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Chemistry
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Chemistry is a branch of physical science that studies the composition, structure, properties and change of matter. Chemistry is sometimes called the science because it bridges other natural sciences, including physics. For the differences between chemistry and physics see comparison of chemistry and physics, the history of chemistry can be traced to alchemy, which had been practiced for several millennia in various parts of the world. The word chemistry comes from alchemy, which referred to a set of practices that encompassed elements of chemistry, metallurgy, philosophy, astrology, astronomy, mysticism. An alchemist was called a chemist in popular speech, and later the suffix -ry was added to this to describe the art of the chemist as chemistry, the modern word alchemy in turn is derived from the Arabic word al-kīmīā. In origin, the term is borrowed from the Greek χημία or χημεία and this may have Egyptian origins since al-kīmīā is derived from the Greek χημία, which is in turn derived from the word Chemi or Kimi, which is the ancient name of Egypt in Egyptian. Alternately, al-kīmīā may derive from χημεία, meaning cast together, in retrospect, the definition of chemistry has changed over time, as new discoveries and theories add to the functionality of the science. The term chymistry, in the view of noted scientist Robert Boyle in 1661, in 1837, Jean-Baptiste Dumas considered the word chemistry to refer to the science concerned with the laws and effects of molecular forces. More recently, in 1998, Professor Raymond Chang broadened the definition of chemistry to mean the study of matter, early civilizations, such as the Egyptians Babylonians, Indians amassed practical knowledge concerning the arts of metallurgy, pottery and dyes, but didnt develop a systematic theory. Greek atomism dates back to 440 BC, arising in works by such as Democritus and Epicurus. In 50 BC, the Roman philosopher Lucretius expanded upon the theory in his book De rerum natura, unlike modern concepts of science, Greek atomism was purely philosophical in nature, with little concern for empirical observations and no concern for chemical experiments. Work, particularly the development of distillation, continued in the early Byzantine period with the most famous practitioner being the 4th century Greek-Egyptian Zosimos of Panopolis. He formulated Boyles law, rejected the four elements and proposed a mechanistic alternative of atoms. Before his work, though, many important discoveries had been made, the Scottish chemist Joseph Black and the Dutchman J. B. English scientist John Dalton proposed the theory of atoms, that all substances are composed of indivisible atoms of matter. Davy discovered nine new elements including the alkali metals by extracting them from their oxides with electric current, british William Prout first proposed ordering all the elements by their atomic weight as all atoms had a weight that was an exact multiple of the atomic weight of hydrogen. The inert gases, later called the noble gases were discovered by William Ramsay in collaboration with Lord Rayleigh at the end of the century, thereby filling in the basic structure of the table. Organic chemistry was developed by Justus von Liebig and others, following Friedrich Wöhlers synthesis of urea which proved that organisms were, in theory
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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
3.
Physical model
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Physical model is a smaller or larger physical copy of an object. The object being modelled may be small or large, the geometry of the model and the object it represents are often similar in the sense that one is a rescaling of the other, in such cases the scale is an important characteristic. However, in cases the similarity is only approximate or even intentionally distorted. Sometimes the distortion is systematic with e. g. a fixed scale horizontally, physical models allow visualization, from examining the model, of information about the thing the model represents. A model can be an object such as an architectural model of a building. Uses of a model include visualization of internal relationships within the structure or external relationships of the structure to the environment. Other uses of models in this sense are as toys, instrumented physical models are the most effective way of investigating fluid flows such as around hydraulic structures. These models are scaled in terms of geometry and important forces, for example using Froude number or Reynolds number scaling. A physical model of something large is usually smaller, and of something very small is larger, a physical model of something that can move, like a vehicle or machine, may be completely static, or have parts that can be moved manually, or be powered. A physical model may show inner parts that are not visible. The purpose of a model on a smaller scale may be to have a better overview, for testing purposes. A physical model of an animal shows the physical composition without it walking or flying away, and without danger. A soft model of an animal is popular among children and some adults as cuddly toy. some models can be used in different ways as of like prototypes for cars. A model of a person may e. g. be a doll, a statue, and in fiction a robotic humanoid, e. g. the mechas in the movie A. I. A model is a 3D alternative for a 2D representation such as a drawing or photograph, or in the case of a globe, scale model Mathematical model Model organism Model nation Metamodeling Model airplane Model car Model railway Model rocket Model house
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Experiment
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An experiment is a procedure carried out to support, refute, or validate a hypothesis. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated, experiments vary greatly in goal and scale, but always rely on repeatable procedure and logical analysis of the results. There also exists natural experimental studies, a child may carry out basic experiments to understand gravity, while teams of scientists may take years of systematic investigation to advance their understanding of a phenomenon. Experiments and other types of activities are very important to student learning in the science classroom. Experiments can raise test scores and help a student become more engaged and interested in the material they are learning, experiments can vary from personal and informal natural comparisons, to highly controlled. Uses of experiments vary considerably between the natural and human sciences, experiments typically include controls, which are designed to minimize the effects of variables other than the single independent variable. This increases the reliability of the results, often through a comparison between control measurements and the other measurements, scientific controls are a part of the scientific method. Ideally, all variables in an experiment are controlled and none are uncontrolled, in such an experiment, if all controls work as expected, it is possible to conclude that the experiment works as intended, and that results are due to the effect of the tested variable. In the scientific method, an experiment is a procedure that arbitrates between competing models or hypotheses. Researchers also use experimentation to test existing theories or new hypotheses to support or disprove them, an experiment usually tests a hypothesis, which is an expectation about how a particular process or phenomenon works. However, an experiment may also aim to answer a question, without a specific expectation about what the experiment reveals. If an experiment is conducted, the results usually either support or disprove the hypothesis. According to some philosophies of science, an experiment can never prove a hypothesis, on the other hand, an experiment that provides a counterexample can disprove a theory or hypothesis. An experiment must also control the possible confounding factors—any factors that would mar the accuracy or repeatability of the experiment or the ability to interpret the results, confounding is commonly eliminated through scientific controls and/or, in randomized experiments, through random assignment. In engineering and the sciences, experiments are a primary component of the scientific method. They are used to test theories and hypotheses about how physical processes work under particular conditions, typically, experiments in these fields focus on replication of identical procedures in hopes of producing identical results in each replication. In medicine and the sciences, the prevalence of experimental research varies widely across disciplines. In contrast to norms in the sciences, the focus is typically on the average treatment effect or another test statistic produced by the experiment
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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
6.
Quantization (physics)
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In physics, quantization is the process of transition from a classical understanding of physical phenomena to a newer understanding known as quantum mechanics. It is a procedure for constructing a quantum field theory starting from a field theory. This is a generalization of the procedure for building quantum mechanics from classical mechanics, one also speaks of field quantization, as in the quantization of the electromagnetic field, where one refers to photons as field quanta. This procedure is basic to theories of physics, nuclear physics, condensed matter physics. Quantization converts classical fields into operators acting on states of the field theory. The lowest energy state is called the vacuum state, the reason for quantizing a theory is to deduce properties of materials, objects or particles through the computation of quantum amplitudes, which may be very complicated. Such computations have to deal with certain subtleties called renormalization, which, if neglected, can lead to nonsense results. The full specification of a procedure requires methods of performing renormalization. The first method to be developed for quantization of field theories was canonical quantization, however, the use of canonical quantization has left its mark on the language and interpretation of quantum field theory. Canonical quantization of a theory is analogous to the construction of quantum mechanics from classical mechanics. The classical field is treated as a variable called the canonical coordinate. One introduces a commutation relation between these which is exactly the same as the relation between a particles position and momentum in quantum mechanics. Technically, one converts the field to an operator, through combinations of creation and annihilation operators, the field operator acts on quantum states of the theory. The lowest energy state is called the vacuum state, the procedure is also called second quantization. This procedure can be applied to the quantization of any theory, whether of fermions or bosons. There is a way to perform a canonical quantization without having to resort to the non covariant approach of foliating spacetime and this method is based upon a classical action, but is different from the functional integral approach. The method does not apply to all possible actions and it starts with the classical algebra of all functionals over the configuration space. This algebra is quotiented over by the ideal generated by the Euler–Lagrange equations, then, this quotient algebra is converted into a Poisson algebra by introducing a Poisson bracket derivable from the action, called the Peierls bracket
7.
Infrared spectroscopy
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Infrared spectroscopy involves the interaction of infrared radiation with matter. It covers a range of techniques, mostly based on absorption spectroscopy, as with all spectroscopic techniques, it can be used to identify and study chemicals. Sample may be solid, liquid, or gas, the method or technique of infrared spectroscopy is conducted with an instrument called an infrared spectrometer to produce an infrared spectrum. An IR spectrum is essentially a graph of infrared light absorbance on the vertical axis vs. frequency or wavelength on the horizontal axis, typical units of frequency used in IR spectra are reciprocal centimeters, with the symbol cm−1. Units of IR wavelength are commonly given in micrometers, symbol μm, a common laboratory instrument that uses this technique is a Fourier transform infrared spectrometer. Two-dimensional IR is also possible as discussed below, the infrared portion of the electromagnetic spectrum is usually divided into three regions, the near-, mid- and far- infrared, named for their relation to the visible spectrum. The higher-energy near-IR, approximately 14000–4000 cm−1 can excite overtone or harmonic vibrations, the mid-infrared, approximately 4000–400 cm−1 may be used to study the fundamental vibrations and associated rotational-vibrational structure. The far-infrared, approximately 400–10 cm−1, lying adjacent to the region, has low energy. The names and classifications of these subregions are conventions, and are loosely based on the relative molecular or electromagnetic properties. Infrared spectroscopy exploits the fact that molecules absorb frequencies that are characteristic of their structure and these absorptions occur at resonant frequencies, i. e. the frequency of the absorbed radiation matches the vibrational frequency. The energies are affected by the shape of the potential energy surfaces, the masses of the atoms. In particular, in the Born–Oppenheimer and harmonic approximations, i. e, the resonant frequencies are also related to the strength of the bond and the mass of the atoms at either end of it. Thus, the frequency of the vibrations are associated with a normal mode of motion. In order for a mode in a sample to be IR active. A permanent dipole is not necessary, as the rule requires only a change in dipole moment, a molecule can vibrate in many ways, and each way is called a vibrational mode. For molecules with N number of atoms, linear molecules have 3N –5 degrees of vibrational modes, as an example H2O, a non-linear molecule, will have 3 ×3 –6 =3 degrees of vibrational freedom, or modes. Simple diatomic molecules have only one bond and only one vibrational band, if the molecule is symmetrical, e. g. N2, the band is not observed in the IR spectrum, but only in the Raman spectrum. Asymmetrical diatomic molecules, e. g. CO, absorb in the IR spectrum, more complex molecules have many bonds, and their vibrational spectra are correspondingly more complex, i. e. big molecules have many peaks in their IR spectra
8.
Nuclear magnetic resonance spectroscopy
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Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy, is a research technique that exploits the magnetic properties of certain atomic nuclei. This type of spectroscopy determines the physical and chemical properties of atoms or the molecules in which they are contained and it relies on the phenomenon of nuclear magnetic resonance and can provide detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. Suitable samples range from small compounds analyzed with 1-dimensional proton or carbon-13 NMR spectroscopy to large proteins or nucleic acids using 3 or 4-dimensional techniques. The impact of NMR spectroscopy on the sciences has been substantial because of the range of information, NMR spectra are unique, well-resolved, analytically tractable and often highly predictable for small molecules. Thus, in organic chemistry practice, NMR analysis is used to confirm the identity of a substance, different functional groups are obviously distinguishable, and identical functional groups with differing neighboring substituents still give distinguishable signals. NMR has largely replaced traditional wet chemistry tests such as reagents or typical chromatography for identification. A disadvantage is that a large amount, 2–50 mg, of a purified substance is required. Preferably, the sample should be dissolved in a solvent, because NMR analysis of solids requires a dedicated MAS machine, the timescale of NMR is relatively long, and thus it is not suitable for observing fast phenomena, producing only an averaged spectrum. NMR spectrometers are relatively expensive, universities usually have them, modern NMR spectrometers have a very strong, large and expensive liquid helium-cooled superconducting magnet, because resolution directly depends on magnetic field strength. There are even benchtop NMR spectrometers, the Purcell group at Harvard University and the Bloch group at Stanford University independently developed NMR spectroscopy in the late 1940s and early 1950s. Edward Mills Purcell and Felix Bloch shared the 1952 Nobel Prize in Physics for their discoveries, when placed in a magnetic field, NMR active nuclei absorb electromagnetic radiation at a frequency characteristic of the isotope. The resonant frequency, energy of the absorption, and the intensity of the signal are proportional to the strength of the magnetic field, for example, in a 21 Tesla magnetic field, protons resonate at 900 MHz. It is common to refer to a 21 T magnet as a 900 MHz magnet, spinning the sample is necessary to average out diffusional motion. Whereas, measurements of diffusion constants are done the sample stationary and spinning off, the vast majority of nuclei in a solution would belong to the solvent, and most regular solvents are hydrocarbons and would contain NMR-reactive protons. The most used deuterated solvent is deuterochloroform, although deuterium oxide and deuterated DMSO are used for hydrophilic analytes, the chemical shifts are slightly different in different solvents, depending on electronic solvation effects. NMR spectra are often calibrated against the known solvent residual proton peak instead of added tetramethylsilane, to detect the very small frequency shifts due to nuclear magnetic resonance, the applied magnetic field must be constant throughout the sample volume. High resolution NMR spectrometers use shims to adjust the homogeneity of the field to parts per billion in a volume of a few cubic centimeters. In order to detect and compensate for inhomogeneity and drift in the magnetic field, in modern NMR spectrometers shimming is adjusted automatically, though in some cases the operator has to optimize the shim parameters manually to obtain the best possible resolution
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Scanning probe microscopy
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Scanning probe microscopy is a branch of microscopy that forms images of surfaces using a physical probe that scans the specimen. SPM was founded in 1981, with the invention of the scanning tunneling microscope, the first successful scanning tunneling microscope experiment was done by Binnig and Rohrer. The key to their success was using a loop to regulate gap distance between the sample and the probe. Many scanning probe microscopes can image several interactions simultaneously, the manner of using these interactions to obtain an image is generally called a mode. The resolution varies somewhat from technique to technique, but some probe techniques reach a rather impressive atomic resolution and this is due largely because piezoelectric actuators can execute motions with a precision and accuracy at the atomic level or better on electronic command. This family of techniques can be called piezoelectric techniques, the other common denominator is that the data are typically obtained as a two-dimensional grid of data points, visualized in false color as a computer image. To form images, scanning probe microscopes raster scan the tip over the surface, at discrete points in the raster scan a value is recorded. These recorded values are displayed as a map to produce the final STM images, usually using a black. In constant interaction mode, a loop is used to physically move the probe closer to or further from the surface under study to maintain a constant interaction. This interaction depends on the type of SPM, for scanning tunneling microscopy the interaction is the current, for contact mode AFM or MFM it is the cantilever deflection. The type of loop used is usually a PI-loop, which is a PID-loop where the differential gain has been set to zero. The z position of the tip is recorded periodically and displayed as a heat map and this is normally referred to as a topography image. In this mode a second image, known as the signal or error image is also taken. Under perfect operation this image would be a blank at a constant value which was set on the feedback loop, under real operation the image shows noise and often some indication of the surface structure. The user can use this image to edit the feedback gains to minimise features in the error signal, if the gains are set incorrectly, many imaging artifacts are possible. If gains are too low features can appear smeared, if the gains are too high the feedback can become unstable and oscillate, producing striped features in the images which are not physical. In constant height mode the probe is not moved in the z-axis during the raster scan, instead the value of the interaction under study is recorded. This recorded information is displayed as a map, and is usually referred to as a constant height image
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Computational chemistry
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Computational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into efficient computer programs, to calculate the structures and properties of molecules and solids. It is necessary because, apart from relatively recent results concerning the molecular ion. While computational results normally complement the information obtained by chemical experiments and it is widely used in the design of new drugs and materials. The methods used cover both static and dynamic situations, in all cases, the computer time and other resources increase rapidly with the size of the system being studied. That system can be one molecule, a group of molecules, Computational chemistry methods range from very approximate to highly accurate, the latter are usually feasible for small systems only. Ab initio methods are based entirely on quantum mechanics and basic physical constants, other methods are called empirical or semi-empirical because they use additional empirical parameters. Both ab initio and semi-empirical approaches involve approximations, in principle, ab initio methods eventually converge to the exact solution of the underlying equations as the number of approximations is reduced. In practice, however, it is impossible to eliminate all approximations, the goal of computational chemistry is to minimize this residual error while keeping the calculations tractable. In some cases, the details of structure are less important than the long-time phase space behavior of molecules. This is the case in conformational studies of proteins and protein-ligand binding thermodynamics, classical approximations to the potential energy surface are used, as they are computationally less intensive than electronic calculations, to enable longer simulations of molecular dynamics. Furthermore, cheminformatics uses even more empirical methods like machine learning based on physicochemical properties, one typical problem in cheminformatics is to predict the binding affinity of drug molecules to a given target. Building on the discoveries and theories in the history of quantum mechanics. The books that were influential in the development of computational quantum chemistry include Linus Pauling. With the development of efficient computer technology in the 1940s, the solutions of elaborate wave equations for complex atomic systems began to be a realizable objective, in the early 1950s, the first semi-empirical atomic orbital calculations were performed. Theoretical chemists became extensive users of the digital computers. A very detailed account of use in the United Kingdom is given by Smith. The first ab initio Hartree–Fock method calculations on diatomic molecules were performed in 1956 at MIT, for diatomic molecules, a systematic study using a minimum basis set and the first calculation with a larger basis set were published by Ransil and Nesbet respectively in 1960
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Computer
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A computer is a device that can be instructed to carry out an arbitrary set of arithmetic or logical operations automatically. The ability of computers to follow a sequence of operations, called a program, such computers are used as control systems for a very wide variety of industrial and consumer devices. The Internet is run on computers and it millions of other computers. Since ancient times, simple manual devices like the abacus aided people in doing calculations, early in the Industrial Revolution, some mechanical devices were built to automate long tedious tasks, such as guiding patterns for looms. More sophisticated electrical machines did specialized analog calculations in the early 20th century, the first digital electronic calculating machines were developed during World War II. The speed, power, and versatility of computers has increased continuously and dramatically since then, conventionally, a modern computer consists of at least one processing element, typically a central processing unit, and some form of memory. The processing element carries out arithmetic and logical operations, and a sequencing, peripheral devices include input devices, output devices, and input/output devices that perform both functions. Peripheral devices allow information to be retrieved from an external source and this usage of the term referred to a person who carried out calculations or computations. The word continued with the same meaning until the middle of the 20th century, from the end of the 19th century the word began to take on its more familiar meaning, a machine that carries out computations. The Online Etymology Dictionary gives the first attested use of computer in the 1640s, one who calculates, the Online Etymology Dictionary states that the use of the term to mean calculating machine is from 1897. The Online Etymology Dictionary indicates that the use of the term. 1945 under this name, theoretical from 1937, as Turing machine, devices have been used to aid computation for thousands of years, mostly using one-to-one correspondence with fingers. The earliest counting device was probably a form of tally stick, later record keeping aids throughout the Fertile Crescent included calculi which represented counts of items, probably livestock or grains, sealed in hollow unbaked clay containers. The use of counting rods is one example, the abacus was initially used for arithmetic tasks. The Roman abacus was developed from used in Babylonia as early as 2400 BC. Since then, many forms of reckoning boards or tables have been invented. In a medieval European counting house, a checkered cloth would be placed on a table, the Antikythera mechanism is believed to be the earliest mechanical analog computer, according to Derek J. de Solla Price. It was designed to calculate astronomical positions and it was discovered in 1901 in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated to circa 100 BC
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Ground state
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The ground state of a quantum mechanical system is its lowest-energy state, the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with greater than the ground state. In the quantum theory, the ground state is usually called the vacuum state or the vacuum. If more than one ground state exists, they are said to be degenerate, many systems have degenerate ground states. Degeneracy occurs whenever there exists a unitary operator which acts non-trivially on a ground state, according to the third law of thermodynamics, a system at absolute zero temperature exists in its ground state, thus, its entropy is determined by the degeneracy of the ground state. Many systems, such as a crystal lattice, have a unique ground state. It is also possible for the highest excited state to have zero temperature for systems that exhibit negative temperature. In 1D, the state of the Schrödinger equation has no nodes. This can be proved considering the energy of a state with a node at x =0, i. e. ψ =0. Consider the average energy in this state ⟨ ψ | H | ψ ⟩ = ∫ d x where V is the potential, now consider a small interval around x =0, i. e. x ∈. Take a new wave function ψ ′ to be defined as ψ ′ = ψ, x < − ϵ and ψ ′ = − ψ, x > ϵ, if ϵ is small enough then this is always possible to do so that ψ ′ is continuous. Note that the energy density | d ψ ′ d x |2 < | d ψ d x |2 everywhere because of the normalization. For definiteness let us choose V ≥0, then it is clear that outside the interval x ∈ the potential energy density is smaller for the ψ ′ because | ψ ′ | < | ψ | there. Therefore, the energy is unchanged up to order ϵ2 if we deform the state with a node ψ into a state without a node ψ ′. We can therefore remove all nodes and reduce the energy, which implies that the wave function cannot have a node. The wave function of the state of a particle in a one-dimensional well is a half-period sine wave which goes to zero at the two edges of the well. The wave function of the state of a hydrogen atom is a spherically-symmetric distribution centred on the nucleus. The electron is most likely to be found at a distance from the equal to the Bohr radius
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Excited state
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In quantum mechanics, an excited state of a system is any quantum state of the system that has a higher energy than the ground state. Excitation is an elevation in energy level above a baseline energy state. In physics there is a technical definition for energy level which is often associated with an atom being raised to an excited state. The temperature of a group of particles is indicative of the level of excitation and this return to a lower energy level is often loosely described as decay and is the inverse of excitation. Long-lived excited states are called metastable. Long-lived nuclear isomers and singlet oxygen are two examples of this, a simple example of this concept comes by considering the hydrogen atom. The ground state of the hydrogen atom corresponds to having the single electron in the lowest possible orbit. By giving the additional energy, the electron is able to move into an excited state. If the photon has too much energy, the electron will cease to be bound to the atom, after excitation the atom may return to the ground state or a lower excited state, by emitting a photon with a characteristic energy. Emission of photons from atoms in excited states leads to an electromagnetic spectrum showing a series of characteristic emission lines An atom in a high excited state is termed Rydberg atom. A system of highly excited atoms can form a long-lived condensed excited state e. g. a condensed phase made completely of excited atoms, hydrogen can also be excited by heat or electricity. This phenomenon has been studied in the case of a gas in some detail. These calculations are more difficult than non-excited state calculations, a further consequence is reaction of the atom in the excited state, as in photochemistry. Excited states give rise to chemical reaction, Rydberg formula Stationary state Repulsive state NASA background information on ground and excited states
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Transition state
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The transition state of a chemical reaction is a particular configuration along the reaction coordinate. It is defined as the corresponding to the highest potential energy along this reaction coordinate. At this point, assuming a perfectly irreversible reaction, colliding reactant molecules always go on to form products and it is often marked with the double dagger ‡ symbol. The concept of a state has been important in many theories of the rates at which chemical reactions occur. This started with the state theory, which was first developed around 1935 by Eyring, Evans and Polanyi. A collision between reactant molecules may or may not result in a successful reaction, the outcome depends on factors such as the relative kinetic energy, relative orientation and internal energy of the molecules. Even if the partners form an activated complex they are not bound to go on and form products. Because of the rules of quantum mechanics, the state cannot be captured or directly observed. This is sometimes expressed by stating that the state has a fleeting existence. However, cleverly manipulated spectroscopic techniques can get us as close as the timescale of the technique allows, femtochemical IR spectroscopy was developed for precisely that reason, and it is possible to probe molecular structure extremely close to the transition point. Often along the reaction coordinate reactive intermediates are present not much lower in energy from a transition state making it difficult to distinguish between the two, Transition state structures can be determined by searching for first-order saddle points on the potential energy surface of the chemical species of interest. A first-order saddle point is a point of index one, that is. This is further described in the geometry optimization. The Hammond–Leffler Postulate states that the structure of the state more closely resembles either the products or the starting material. A transition state resembles the reactants more than the products is said to be early. Thus, the Hammond–Leffler Postulate predicts a transition state for an endothermic reaction. A dimensionless reaction coordinate that quantifies the lateness of a state can be used to test the validity of the Hammond–Leffler Postulate for a particular reaction. One demonstration of principle is found in the two bicyclic compounds depicted below
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Chemical reaction
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A chemical reaction is a process that leads to the transformation of one set of chemical substances to another. Nuclear chemistry is a sub-discipline of chemistry that involves the reactions of unstable. The substance initially involved in a reaction are called reactants or reagents. Chemical reactions are characterized by a chemical change, and they yield one or more products. Reactions often consist of a sequence of individual sub-steps, the elementary reactions. Chemical reactions are described with chemical equations, which present the starting materials, end products. Chemical reactions happen at a characteristic reaction rate at a given temperature, typically, reaction rates increase with increasing temperature because there is more thermal energy available to reach the activation energy necessary for breaking bonds between atoms. Reactions may proceed in the forward or reverse direction until they go to completion or reach equilibrium, Reactions that proceed in the forward direction to approach equilibrium are often described as spontaneous, requiring no input of free energy to go forward. Non-spontaneous reactions require input of energy to go forward. Different chemical reactions are used in combinations during chemical synthesis in order to obtain a desired product, in biochemistry, a consecutive series of chemical reactions form metabolic pathways. These reactions are catalyzed by protein enzymes. Chemical reactions such as combustion in fire, fermentation and the reduction of ores to metals were known since antiquity, in the Middle Ages, chemical transformations were studied by Alchemists. They attempted, in particular, to lead into gold, for which purpose they used reactions of lead. The process involved heating of sulfate and nitrate minerals such as sulfate, alum. In the 17th century, Johann Rudolph Glauber produced hydrochloric acid and sodium sulfate by reacting sulfuric acid, further optimization of sulfuric acid technology resulted in the contact process in the 1880s, and the Haber process was developed in 1909–1910 for ammonia synthesis. From the 16th century, researchers including Jan Baptist van Helmont, Robert Boyle, the phlogiston theory was proposed in 1667 by Johann Joachim Becher. It postulated the existence of an element called phlogiston, which was contained within combustible bodies. This proved to be false in 1785 by Antoine Lavoisier who found the explanation of the combustion as reaction with oxygen from the air
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Walter Heitler
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Walter Heinrich Heitler was a German physicist who made contributions to quantum electrodynamics and quantum field theory. He brought chemistry under quantum mechanics through his theory of valence bonding and he then became an assistant to Max Born at the Institute for Theoretical Physics at the Georg-August University of Göttingen. Heitler completed his Habilitation, under Born, in 1929, in that year, he was let go by the university because he was Jewish. These institutes were located at the LMU, under Arnold Sommerfeld, the University of Göttingen, under Max Born, furthermore, Werner Heisenberg and Born had just recently published their trilogy of papers which launched the matrix mechanics formulation of quantum mechanics. These papers immediately put the personnel at the theoretical physics institutes onto applying these new tools to understanding atomic. In Zurich, with Fritz London, Heitler applied the new mechanics to deal with the saturable, nondynamic forces of attraction and repulsion, i. e. exchange forces. Their valence bond treatment of this problem, was a landmark in that it brought chemistry under quantum mechanics, the application of quantum mechanics to chemistry would be a prominent theme in Heitlers career. While Heitler was at Göttingen, Adolf Hitler came to power in 1933, with the rising prominence of anti-Semitism under Hitler, Born took it upon himself to take the younger Jewish generation under his wing. In doing so, Born arranged for Heitler to get a position that year as a Research Fellow at the University of Bristol, at Bristol, Heitler was a Research Fellow of the Academic Assistance Council, in the H. H. With Bethe, he published a paper on production of gamma rays in the Coulomb field of an atomic nucleus. Heitler also contributed to the understanding of cosmic rays, as well as predicted the existence of the electrically neutral pi meson, in 1936, Heitler published his major work on quantum electrodynamics, The Quantum Theory of Radiation, which marked the direction for future developments in quantum theory. The book appeared in many editions and printings, even being translated in Russian, after the fall of France in 1940, Heitler was briefly interned on the Isle of Man for several months. At Dublin, Heitlers work with H. W. Peng on radiation damping theory, during the 1942-1943 academic year, Heitler gave a course on elementary wave mechanics, during which W. S. E. Hickson took notes and prepared a finished copy. These notes were the basis for Heitlers book Elementary Wave Mechanics, Introductory Course of Lectures, a new edition was published as Elementary Wave Mechanics in 1945. This version was revised and republished many times, as well as being translated into French and Italian and published in 1949, a further revised version appeared as Elementary Wave Mechanics With Applications to Quantum Chemistry in 1956, as well as in German in 1961. Schrödinger resigned as Director of the School for Theoretical Physics in 1946, in 1958, Heitler held the Lorentz Chair for Theoretical Physics at the University of Leiden. While in Zurich, after years, he began writing on the philosophical relationship of science to religion. His books were published in German, English, and French, Physics eats chemistry with a spoon. S. E
17.
Fritz London
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Fritz Wolfgang London was a Jewish-German physicist and professor at Duke University. His fundamental contributions to the theories of bonding and of intermolecular forces are today considered classic and are discussed in standard textbooks of physical chemistry. London was born in Breslau, Germany as the son of Franz London, being a Jew, London lost his position at the University of Berlin after Hitlers Nazi Party passed the 1933 racial laws. He took visiting positions in England and France, and eventually emigrated to the United States in 1939, London was in his later life a professor at Duke University. He was awarded the Lorentz Medal in 1953 and he died in Durham, North Carolina in 1954. Londons early work with Walter Heitler on chemical bonding is now treated in any textbook on physical chemistry and this paper was the first to properly explain the bonding in a homonuclear molecule as H2. Another necessary ingredient was the realization that electrons are indistinguishable, as expressed in the Pauli principle, other early work of London was in the area of intermolecular forces. He coined the expression dispersion effect for the attraction between two rare gas atoms at distance from each other. Nowadays this attraction is often referred to as London force, in 1930 he gave a unified treatment of the interaction between two noble gas atoms that attract each other at large distance, but repel each other at short distances. Eisenschitz and London showed that this repulsion is a consequence of enforcing the electronic wavefunction to be antisymmetric under electron permutations and this antisymmetry is required by the Pauli principle and the fact that electrons are fermions. For atoms and nonpolar molecules, the London dispersion force is the intermolecular force. For polar molecules, this force is one part of the van der Waals force, bose recognized that the statistics of massless photons could also be applied to massive particles, he did not contribute to the theory of the condensation of bosons. London was also one of the authors to have properly understood the principle of local gauge invariance in the context of the then new quantum mechanics. London predicted the effect of flux quantization in superconductors and with his brother Heinz postulated that the electrodynamics of superconductors is described by a massive field. I. e. that whilst magnetic flux is expelled from a superconductor, London also developed a theory of a rotational response of a superconductor, pointing out that rotation of a superconductor generates magnetic field London moment. This effect is used in models of rotational dynamics of neutron stars, since 1956, the Fritz London Memorial Lectures have brought to the scientific community at Duke University a distinguished group of lecturers including twenty Nobel laureates. The scientific interests of each lecturer impinge at one or more points upon the fields of physics. Gavroglu, Kostas Fritz London, A Scientific Biography Fritz London, A Scientific Biography, by Kostas Gavroglu, Article about Fritz London Article from Duke Physics Dept
18.
Edward Teller
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Edward Teller was a Hungarian-American theoretical physicist who was born in Hungary, and is known colloquially as the father of the hydrogen bomb, although he claimed he did not care for the title. He made numerous contributions to nuclear and molecular physics, spectroscopy, Teller also made contributions to Thomas–Fermi theory, the precursor of density functional theory, a standard modern tool in the quantum mechanical treatment of complex molecules. Teller emigrated to the United States in the 1930s, and was an member of the Manhattan Project. During this time he made a push to develop the first fusion-based weapons as well. After his controversial testimony in the security clearance hearing of his former Los Alamos Laboratory superior J. Robert Oppenheimer, Teller was ostracized by much of the scientific community. He was a co-founder of Lawrence Livermore National Laboratory, and was both its director and associate director for many years and he was a vigorous advocate of Ronald Reagans Strategic Defense Initiative. Strangelove in the 1964 movie of the same name, ede Teller was born on January 15,1908, in Budapest, Hungary, into a Jewish family. His parents were Ilona, a pianist, and Max Teller, raised in a Jewish family, he later on became an agnostic. Religion was not an issue in my family, he wrote, indeed. My only religious training came because the Minta required that all students take classes in their respective religions and my family celebrated one holiday, the Day of Atonement, when we all fasted. Yet my father said prayers for his parents on Saturdays and on all the Jewish holidays, the idea of God that I absorbed was that it would be wonderful if He existed, We needed Him desperately but had not seen Him in many thousands of years. Like Einstein and Feynman, Teller was a late talker and he developed the ability to speak later than most children but became very interested in numbers, and would calculate large numbers in his head for fun. Teller left Hungary in 1926, partly due to the discriminatory numerus clausus rule under Miklós Horthys regime, the political climate and revolutions in Hungary during his youth instilled a lingering animosity for both Communism and Fascism in Teller. When he was a student, his right foot was severed in a streetcar accident in Munich, requiring him to wear a prosthetic foot. Werner Heisenberg said that it was the hardiness of Tellers spirit, rather than stoicism, Teller graduated in chemical engineering at the University of Karlsruhe, and received his Ph. D. in physics under Werner Heisenberg at the University of Leipzig. Tellers dissertation dealt with one of the first accurate quantum mechanical treatments of the molecular ion. In 1930 he befriended Russian physicists George Gamow and Lev Landau, Tellers lifelong friendship with a Czech physicist, George Placzek, was also very important for his scientific and philosophical development. It was Placzek who arranged a stay in Rome with Enrico Fermi in 1932
19.
Robert S. Mulliken
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Dr. Mulliken received the Nobel Prize for chemistry in 1966. He received the Priestley Medal in 1983, Mulliken was born in Newburyport, Massachusetts. His father, Samuel Parsons Mulliken, was a professor of chemistry at the Massachusetts Institute of Technology. As a child, Robert Mulliken learned the name and botanical classification of plants and, in general, had an excellent, but selective, memory. For example, he learned German well enough to skip the course in scientific German in college and he also made the acquaintance, while still a child, of the physical chemist Arthur Amos Noyes. Mulliken helped with some of the work when his father wrote his four-volume text on organic compound identification. In high school in Newburyport, Mulliken followed a scientific curriculum and he graduated in 1913 and succeeded in getting a scholarship to MIT which had earlier been won by his father. Like his father, he majored in chemistry, already as an undergraduate, he conducted his first publishable research, on the synthesis of organic chlorides. Because he was unsure of his direction, he included some chemical engineering courses in his curriculum and spent a summer touring chemical plants in Massachusetts. He received his B. S. degree in chemistry from MIT in 1917, at this time, the United States had just entered World War I, and Mulliken took a position at American University in Washington, D. C. making poison gas under James B. After nine months, he was drafted into the Armys Chemical Warfare Service and his laboratory techniques left much to be desired, and he was out of service for months with burns. Later he got a bad case of influenza, and was still in the hospital at wars end. After the war, he took a job investigating the effects of zinc oxide and carbon black on rubber, so in 1919 he entered the Ph. D. program at the University of Chicago. He got his doctorate in 1921 based on research into the separation of isotopes of mercury by evaporation, while at Chicago, he took a course under the Nobel Prize-winning physicist Robert A. Millikan, which exposed him to the old quantum theory. He also became interested in strange molecules after exposure to work by Hermann I. Schlesinger on diborane, at Chicago, he had received a grant from the National Research Council which had paid for much of his work on isotope separation. The NRC grant was extended in 1923 for two years so he could study isotope effects on band spectra of diatomic molecules as boron nitride. He went to Harvard University to learn spectrographic technique from Frederick A. Saunders, at the time, he was able to associate with many future luminaries, including J. Robert Oppenheimer, John H. Van Vleck, and Harold C. Slater, who had worked with Niels Bohr and they all, as well as Wolfgang Pauli, were developing the new quantum mechanics that would eventually supersede the old quantum theory
20.
Max Born
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Max Born was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to physics and optics and supervised the work of a number of notable physicists in the 1920s and 1930s. Born won the 1954 Nobel Prize in Physics for his research in Quantum Mechanics. He wrote his Ph. D. thesis on the subject of Stability of Elastica in a Plane and Space, in 1905, he began researching special relativity with Minkowski, and subsequently wrote his habilitation thesis on the Thomson model of the atom. In the First World War, after originally being placed as a radio operator, in 1921, Born returned to Göttingen, arranging another chair for his long-time friend and colleague James Franck. Under Born, Göttingen became one of the worlds foremost centres for physics, in 1925, Born and Werner Heisenberg formulated the matrix mechanics representation of quantum mechanics. The following year, he formulated the now-standard interpretation of the probability density function for ψ*ψ in the Schrödinger equation and his influence extended far beyond his own research. Max Delbrück, Siegfried Flügge, Friedrich Hund, Pascual Jordan, Maria Goeppert-Mayer, Lothar Wolfgang Nordheim, Robert Oppenheimer, in January 1933, the Nazi Party came to power in Germany, and Born, who was Jewish, was suspended. Max Born became a naturalised British subject on 31 August 1939 and he remained at Edinburgh until 1952. He retired to Bad Pyrmont, in West Germany, and died in a hospital in Göttingen on 5 January 1970. Max Born was born on 11 December 1882 in Breslau, which at the time of Borns birth was part of the Prussian Province of Silesia in the German Empire and she died when Max was four years old, on 29 August 1886. Max had a sister, Käthe, who was born in 1884, Wolfgang later became Professor of Art History at the City College of New York. Initially educated at the König-Wilhelm-Gymnasium in Breslau, Born entered the University of Breslau in 1901, the German university system allowed students to move easily from one university to another, so he spent summer semesters at Heidelberg University in 1902 and the University of Zurich in 1903. Fellow students at Breslau, Otto Toeplitz and Ernst Hellinger, told Born about the University of Göttingen, at Göttingen he found three renowned mathematicians, Felix Klein, David Hilbert and Hermann Minkowski. Very soon after his arrival, Born formed close ties to the two men. Being class scribe put Born into regular, invaluable contact with Hilbert, Hilbert became Borns mentor after selecting him to be the first to hold the unpaid, semi-official position of assistant. Borns introduction to Minkowski came through Borns stepmother, Bertha, as she knew Minkowski from dancing classes in Königsberg, the introduction netted Born invitations to the Minkowski household for Sunday dinners. In addition, while performing his duties as scribe and assistant, Borns relationship with Klein was more problematic
21.
J. Robert Oppenheimer
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Julius Robert Oppenheimer was an American theoretical physicist and professor of physics at the University of California, Berkeley. After the war, Oppenheimer became chairman of the influential General Advisory Committee of the newly created United States Atomic Energy Commission and he used that position to lobby for international control of nuclear power to avert nuclear proliferation and a nuclear arms race with the Soviet Union. Nine years later, President John F. Kennedy awarded him with the Enrico Fermi Award as a gesture of political rehabilitation. As a teacher and promoter of science, he is remembered as a father of the American school of theoretical physics that gained world prominence in the 1930s. After World War II, he director of the Institute for Advanced Study in Princeton. Julius came to America with no money, no baccalaureate studies and he got a job in a textile company and within a decade was an executive with the company. The Oppenheimers were non-observant Ashkenazi Jews, in 1912 the family moved to an apartment on the 11th floor of 155 Riverside Drive, near West 88th Street, Manhattan, an area known for luxurious mansions and townhouses. Their art collection included works by Pablo Picasso and Édouard Vuillard, Robert had a younger brother, Frank, who also became a physicist. Oppenheimer was initially educated at Alcuin Preparatory School, and in 1911 he entered the Ethical Culture Society School and this had been founded by Felix Adler to promote a form of ethical training based on the Ethical Culture movement, whose motto was Deed before Creed. His father had been a member of the Society for many years, Oppenheimer was a versatile scholar, interested in English and French literature, and particularly in mineralogy. He completed the third and fourth grades in one year, during his final year, he became interested in chemistry. He entered Harvard College a year late, at age 18, Oppenheimer majored in chemistry, but Harvard required science students to also study history, literature, and philosophy or mathematics. He compensated for his start by taking six courses each term and was admitted to the undergraduate honor society Phi Beta Kappa. He was attracted to physics by a course on thermodynamics that was taught by Percy Bridgman. He graduated summa cum laude in three years, in 1924 Oppenheimer was informed that he had been accepted into Christs College, Cambridge. He wrote to Ernest Rutherford requesting permission to work at the Cavendish Laboratory, Bridgman provided Oppenheimer with a recommendation, which conceded that Oppenheimers clumsiness in the laboratory made it apparent his forte was not experimental but rather theoretical physics. Rutherford was unimpressed, but Oppenheimer went to Cambridge in the hope of landing another offer and he was ultimately accepted by J. J. Thomson on condition that he complete a basic laboratory course. He developed a relationship with his tutor, Patrick Blackett
22.
Linus Pauling
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Linus Carl Pauling was an American chemist, biochemist, peace activist, author, and educator. He published more than 1,200 papers and books, of which about 850 dealt with scientific topics, new Scientist called him one of the 20 greatest scientists of all time, and as of 2000, he was rated the 16th most important scientist in history. Pauling was one of the founders of the fields of quantum chemistry, for his scientific work, Pauling was awarded the Nobel Prize in Chemistry in 1954. In 1962, for his activism, he was awarded the Nobel Peace Prize. This makes him the person to be awarded two unshared Nobel Prizes. He is one of four individuals to have won more than one Nobel Prize. Pauling is also one of two people to be awarded Nobel Prizes in different fields, the other being Marie Curie. Pauling also worked on DNAs structure, a problem which was solved by James Watson, Francis Crick, Rosalind Franklin, in his later years he promoted nuclear disarmament, as well as orthomolecular medicine, megavitamin therapy, and dietary supplements. None of the latter have gained acceptance in the scientific community. Pauling was born in Portland, Oregon, the child of Herman Henry William Pauling. He was named Linus Carl, in honor of Lucys father, Linus, in 1902, after his sister Pauline was born, Paulings parents decided to move out of Portland, to find more affordable and spacious living quarters than their one-room apartment. Lucy stayed with her husbands parents in Lake Oswego until Herman brought the family to Salem, within a year of Luciles birth in 1904, Herman Pauling moved his family to Oswego, where he opened his own drugstore. He moved his family to Condon, Oregon in 1905, by 1906, Herman Pauling was suffering from recurrent abdominal pain. He died of an ulcer on June 11,1910, leaving Lucy to care for Linus, Lucile. Pauling attributes his interest in becoming a chemist to being amazed by experiments conducted by a friend, Lloyd A. Jeffress, in high school, Pauling conducted chemistry experiments by scavenging equipment and material from an abandoned steel plant. With an older friend, Lloyd Simon, Pauling set up Palmon Laboratories in Simons basement and they approached local dairies offering to perform butterfat samplings at cheap prices but dairymen were wary of trusting two boys with the task, and the business ended in failure. At age 15, the high school senior had enough credits to enter Oregon State University, lacking two American history courses required for his high school diploma, Pauling asked the school principal if he could take the courses concurrently during the spring semester. Denied, he left Washington High School in June without a diploma, the school awarded him a diploma 45 years later, after he had won two Nobel Prizes
23.
Douglas Hartree
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Douglas Hartree was born in Cambridge, England. His father, William, was a lecturer in engineering at Cambridge University and his mother, Eva Rayner, was president of the National Council of Women, one of his great-grandfathers was Samuel Smiles, another was the marine engineer William Hartree, partner of John Penn. He was the oldest of three sons, although his two brothers did not survive to adulthood. He attended St Johns College, Cambridge but the first World War interrupted his studies, after the end of World War I, Hartree returned to Cambridge graduating in 1922 with a Second Class degree in natural sciences. In 1921, a visit by Niels Bohr to Cambridge inspired Hartree to apply his skills to Bohrs theory of the atom. With the publication of Schrödingers equation in the year, Hartree was able to apply his knowledge of differential equations. He derived the Hartree equations for the distribution of electrons in an atom, the wavefunctions from this theory did not satisfy the Pauli exclusion principle for which Slater showed that determinantal functions are required. V. Fock published the equations with exchange now known as Hartree–Fock equations and these are considerably more demanding computationally even with the efficient methods Hartree proposed for the calculation of exchange contributions. In 1929, Hartree was appointed to the Beyer Chair of Applied Mathematics at the University of Manchester, in 1933, he visited Vannevar Bush at the Massachusetts Institute of Technology and learned first hand about his differential analyser. Immediately on his return to Manchester, he set about building his own analyser from Meccano, the first application of the machine, reflecting Hartrees enthusiasm for railways, was calculating timetables for the London, Midland and Scottish Railway. He spent the rest of the applying the differential analyser to find solutions of differential equations arising in physics. These included control theory and laminar boundary layer theory in fluid dynamics making significant contributions to each of the fields, the differential analyser was not suitable for the solution of equations with exchange. When Focks publication pre-empted Hartrees work on equations with exchange, Hartree turned his research to radio-wave propagation that led to the Appleton–Hartree equation, in 1935, his father, William Hartree, offered to do calculations for him. Douglas recognised the importance of interaction that he referred to as superposition of configurations. The first multiconfiguration Hartree–Fock results were published by father, son, at Hartrees suggestion, Bertha Swirles proceeded to derive equations with exchange for atoms using the Dirac equation in 1935. With Hartrees advice, the first relativistic calculations were reported in 1940 by A. O. Williams, during the Second World War Hartree supervised two computing groups. The first group, for the Ministry of Supply, has described by Jack Howlett as a job shop for the solution of differential equations. At the outbreak of World War II, the differential analyser at the University of Manchester was the only full-size differential analyser in the country, arrangements were made to have the machine available for work in support of the national war effort
24.
Vladimir Fock
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Vladimir Aleksandrovich Fock was a Soviet physicist, who did foundational work on quantum mechanics and quantum electrodynamics. He was born in St. Petersburg, Russia, in 1922 he graduated from Petrograd University, then continued postgraduate studies there. He became a professor there in 1932, in 1926 he derived the Klein–Gordon equation. He gave his name to Fock space, the Fock representation and Fock state and he made many subsequent scientific contributions, during the rest of his life. Fock made significant contributions to relativity theory, specifically for the many body problems. In Leningrad, Fock created a school in theoretical physics. He wrote the first textbook on quantum mechanics Foundations of quantum mechanics, historians of science, such as Loren Graham, see Fock as a representative and proponent of Einsteins theory of relativity within the Soviet world. At a time when most Marxist philosophers objected to relativity theory and he was a full member of the USSR Academy of Sciences and a member of the International Academy of Quantum Molecular Science. Fock space Fock matrix Mehler–Fock transform Graham, L, the reception of Einsteins ideas, Two examples from contrasting political cultures. In Holton, G. and Elkana, Y. Albert Einstein, Princeton, NJ, Princeton UP, pp. 107–136 Fock, V. A. The Theory of Space, Time and Gravitation
25.
Cathode ray
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Cathode rays are streams of electrons observed in vacuum tubes. They were first observed in 1869 by German physicist Johann Hittorf, electrons were discovered as the constituents of cathode rays. In 1897 British physicist J. J. Thomson showed the rays were composed of a previously unknown negatively charged particle, Cathode ray tubes use a focused beam of electrons deflected by electric or magnetic fields to create the image in a classic television set. Cathode rays are made up of charged particles. Cathode rays are so named because they are emitted by the electrode, or cathode. This contrasts with cations, which are charged and go — Greek ἰόν — toward a cathode in solution. To release electrons into the tube, they first must be detached from the atoms of the cathode, modern vacuum tubes use thermionic emission, in which the cathode is made of a thin wire filament which is heated by a separate electric current passing through it. The increased random heat motion of the filament knocks electrons out at the surface of the filament, since the electrons have a negative charge, they are repelled by the cathode and attracted to the anode. They travel in straight lines through the empty tube, the voltage applied between the electrodes accelerates these low mass particles to high velocities. Researchers noticed that objects placed in the tube in front of the cathode could cast a shadow on the glowing wall, and realized that something must be travelling in straight lines from the cathode. After the electrons reach the anode, they travel through the wire to the power supply and back to the cathode. The current in a beam of cathode rays through a tube can be controlled by passing it through a screen of wires to which a small voltage is applied. The electric field of the wires deflects some of the electrons, thus a small voltage on the grid can be made to control a much larger voltage on the anode. This is the used in vacuum tubes to amplify electrical signals. These are used in cathode ray tubes, found in televisions and computer monitors, after the 1654 invention of the vacuum pump by Otto von Guericke, physicists began to experiment with passing high voltage electricity through rarefied air. In 1705, it was noted that electrostatic generator sparks travel a distance through low pressure air than through atmospheric pressure air. In 1838, Michael Faraday passed a current through an air filled glass tube and noticed a strange light arc with its beginning at the cathode. In 1857, German physicist and glassblower Heinrich Geissler sucked even more air out with a pump, to a pressure of around 10−3 atm and found that, instead of an arc
26.
Michael Faraday
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Michael Faraday FRS was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, diamagnetism, although Faraday received little formal education, he was one of the most influential scientists in history. It was by his research on the field around a conductor carrying a direct current that Faraday established the basis for the concept of the electromagnetic field in physics. Faraday also established that magnetism could affect rays of light and that there was a relationship between the two phenomena. He similarly discovered the principles of induction and diamagnetism. His inventions of electromagnetic rotary devices formed the foundation of electric motor technology, Faraday ultimately became the first and foremost Fullerian Professor of Chemistry at the Royal Institution of Great Britain, a lifetime position. James Clerk Maxwell took the work of Faraday and others and summarized it in a set of equations which is accepted as the basis of all theories of electromagnetic phenomena. The SI unit of capacitance is named in his honour, the farad, albert Einstein kept a picture of Faraday on his study wall, alongside pictures of Isaac Newton and James Clerk Maxwell. Faraday was born in Newington Butts, which is now part of the London Borough of Southwark but was then a part of Surrey. His family was not well off and his father, James, was a member of the Glassite sect of Christianity. James Faraday moved his wife and two children to London during the winter of 1790 from Outhgill in Westmorland, where he had been an apprentice to the village blacksmith, Michael was born in the autumn of that year. The young Michael Faraday, who was the third of four children, at the age of 14 he became an apprentice to George Riebau, a local bookbinder and bookseller in Blandford Street. During his seven-year apprenticeship Faraday read many books, including Isaac Wattss The Improvement of the Mind, at this time he also developed an interest in science, especially in electricity. Faraday was particularly inspired by the book Conversations on Chemistry by Jane Marcet, many of the tickets for these lectures were given to Faraday by William Dance, who was one of the founders of the Royal Philharmonic Society. Faraday subsequently sent Davy a 300-page book based on notes that he had taken during these lectures, davys reply was immediate, kind, and favourable. In 1813, when Davy damaged his eyesight in an accident with nitrogen trichloride, very soon Davy entrusted Faraday with the preparation of nitrogen trichloride samples, and they both were injured in an explosion of this very sensitive substance. In the class-based English society of the time, Faraday was not considered a gentleman, Faraday was forced to fill the role of valet as well as assistant throughout the trip. Davys wife, Jane Apreece, refused to treat Faraday as an equal, the trip did, however, give him access to the scientific elite of Europe and exposed him to a host of stimulating ideas
27.
Black-body radiation
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Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body. It has a spectrum and intensity that depends only on the bodys temperature. The thermal radiation emitted by many ordinary objects can be approximated as black-body radiation. A black-body at room temperature appears black, as most of the energy it radiates is infra-red, when it becomes a little hotter, it appears dull red. As its temperature increases further it eventually becomes blue-white, although planets and stars are neither in thermal equilibrium with their surroundings nor perfect black bodies, black-body radiation is used as a first approximation for the energy they emit. Black holes are near-perfect black bodies, in the sense that they absorb all the radiation that falls on them and it has been proposed that they emit black-body radiation, with a temperature that depends on the mass of the black hole. The term black body was introduced by Gustav Kirchhoff in 1860, Black-body radiation is also called thermal radiation, cavity radiation, complete radiation or temperature radiation. Black-body radiation has a characteristic, continuous spectrum that depends only on the bodys temperature. As the temperature increases past about 500 degrees Celsius, black start to emit significant amounts of visible light. Viewed in the dark by the eye, the first faint glow appears as a ghostly grey. When the body appears white, it is emitting a substantial fraction of its energy as ultraviolet radiation, Black-body radiation provides insight into the thermodynamic equilibrium state of cavity radiation. Instead, in theory the occupation numbers of the modes are quantized, cutting off the spectrum at high frequency in agreement with experimental observation. The study of the laws of black bodies and the failure of classical physics to describe them helped establish the foundations of quantum mechanics, all normal matter emits electromagnetic radiation when it has a temperature above absolute zero. The radiation represents a conversion of a thermal energy into electromagnetic energy. It is a process of radiative distribution of entropy. Conversely all normal matter absorbs electromagnetic radiation to some degree, an object that absorbs all radiation falling on it, at all wavelengths, is called a black body. When a black body is at a temperature, its emission has a characteristic frequency distribution that depends on the temperature. Its emission is called black-body radiation, the concept of the black body is an idealization, as perfect black bodies do not exist in nature
28.
Gustav Kirchhoff
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Gustav Robert Kirchhoff was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. He coined the term black body radiation in 1862, and two different sets of concepts are named Kirchhoffs laws after him, there is also a Kirchhoffs Law in thermochemistry, the Bunsen–Kirchhoff Award for spectroscopy is named after him and his colleague, Robert Bunsen. Gustav Kirchhoff was born in Königsberg, Prussia, the son of Friedrich Kirchhoff, a lawyer, in the same year, he moved to Berlin, where he stayed until he received a professorship at Breslau. Later, in 1857, He married Clara Richelot, the daughter of his mathematics professor Richelot and he married Luise Brömmel in 1872. Kirchhoff formulated his laws, which are now ubiquitous in electrical engineering, in 1845. He completed this study as an exercise, it later became his doctoral dissertation. In 1857 he calculated that a signal in a resistanceless wire travels along the wire at the speed of light. He proposed his law of radiation in 1859, and gave a proof in 1861. He was called to the University of Heidelberg in 1854, where he collaborated in work with Robert Bunsen. Together Kirchhoff and Bunsen discovered caesium and rubidium in 1861, at Heidelberg he ran a mathematico-physical seminar, modelled on Neumanns, with the mathematician Leo Koenigsberger. Among those who attended this seminar were Arthur Schuster and Sofia Kovalevskaya, in 1875 Kirchhoff accepted the first chair specifically dedicated to theoretical physics at Berlin. In 1862 he was awarded the Rumford Medal for his researches on the lines of the solar spectrum. He also contributed to optics, carefully solving Maxwells equations to provide a foundation for Huygens principle. In 1884 he became member of the Royal Netherlands Academy of Arts. Kirchhoff died in 1887, and was buried in the St Matthäus Kirchhof Cemetery in Schöneberg, leopold Kronecker is buried in the same cemetery. Kirchhoffs first law is that the sum of currents in a network of conductors meeting at a point is zero. The second law is that in a circuit, the directed sums of the voltages in a closed system is zero. A solid, liquid, or dense gas excited to emit light will radiate at all wavelengths, a low-density gas excited to emit light will do so at specific wavelengths and this produces an emission spectrum
29.
Ludwig Boltzmann
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Boltzmann was born in Vienna, the capital of the Austrian Empire. His father, Ludwig Georg Boltzmann, was a revenue official and his grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmanns mother, Katharina Pauernfeind, was originally from Salzburg. He received his education from a private tutor at the home of his parents. Boltzmann attended high school in Linz, Upper Austria, when Boltzmann was 15, his father died. Boltzmann studied physics at the University of Vienna, starting in 1863, among his teachers were Josef Loschmidt, Joseph Stefan, Andreas von Ettingshausen and Jozef Petzval. Boltzmann received his PhD degree in 1866 working under the supervision of Stefan, in 1867 he became a Privatdozent. After obtaining his degree, Boltzmann worked two more years as Stefans assistant. It was Stefan who introduced Boltzmann to Maxwells work, in 1869 at age 25, thanks to a letter of recommendation written by Stefan, he was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. In 1869 he spent several months in Heidelberg working with Robert Bunsen and Leo Königsberger and then in 1871 he was with Gustav Kirchhoff, in 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876. In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler and she was refused permission to audit lectures unofficially. Boltzmann advised her to appeal, which she did, successfully, on July 17,1876 Ludwig Boltzmann married Henriette, they had three daughters and two sons. Boltzmann went back to Graz to take up the chair of Experimental Physics, among his students in Graz were Svante Arrhenius and Walther Nernst. He spent 14 happy years in Graz and it was there that he developed his concept of nature. Boltzmann was appointed to the Chair of Theoretical Physics at the University of Munich in Bavaria, in 1893, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna. Boltzmann spent a deal of effort in his final years defending his theories. He did not get along with some of his colleagues in Vienna, particularly Ernst Mach and that same year Georg Helm and Wilhelm Ostwald presented their position on Energetics at a meeting in Lübeck. They saw energy, and not matter, as the component of the universe. Boltzmanns position carried the day among other physicists who supported his theories in the debate
30.
Max Planck
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Max Karl Ernst Ludwig Planck, FRS was a German theoretical physicist whose discovery of energy quanta won him the Nobel Prize in Physics in 1918. However, his name is known on a broader academic basis, through the renaming in 1948 of the German scientific institution. The MPS now includes 83 institutions representing a range of scientific directions. Planck came from a traditional, intellectual family and his paternal great-grandfather and grandfather were both theology professors in Göttingen, his father was a law professor in Kiel and Munich. Planck was born in Kiel, Holstein, to Johann Julius Wilhelm Planck and his second wife and he was baptised with the name of Karl Ernst Ludwig Marx Planck, of his given names, Marx was indicated as the primary name. However, by the age of ten he signed with the name Max and he was the 6th child in the family, though two of his siblings were from his fathers first marriage. Among his earliest memories was the marching of Prussian and Austrian troops into Kiel during the Second Schleswig War in 1864 and it was from Müller that Planck first learned the principle of conservation of energy. Planck graduated early, at age 17 and this is how Planck first came in contact with the field of physics. Planck was gifted when it came to music and he took singing lessons and played piano, organ and cello, and composed songs and operas. However, instead of music he chose to study physics, the Munich physics professor Philipp von Jolly advised Planck against going into physics, saying, in this field, almost everything is already discovered, and all that remains is to fill a few holes. Planck replied that he did not wish to discover new things, but only to understand the fundamentals of the field. Under Jollys supervision, Planck performed the experiments of his scientific career, studying the diffusion of hydrogen through heated platinum. In 1877 he went to the Friedrich Wilhelms University in Berlin for a year of study with physicists Hermann von Helmholtz and Gustav Kirchhoff and mathematician Karl Weierstrass. He wrote that Helmholtz was never quite prepared, spoke slowly, miscalculated endlessly and he soon became close friends with Helmholtz. While there he undertook a program of mostly self-study of Clausiuss writings, in October 1878 Planck passed his qualifying exams and in February 1879 defended his dissertation, Über den zweiten Hauptsatz der mechanischen Wärmetheorie. He briefly taught mathematics and physics at his school in Munich. In June 1880, he presented his thesis, Gleichgewichtszustände isotroper Körper in verschiedenen Temperaturen. With the completion of his thesis, Planck became an unpaid private lecturer in Munich
31.
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
32.
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
33.
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
34.
Photoelectric effect
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The photoelectric effect or photo ionization is the emission of electrons or other free carriers when light is shone onto a material. Electrons emitted in this manner can be called photo electrons, the phenomenon is commonly studied in electronic physics, as well as in fields of chemistry, such as quantum chemistry or electrochemistry. According to classical theory, this effect can be attributed to the transfer of energy from the light to an electron. From this perspective, an alteration in the intensity of light would induce changes in the energy of the electrons emitted from the metal. Furthermore, according to theory, a sufficiently dim light would be expected to show a time lag between the initial shining of its light and the subsequent emission of an electron. However, the results did not correlate with either of the two predictions made by classical theory. Instead, electrons are dislodged only by the impingement of photons when those photons reach or exceed a threshold frequency, below that threshold, no electrons are emitted from the metal regardless of the light intensity or the length of time of exposure to the light. This shed light on Max Plancks previous discovery of the Planck relation linking energy, the factor h is known as the Planck constant. In 1887, Heinrich Hertz discovered that illuminated with ultraviolet light create electric sparks more easily. In 1900, while studying black-body radiation, the German physicist Max Planck suggested that the energy carried by electromagnetic waves could only be released in packets of energy. In 1905, Albert Einstein published a paper advancing the hypothesis that energy is carried in discrete quantized packets to explain experimental data from the photoelectric effect. This model contributed to the development of quantum mechanics, in 1914, Robert Millikans experiment supported Einsteins model of the photoelectric effect. The photoelectric effect requires photons with energies approaching zero to over 1 MeV for core electrons in elements with an atomic number. Emission of conduction electrons from typical metals usually requires a few electron-volts, study of the photoelectric effect led to important steps in understanding the quantum nature of light and electrons and influenced the formation of the concept of wave–particle duality. Other phenomena where light affects the movement of electric charges include the effect, the photovoltaic effect. It is also usual to have the surface in a vacuum, since gases impede the flow of photoelectrons. When the photoelectron is emitted into a rather than into a vacuum, the term internal photoemission is often used. The photons of a light beam have an energy proportional to the frequency of the light
35.
Albert Einstein
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Albert Einstein was a German-born theoretical physicist. He developed the theory of relativity, one of the two pillars of modern physics, Einsteins work is also known for its influence on the philosophy of science. Einstein is best known in popular culture for his mass–energy equivalence formula E = mc2, near the beginning of his career, Einstein thought that Newtonian mechanics was no longer enough to reconcile the laws of classical mechanics with the laws of the electromagnetic field. This led him to develop his theory of relativity during his time at the Swiss Patent Office in Bern. Briefly before, he aquired the Swiss citizenship in 1901, which he kept for his whole life and he continued to deal with problems of statistical mechanics and quantum theory, which led to his explanations of particle theory and the motion of molecules. He also investigated the properties of light which laid the foundation of the photon theory of light. In 1917, Einstein applied the theory of relativity to model the large-scale structure of the universe. He was visiting the United States when Adolf Hitler came to power in 1933 and, being Jewish, did not go back to Germany and he settled in the United States, becoming an American citizen in 1940. This eventually led to what would become the Manhattan Project, Einstein supported defending the Allied forces, but generally denounced the idea of using the newly discovered nuclear fission as a weapon. Later, with the British philosopher Bertrand Russell, Einstein signed the Russell–Einstein Manifesto, Einstein was affiliated with the Institute for Advanced Study in Princeton, New Jersey, until his death in 1955. Einstein published more than 300 scientific papers along with over 150 non-scientific works, on 5 December 2014, universities and archives announced the release of Einsteins papers, comprising more than 30,000 unique documents. Einsteins intellectual achievements and originality have made the word Einstein synonymous with genius, Albert Einstein was born in Ulm, in the Kingdom of Württemberg in the German Empire, on 14 March 1879. His parents were Hermann Einstein, a salesman and engineer, the Einsteins were non-observant Ashkenazi Jews, and Albert attended a Catholic elementary school in Munich from the age of 5 for three years. At the age of 8, he was transferred to the Luitpold Gymnasium, the loss forced the sale of the Munich factory. In search of business, the Einstein family moved to Italy, first to Milan, when the family moved to Pavia, Einstein stayed in Munich to finish his studies at the Luitpold Gymnasium. His father intended for him to electrical engineering, but Einstein clashed with authorities and resented the schools regimen. He later wrote that the spirit of learning and creative thought was lost in strict rote learning, at the end of December 1894, he travelled to Italy to join his family in Pavia, convincing the school to let him go by using a doctors note. During his time in Italy he wrote an essay with the title On the Investigation of the State of the Ether in a Magnetic Field
36.
Light
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Light is electromagnetic radiation within a certain portion of the electromagnetic spectrum. The word usually refers to light, which is visible to the human eye and is responsible for the sense of sight. Visible light is defined as having wavelengths in the range of 400–700 nanometres, or 4.00 × 10−7 to 7.00 × 10−7 m. This wavelength means a range of roughly 430–750 terahertz. The main source of light on Earth is the Sun, sunlight provides the energy that green plants use to create sugars mostly in the form of starches, which release energy into the living things that digest them. This process of photosynthesis provides virtually all the used by living things. Historically, another important source of light for humans has been fire, with the development of electric lights and power systems, electric lighting has effectively replaced firelight. Some species of animals generate their own light, a process called bioluminescence, for example, fireflies use light to locate mates, and vampire squids use it to hide themselves from prey. Visible light, as all types of electromagnetic radiation, is experimentally found to always move at this speed in a vacuum. In physics, the term sometimes refers to electromagnetic radiation of any wavelength. In this sense, gamma rays, X-rays, microwaves and radio waves are also light, like all types of light, visible light is emitted and absorbed in tiny packets called photons and exhibits properties of both waves and particles. This property is referred to as the wave–particle duality, the study of light, known as optics, is an important research area in modern physics. Generally, EM radiation, or EMR, is classified by wavelength into radio, microwave, infrared, the behavior of EMR depends on its wavelength. Higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths, when EMR interacts with single atoms and molecules, its behavior depends on the amount of energy per quantum it carries. There exist animals that are sensitive to various types of infrared, infrared sensing in snakes depends on a kind of natural thermal imaging, in which tiny packets of cellular water are raised in temperature by the infrared radiation. EMR in this range causes molecular vibration and heating effects, which is how these animals detect it, above the range of visible light, ultraviolet light becomes invisible to humans, mostly because it is absorbed by the cornea below 360 nanometers and the internal lens below 400. Furthermore, the rods and cones located in the retina of the eye cannot detect the very short ultraviolet wavelengths and are in fact damaged by ultraviolet. Many animals with eyes that do not require lenses are able to detect ultraviolet, by quantum photon-absorption mechanisms, various sources define visible light as narrowly as 420 to 680 to as broadly as 380 to 800 nm
37.
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
38.
Dirac equation
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In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. In its free form, or including electromagnetic interactions, it describes all spin-1/2 massive particles such as electrons and it was validated by accounting for the fine details of the hydrogen spectrum in a completely rigorous way. The equation also implied the existence of a new form of matter, antimatter, previously unsuspected and unobserved, moreover, in the limit of zero mass, the Dirac equation reduces to the Weyl equation. This accomplishment has been described as fully on a par with the works of Newton, Maxwell, in the context of quantum field theory, the Dirac equation is reinterpreted to describe quantum fields corresponding to spin-1/2 particles. The Dirac equation in the originally proposed by Dirac is. The p1, p2, p3 are the components of the momentum, also, c is the speed of light, and ħ is the Planck constant divided by 2π. These fundamental physical constants reflect special relativity and quantum mechanics, respectively, Diracs purpose in casting this equation was to explain the behavior of the relativistically moving electron, and so to allow the atom to be treated in a manner consistent with relativity. His rather modest hope was that the corrections introduced this way might have a bearing on the problem of atomic spectra, the new elements in this equation are the 4 ×4 matrices αk and β, and the four-component wave function ψ. There are four components in ψ because the evaluation of it at any point in configuration space is a bispinor. It is interpreted as a superposition of an electron, a spin-down electron, a spin-up positron. These matrices and the form of the function have a deep mathematical significance. The algebraic structure represented by the matrices had been created some 50 years earlier by the English mathematician W. K. Clifford. In turn, Cliffords ideas had emerged from the work of the German mathematician Hermann Grassmann in his Lineale Ausdehnungslehre. The latter had been regarded as well-nigh incomprehensible by most of his contemporaries, the appearance of something so seemingly abstract, at such a late date, and in such a direct physical manner, is one of the most remarkable chapters in the history of physics. The Dirac equation is similar to the Schrödinger equation for a massive free particle. The left side represents the square of the momentum operator divided by twice the mass, space and time derivatives both enter to second order. This has a consequence for the interpretation of the equation. Because the equation is second order in the derivative, one must specify initial values both of the wave function itself and of its first-time derivative in order to solve definite problems
39.
Relativistic quantum chemistry
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Relativistic quantum chemistry invokes quantum chemical and relativistic mechanical arguments to explain elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example of such an explanation is the color of gold, due to relativistic effects, the term relativistic effects was developed in light of the history of quantum mechanics. Initially quantum mechanics was developed without considering the theory of relativity, by convention, relativistic effects are those discrepancies between values calculated by models considering and not considering relativity. Relativistic effects are important for the elements with high atomic numbers. In the most common layout of the table, these elements are shown in the lower area. Examples are the lanthanides and actinides and these corrections affect the electrons differently depending on the electron speed relative to the speed of light. Relativistic effects are more prominent in heavy elements because only in these elements do electrons attain more pronounced relativistic speeds, beginning in 1935, Bertha Swirles described a relativistic treatment of a many-electron system, in spite of Paul Diracs 1929 assertion that the only imperfections remaining in quantum mechanics. Theoretical chemists by and large agreed with Diracs sentiment until the 1970s, the Schrödinger equation had been developed without considering relativity in Schrödingers 1926 paper. The figure at the right illustrates the effects on the mass of an electron as a function of its velocity. This has an implication on the Bohr radius which is given by a 0 = ℏ m e c α where ℏ is the reduced Plancks constant. Arnold Sommerfeld calculated that, for a 1s electron of an atom with an orbiting radius of 0.0529 nm. That is to say, the constant shows the electron traveling at nearly 1/137 the speed of light. One can extend this to an element by using the expression v ≈ Zc/137 for a 1s electron where v is its radial velocity. For gold with the 1s electron will be going 58% of the speed of light. Plugging this in for v/c for the mass one finds that mrel =1. 22me. Notice how the model shows the radius decreasing with increasing velocity. From quantum mechanics the angular momentum is given as m v e r = n ℏ and this fits with intuition, electrons with lower principal quantum numbers will have a higher probability density of being nearer to the nucleus. A nucleus with a charge will cause an electron to have a high velocity
40.
Dihydrogen cation
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The hydrogen molecular ion, dihydrogen cation, or H+2, is the simplest molecular ion. It is composed of two positively charged protons and one negatively charged electron, and can be formed from ionization of a hydrogen molecule. The analytical solutions for the eigenvalues are a generalization of the Lambert W function. Thus, the case of clamped nuclei can be completely done analytically using a computer algebra system within an experimental mathematics approach, consequently, it is included as an example in most quantum chemistry textbooks. The first successful quantum mechanical treatment of H+2 was published by the Danish physicist Øyvind Burrau in 1927, earlier attempts using the old quantum theory had been published in 1922 by Karel Niessen and Wolfgang Pauli, and in 1925 by Harold Urey. In 1928, Linus Pauling published a review putting together the work of Burrau with the work of Walter Heitler, bonding in H+2 can be described as a covalent one-electron bond, which has a formal bond order of one half. The ion is formed in molecular clouds in space, and is important in the chemistry of the interstellar medium. The simplest electronic Schrödinger wave equation for the molecular ion H+2 is modeled with two fixed nuclear centers, labeled A and B, and one electron. An additive term 1/R, which is constant for fixed internuclear distance R, has been omitted from the potential V, the distances between the electron and the nuclei are denoted ra and rb. In atomic units the equation is ψ = E ψ with V = −1 r a −1 r b. We can choose the midpoint between the nuclei as the origin of coordinates and it follows from general symmetry principles that the wave functions can be characterized by their symmetry behavior with respect to space inversion. There are wave functions ψ+, which are symmetric with respect to inversion, and there are wave functions ψ−. The symmetry-adapted wave functions satisfy the same Schrödinger equation, the ground state of H+2 is denoted X2Σ+ g or 1sσg and it is symmetric. There is also the first excited state A2Σ+ u, which is antisymmetric, occurring here denote just the symmetry behavior under space inversion. Their use is standard practice for the designation of electronic states of molecules, whereas for atomic states the terms even. The lead term 4/eRe−R was first obtained by the Holstein–Herring method, similarly, asymptotic expansions in powers of 1/R have been obtained to high order by Cizek et al. for the lowest ten discrete states of the hydrogen molecular ion. These are of importance in stellar and atmospheric physics. The energies for the lowest discrete states are shown in the graph above, the red solid lines are 2Σ+ g states
41.
Lambert W function
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Since the function ƒ is not injective, the relation W is multivalued. If we restrict attention to real-valued W, the variable z is then replaced by the real variable x, and the relation is defined only for x ≥ −1/e. The additional constraint W ≥ −1 defines a single-valued function W0 and we have W0 =0 and W0 = −1. Meanwhile, the branch has W ≤ −1 and is denoted W−1. It decreases from W−1 = −1 to W−1 = −∞, the Lambert W relation cannot be expressed in terms of elementary functions. It is useful in combinatorics, for instance in the enumeration of trees and it can be used to solve various equations involving exponentials and also occurs in the solution of delay differential equations, such as y = a y. In biochemistry, and in particular enzyme kinetics, a solution for the time course kinetics analysis of Michaelis–Menten kinetics is described in terms of the Lambert W function. The Lambert-W function is named after Johann Heinrich Lambert, the main branch W0 is denoted by Wp in the Digital Library of Mathematical Functions and the branch W−1 is denoted by Wm there. The notation convention chosen here follows the canonical reference on the Lambert-W function by Corless, Gonnet, Hare, Jeffrey, Lambert first considered the related Lamberts Transcendental Equation in 1758, which led to a paper by Leonhard Euler in 1783 that discussed the special case of wew. The Lambert W function was re-discovered every decade or so in specialized applications, by implicit differentiation, one can show that all branches of W satisfy the differential equation z d W d z = W for z ≠ −1 / e. As a consequence, we get the formula for the derivative of W, d W d z = W z for z ∉. Using the identity e W = z / W, we get the equivalent formula which holds for all z ≠ −1 / e, d W d z =1 z + e W. The function W, and many expressions involving W, can be integrated using the substitution w = W, i. e. x = w ew, ∫ W d x = x W − x + e W + C = x + C. X n = x − x 2 +32 x 3 −83 x 4 +12524 x 5 − ⋯ The radius of convergence is 1/e, keeping only the first two terms of the expansion, W0 = ln − ln + o. ∫ W x d x =122 + C ∫ W d x =12 B2 + C Many equations involving exponentials can be solved using the W function. The solution for the current in a series diode/resistor circuit can also be written in terms of the Lambert W. See diode modeling. The delay differential equation y ˙ = a y has characteristic equation λ = a e − λ, leading to λ = W k and y = e W k t, if a ≥ e −1, only W0 need be considered. The Lambert-W function has been shown to be the optimal solution for the required magnetic field of a Zeeman slower
42.
Atomic nucleus
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After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. Almost all of the mass of an atom is located in the nucleus, protons and neutrons are bound together to form a nucleus by the nuclear force. The diameter of the nucleus is in the range of 6985175000000000000♠1.75 fm for hydrogen to about 6986150000000000000♠15 fm for the heaviest atoms and these dimensions are much smaller than the diameter of the atom itself, by a factor of about 23,000 to about 145,000. The branch of physics concerned with the study and understanding of the nucleus, including its composition. The nucleus was discovered in 1911, as a result of Ernest Rutherfords efforts to test Thomsons plum pudding model of the atom, the electron had already been discovered earlier by J. J. Knowing that atoms are electrically neutral, Thomson postulated that there must be a charge as well. In his plum pudding model, Thomson suggested that an atom consisted of negative electrons randomly scattered within a sphere of positive charge, to his surprise, many of the particles were deflected at very large angles. This justified the idea of an atom with a dense center of positive charge. The term nucleus is from the Latin word nucleus, a diminutive of nux, in 1844, Michael Faraday used the term to refer to the central point of an atom. The modern atomic meaning was proposed by Ernest Rutherford in 1912, the adoption of the term nucleus to atomic theory, however, was not immediate. In 1916, for example, Gilbert N, the nuclear strong force extends far enough from each baryon so as to bind the neutrons and protons together against the repulsive electrical force between the positively charged protons. The nuclear strong force has a short range, and essentially drops to zero just beyond the edge of the nucleus. The collective action of the charged nucleus is to hold the electrically negative charged electrons in their orbits about the nucleus. The collection of negatively charged electrons orbiting the nucleus display an affinity for certain configurations, which chemical element an atom represents is determined by the number of protons in the nucleus, the neutral atom will have an equal number of electrons orbiting that nucleus. Individual chemical elements can create more stable electron configurations by combining to share their electrons and it is that sharing of electrons to create stable electronic orbits about the nucleus that appears to us as the chemistry of our macro world. Protons define the entire charge of a nucleus, and hence its chemical identity, neutrons are electrically neutral, but contribute to the mass of a nucleus to nearly the same extent as the protons. Neutrons explain the phenomenon of isotopes – varieties of the chemical element which differ only in their atomic mass. They are sometimes viewed as two different quantum states of the particle, the nucleon
43.
Wave function
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A wave function in quantum physics is a description of the quantum state of a system. The wave function is a probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a function are the Greek letters ψ or Ψ. The wave function is a function of the degrees of freedom corresponding to some set of commuting observables. Once such a representation is chosen, the function can be derived from the quantum state. For a given system, the choice of which commuting degrees of freedom to use is not unique, some particles, like electrons and photons, have nonzero spin, and the wave function for such particles includes spin as an intrinsic, discrete degree of freedom. Other discrete variables can also be included, such as isospin and these values are often displayed in a column matrix. According to the principle of quantum mechanics, wave functions can be added together and multiplied by complex numbers to form new wave functions. The Schrödinger equation determines how wave functions evolve over time, a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name wave function, and gives rise to wave–particle duality, however, the wave function in quantum mechanics describes a kind of physical phenomenon, still open to different interpretations, which fundamentally differs from that of classic mechanical waves. The integral of this quantity, over all the degrees of freedom. This general requirement a wave function must satisfy is called the normalization condition, since the wave function is complex valued, only its relative phase and relative magnitude can be measured. In 1905 Einstein postulated the proportionality between the frequency of a photon and its energy, E = hf, and in 1916 the corresponding relation between photon momentum and wavelength, λ = h/p, the equations represent wave–particle duality for both massless and massive particles. In the 1920s and 1930s, quantum mechanics was developed using calculus and those who used the techniques of calculus included Louis de Broglie, Erwin Schrödinger, and others, developing wave mechanics. Those who applied the methods of linear algebra included Werner Heisenberg, Max Born, Schrödinger subsequently showed that the two approaches were equivalent. However, no one was clear on how to interpret it, at first, Schrödinger and others thought that wave functions represent particles that are spread out with most of the particle being where the wave function is large. This was shown to be incompatible with the scattering of a wave packet representing a particle off a target. While a scattered particle may scatter in any direction, it not break up
