrino. In comparison to other beta radiation-emi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sulfur-35
Sulfur (16S) has 23 known isotopes with mass numbers ranging from 27 to 49, four of which are stable: 32S (95.02%), 33S (0.75%), 34S (4.21%), and 36S (0.02%). The preponderance of sulfur-32 is explained by its production from carbon-12 plus successive fusion capture of five helium-4 nuclei, in the so-called alpha process of exploding type II supernovas (see silicon burning). Other than 35S, the radioactive isotopes of sulfur are all comparatively short-lived. 35S is formed from cosmic ray spallation of 40 Ar in the atmosphere. It has a half-life of 87 days. The next longest-lived radioisotope is sulfur-38, with a half-life of 170 minutes. The shortest-lived is 49S, with a half-life shorter than 200 nanoseconds. Heavier radioactive isotopes of sulfur decay to chlorine. When sulfide minerals are precipitated, isotopic equilibration among solids and liquid may cause small differences in the δ34S values of co-genetic minerals. The differences between minerals can be used to estimate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carbon-14
Carbon-14, C-14, or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and colleagues (1949) to date archaeological, geological and hydrogeological samples. Carbon-14 was discovered on February 27, 1940, by Martin Kamen and Sam Ruben at the University of California Radiation Laboratory in Berkeley, California. Its existence had been suggested by Franz N. D. Kurie, Franz Kurie in 1934. There are three naturally occurring isotopes of carbon on Earth: carbon-12 (), which makes up 99% of all carbon on Earth; carbon-13 (), which makes up 1%; and carbon-14 (), which occurs in trace amounts, making up about 1 or 1.5 atoms per 1012 atoms of carbon in the atmosphere. Carbon-12 and carbon-13 are both stable, while carbon-14 is unstable and has a half-life of 5,730 ± 40 years. Carbon-14 decays into nitrogen-14 () through bet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Manhattan Project
The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project was under the direction of Major General Leslie Groves of the United States Army Corps of Engineers, U.S. Army Corps of Engineers. Nuclear physicist Robert Oppenheimer was the director of the Los Alamos Laboratory that designed the actual bombs. The Army component of the project was designated the Manhattan District as its first headquarters were in Manhattan; the placename gradually superseded the official codename, Development of Substitute Materials, for the entire project. Along the way, the project absorbed its earlier British counterpart, Tube Alloys. The Manhattan Project began modestly in 1939, but grew to employ more than 130,000 people and cost nearly US$2 billion (equivalent to about $ billion in ). Over 90 percent of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path Integral Formulation
The path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization. Unlike previous methods, the path integral allows one to easily change coordinates between very different canonical descriptions of the same quantum system. Another advantage is that it is in practice easier to guess the correct form of the Lagrangian of a theory, which naturally enters the path integrals (for interactions of a certain type, these are ''coordinat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrogen–deuterium Exchange
Hydrogen–deuterium exchange (also called H–D or H/D exchange) is a chemical reaction in which a covalently bonded hydrogen atom is replaced by a deuterium atom, or vice versa. It can be applied most easily to exchangeable protons and deuterons, where such a transformation occurs in the presence of a suitable deuterium source, without any catalyst. The use of acid, base or metal catalysts, coupled with conditions of increased temperature and pressure, can facilitate the exchange of non-exchangeable hydrogen atoms, so long as the substrate is robust to the conditions and reagents employed. This often results in perdeuteration: hydrogen-deuterium exchange of all non-exchangeable hydrogen atoms in a molecule. An example of exchangeable protons which are commonly examined in this way are the protons of the amides in the backbone of a protein. The method gives information about the solvent accessibility of various parts of the molecule, and thus the tertiary structure of the protein. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anharmonicity
In classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator. An oscillator that is not oscillating in harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmonic oscillator and the anharmonicity can be calculated using perturbation theory. If the anharmonicity is large, then other numerical techniques have to be used. In reality all oscillating systems are anharmonic, but most approximate the harmonic oscillator the smaller the amplitude of the oscillation is. As a result, oscillations with frequencies 2\omega and 3\omega etc., where \omega is the fundamental frequency of the oscillator, appear. Furthermore, the frequency \omega deviates from the frequency \omega_0 of the harmonic oscillations. See also intermodulation and combination tones. As a first approximation, the frequency shift \Delta \omega=\omega-\omega_0 is proportional to the square of the oscillation amplitude A: :\Delta \omeg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
