1.
Atomic physics
–
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and this comprises ions, neutral atoms and, unless otherwise stated, it can be assumed that the term atom includes ions. The term atomic physics can be associated with power and nuclear weapons, due to the synonymous use of atomic. Physicists distinguish between atomic physics — which deals with the atom as a system consisting of a nucleus and electrons — and nuclear physics, which considers atomic nuclei alone. As with many fields, strict delineation can be highly contrived and atomic physics is often considered in the wider context of atomic, molecular. Physics research groups are usually so classified, Atomic physics primarily considers atoms in isolation. Atomic models will consist of a nucleus that may be surrounded by one or more bound electrons. It is not concerned with the formation of molecules, nor does it examine atoms in a state as condensed matter. It is concerned with such as ionization and excitation by photons or collisions with atomic particles. This means that the atoms can be treated as if each were in isolation. By this consideration atomic physics provides the underlying theory in physics and atmospheric physics. Electrons form notional shells around the nucleus and these are normally in a ground state but can be excited by the absorption of energy from light, magnetic fields, or interaction with a colliding particle. Electrons that populate a shell are said to be in a bound state, the energy necessary to remove an electron from its shell is called the binding energy. Any quantity of energy absorbed by the electron in excess of this amount is converted to kinetic energy according to the conservation of energy, the atom is said to have undergone the process of ionization. If the electron absorbs a quantity of less than the binding energy. After a certain time, the electron in a state will jump to a lower state. In a neutral atom, the system will emit a photon of the difference in energy, if an inner electron has absorbed more than the binding energy, then a more outer electron may undergo a transition to fill the inner orbital. The Auger effect allows one to multiply ionize an atom with a single photon, there are rather strict selection rules as to the electronic configurations that can be reached by excitation by light — however there are no such rules for excitation by collision processes
2.
Energy level
–
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy. This contrasts with classical particles, which can have any energy and these discrete values are called energy levels. The energy spectrum of a system with discrete energy levels is said to be quantized. In chemistry and atomic physics, a shell, or a principal energy level. The closest shell to the nucleus is called the 1 shell, followed by the 2 shell, then the 3 shell, the shells correspond with the principal quantum numbers or are labeled alphabetically with letters used in the X-ray notation. Each shell can contain only a number of electrons, The first shell can hold up to two electrons, the second shell can hold up to eight electrons, the third shell can hold up to 18. The general formula is that the nth shell can in principle hold up to 2 electrons, since electrons are electrically attracted to the nucleus, an atoms electrons will generally occupy outer shells only if the more inner shells have already been completely filled by other electrons. However, this is not a requirement, atoms may have two or even three incomplete outer shells. For an explanation of why electrons exist in these shells see electron configuration, if the potential energy is set to zero at infinite distance from the atomic nucleus or molecule, the usual convention, then bound electron states have negative potential energy. If an atom, ion, or molecule is at the lowest possible level, it. If it is at an energy level, it is said to be excited. If more than one quantum state is at the same energy. They are then called degenerate energy levels, quantized energy levels result from the relation between a particles energy and its wavelength. For a confined particle such as an electron in an atom, only stationary states with energies corresponding to integral numbers of wavelengths can exist, for other states the waves interfere destructively, resulting in zero probability density. Elementary examples that show mathematically how energy levels come about are the particle in a box, the first evidence of quantization in atoms was the observation of spectral lines in light from the sun in the early 1800s by Joseph von Fraunhofer and William Hyde Wollaston. The notion of levels was proposed in 1913 by Danish physicist Niels Bohr in the Bohr theory of the atom. The modern quantum mechanical theory giving an explanation of these levels in terms of the Schrödinger equation was advanced by Erwin Schrödinger and Werner Heisenberg in 1926. When the electron is bound to the atom in any closer value of n, assume there is one electron in a given atomic orbital in a hydrogen-like atom
3.
Atom
–
An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms, Atoms are very small, typical sizes are around 100 picometers. Atoms are small enough that attempting to predict their behavior using classical physics - as if they were billiard balls, through the development of physics, atomic models have incorporated quantum principles to better explain and predict the behavior. Every atom is composed of a nucleus and one or more bound to the nucleus. The nucleus is made of one or more protons and typically a number of neutrons. Protons and neutrons are called nucleons, more than 99. 94% of an atoms mass is in the nucleus. The protons have an electric charge, the electrons have a negative electric charge. If the number of protons and electrons are equal, that atom is electrically neutral, if an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively, and it is called an ion. The electrons of an atom are attracted to the protons in a nucleus by this electromagnetic force. The number of protons in the nucleus defines to what chemical element the atom belongs, for example, the number of neutrons defines the isotope of the element. The number of influences the magnetic properties of an atom. Atoms can attach to one or more other atoms by chemical bonds to form compounds such as molecules. The ability of atoms to associate and dissociate is responsible for most of the changes observed in nature. The idea that matter is made up of units is a very old idea, appearing in many ancient cultures such as Greece. The word atom was coined by ancient Greek philosophers, however, these ideas were founded in philosophical and theological reasoning rather than evidence and experimentation. As a result, their views on what look like. They also could not convince everybody, so atomism was but one of a number of competing theories on the nature of matter. It was not until the 19th century that the idea was embraced and refined by scientists, in the early 1800s, John Dalton used the concept of atoms to explain why elements always react in ratios of small whole numbers
4.
Molecule
–
A molecule is an electrically neutral group of two or more atoms held together by chemical bonds. Molecules are distinguished from ions by their lack of electrical charge, however, in quantum physics, organic chemistry, and biochemistry, the term molecule is often used less strictly, also being applied to polyatomic ions. In the kinetic theory of gases, the molecule is often used for any gaseous particle regardless of its composition. According to this definition, noble gas atoms are considered molecules as they are in fact monoatomic molecules. A molecule may be homonuclear, that is, it consists of atoms of one element, as with oxygen, or it may be heteronuclear. Atoms and complexes connected by non-covalent interactions, such as hydrogen bonds or ionic bonds, are not considered single molecules. Molecules as components of matter are common in organic substances and they also make up most of the oceans and atmosphere. Also, no typical molecule can be defined for ionic crystals and covalent crystals, the theme of repeated unit-cellular-structure also holds for most condensed phases with metallic bonding, which means that solid metals are also not made of molecules. In glasses, atoms may also be together by chemical bonds with no presence of any definable molecule. The science of molecules is called molecular chemistry or molecular physics, in practice, however, this distinction is vague. In molecular sciences, a molecule consists of a system composed of two or more atoms. Polyatomic ions may sometimes be thought of as electrically charged molecules. The term unstable molecule is used for very reactive species, i. e, according to Merriam-Webster and the Online Etymology Dictionary, the word molecule derives from the Latin moles or small unit of mass. Molecule – extremely minute particle, from French molécule, from New Latin molecula, diminutive of Latin moles mass, a vague meaning at first, the vogue for the word can be traced to the philosophy of Descartes. The definition of the molecule has evolved as knowledge of the structure of molecules has increased, earlier definitions were less precise, defining molecules as the smallest particles of pure chemical substances that still retain their composition and chemical properties. Molecules are held together by covalent bonding or ionic bonding. Several types of non-metal elements exist only as molecules in the environment, for example, hydrogen only exists as hydrogen molecule. A molecule of a compound is made out of two or more elements, a covalent bond is a chemical bond that involves the sharing of electron pairs between atoms
5.
Ion
–
An ion is an atom or a molecule in which the total number of electrons is not equal to the total number of protons, giving the atom or molecule a net positive or negative electrical charge. Ions can be created, by chemical or physical means. In chemical terms, if an atom loses one or more electrons. If an atom gains electrons, it has a net charge and is known as an anion. Ions consisting of only a single atom are atomic or monatomic ions, because of their electric charges, cations and anions attract each other and readily form ionic compounds, such as salts. In the case of ionization of a medium, such as a gas, which are known as ion pairs are created by ion impact, and each pair consists of a free electron. The word ion comes from the Greek word ἰόν, ion, going and this term was introduced by English physicist and chemist Michael Faraday in 1834 for the then-unknown species that goes from one electrode to the other through an aqueous medium. Faraday also introduced the words anion for a charged ion. In Faradays nomenclature, cations were named because they were attracted to the cathode in a galvanic device, arrhenius explanation was that in forming a solution, the salt dissociates into Faradays ions. Arrhenius proposed that ions formed even in the absence of an electric current, ions in their gas-like state are highly reactive, and do not occur in large amounts on Earth, except in flames, lightning, electrical sparks, and other plasmas. These gas-like ions rapidly interact with ions of charge to give neutral molecules or ionic salts. These stabilized species are commonly found in the environment at low temperatures. A common example is the present in seawater, which are derived from the dissolved salts. Electrons, due to their mass and thus larger space-filling properties as matter waves, determine the size of atoms. Thus, anions are larger than the parent molecule or atom, as the excess electron repel each other, as such, in general, cations are smaller than the corresponding parent atom or molecule due to the smaller size of its electron cloud. One particular cation contains no electrons, and thus consists of a single proton - very much smaller than the parent hydrogen atom. Since the electric charge on a proton is equal in magnitude to the charge on an electron, an anion, from the Greek word ἄνω, meaning up, is an ion with more electrons than protons, giving it a net negative charge. A cation, from the Greek word κατά, meaning down, is an ion with fewer electrons than protons, there are additional names used for ions with multiple charges
6.
Nuclear magnetic moment
–
The nuclear magnetic moment is the magnetic moment of an atomic nucleus and arises from the spin of the protons and neutrons. It is mainly a magnetic moment, the quadrupole moment does cause some small shifts in the hyperfine structure as well. All nuclei that have nonzero spin also possess a magnetic moment and vice versa. The nuclear magnetic moment varies from isotope to isotope of an element, for a nucleus of which the numbers of protons and of neutrons are both even in its ground state, the nuclear spin and magnetic moment are both always zero. In cases with odd numbers of either or both protons and neutrons, the nucleus often has nonzero spin and magnetic moment, the methods for measuring nuclear magnetic moments can be divided into two broad groups in regard to the interaction with internal or external applied fields. Generally the methods based on external fields are more accurate, according to the shell model, protons or neutrons tend to form pairs of opposite total angular momentum. For a nucleus with odd numbers of protons and neutrons. The magnetic moment is calculated through j, l and s of the unpaired nucleon, furthermore, for odd–odd nuclei, there are two unpaired nucleons to be considered, as in deuterium. There is consequently a value for the magnetic moment associated with each possible l and s state combination. Thus the real nuclear magnetic moment is between the associated with the pure states, though it may be close to one or the other. The values of g and g are known as the g-factors of the nucleons, the measured values of g for the neutron and the proton are according to their electric charge. Thus, in units of nuclear magneton, g =0 for the neutron, the measured values of g for the neutron and the proton are twice their magnetic moment. In nuclear magneton units, g = −3.8263 for the neutron, the gyromagnetic ratio, expressed in Larmor precession frequency f = γ2 π B, is of great relevance to nuclear magnetic resonance analysis. These g-factors may be multiplied by 7.622593285 MHz/T, which is the nuclear magneton divided by Plancks constant, to yield Larmor frequencies in MHz/T. If divided instead by the reduced Planck constant, which is 2π less, a gyromagnetic ratio expressed in radians is obtained, the quantized difference between energy levels corresponding to different orientations of the nuclear spin Δ E = γ ℏ B. The ratio of nuclei in the energy state, with spin aligned to the external magnetic field, is determined by the Boltzmann distribution. Thus, multiplying the dimensionless g-factor by the nuclear magneton and the magnetic field, and dividing by Boltzmanns constant. Fundamentals of atomic and nuclear physics
7.
Magnetic field
–
A magnetic field is the magnetic effect of electric currents and magnetic materials. The magnetic field at any point is specified by both a direction and a magnitude, as such it is represented by a vector field. The term is used for two distinct but closely related fields denoted by the symbols B and H, where H is measured in units of amperes per meter in the SI, B is measured in teslas and newtons per meter per ampere in the SI. B is most commonly defined in terms of the Lorentz force it exerts on moving electric charges, Magnetic fields can be produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. In quantum physics, the field is quantized and electromagnetic interactions result from the exchange of photons. Magnetic fields are used throughout modern technology, particularly in electrical engineering. The Earth produces its own field, which is important in navigation. Rotating magnetic fields are used in electric motors and generators. Magnetic forces give information about the carriers in a material through the Hall effect. The interaction of magnetic fields in electric devices such as transformers is studied in the discipline of magnetic circuits, noting that the resulting field lines crossed at two points he named those points poles in analogy to Earths poles. He also clearly articulated the principle that magnets always have both a north and south pole, no matter how finely one slices them, almost three centuries later, William Gilbert of Colchester replicated Petrus Peregrinus work and was the first to state explicitly that Earth is a magnet. Published in 1600, Gilberts work, De Magnete, helped to establish magnetism as a science, in 1750, John Michell stated that magnetic poles attract and repel in accordance with an inverse square law. Charles-Augustin de Coulomb experimentally verified this in 1785 and stated explicitly that the north and south poles cannot be separated, building on this force between poles, Siméon Denis Poisson created the first successful model of the magnetic field, which he presented in 1824. In this model, a magnetic H-field is produced by magnetic poles, three discoveries challenged this foundation of magnetism, though. First, in 1819, Hans Christian Ørsted discovered that an electric current generates a magnetic field encircling it, then in 1820, André-Marie Ampère showed that parallel wires having currents in the same direction attract one another. Finally, Jean-Baptiste Biot and Félix Savart discovered the Biot–Savart law in 1820, extending these experiments, Ampère published his own successful model of magnetism in 1825. This has the benefit of explaining why magnetic charge can not be isolated. Also in this work, Ampère introduced the term electrodynamics to describe the relationship between electricity and magnetism, in 1831, Michael Faraday discovered electromagnetic induction when he found that a changing magnetic field generates an encircling electric field
8.
Quadrupole
–
The quadrupole moment tensor Q is a rank-two tensor and is traceless. The quadrupole moment tensor has thus 9 components, but because of the symmetry and zero-trace property, only 5 of these are independent. For a discrete system of point charges, each with charge q l and position r l → = relative to the coordinate system origin, the indices i, j run over the Cartesian coordinates x, y, z and δ i j is the Kronecker delta. In contrast, if the monopole and dipole moments vanish, but the moment does not. Here, k is a constant that depends on the type of field, the factors n i, n j are components of the unit vector from the point of interest to the location of the quadrupole moment. The simplest example of an electric quadrupole consists of alternating positive and negative charges, the monopole moment of this arrangement is zero. Similarly, the moment is zero, regardless of the coordinate origin that has been chosen. But the quadrupole moment of the arrangement in the diagram cannot be reduced to zero, an extreme generalization would be, Eight alternating point charges at the eight corners of a parallelepiped, e. g. of a cube with edge length a. The octopole moment of this arrangement would correspond, in the limit lim a →0. Still higher multipoles, e. g. of order 2l, would be obtained by dipolar arrangements of point dipoles, not point monopoles, of lower order, all known magnetic sources give dipole fields. However, to make a magnetic quadrupole it is possible to place four identical bar magnets perpendicular to other such that the north pole of one is next to the south of the other. Such a configuration cancels the dipole moment and gives a quadrupole moment, an example of a magnetic quadrupole, involving permanent magnets, is depicted on the right. Electromagnets of similar design are commonly used to focus beams of charged particles in particle accelerators and beam transport lines. The quadrupole-dipole intersect can be found by multiplying the spin of the unpaired nucleon by its parent atom, there are four steel pole tips, two opposing magnetic north poles and two opposing magnetic south poles. The steel is magnetized by an electric current that flows in the coils of tubing wrapped around the poles. A changing magnetic quadrupole moment produces electromagnetic radiation, the gravitational potential is then expressed as, V q = − G121 | R |3 ∑ i, j Q i j n i n j. For example, because the Earth is rotating, it is oblate and this gives it a nonzero quadrupole moment. However, only quadrupole and higher moments can radiate gravitationally, the mass monopole represents the total mass-energy in a system, which is conserved—thus it gives off no radiation
9.
Fine structure
–
In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to electron spin and relativistic corrections to the non-relativistic Schrödinger equation. The gross structure of spectra is the line spectra predicted by the quantum mechanics of non-relativistic electrons with no spin. For a hydrogenic atom, the gross structure energy levels depend on the principal quantum number n. However, an accurate model takes into account relativistic and spin effects. The fine structure energy corrections can be obtained by using perturbation theory, to do this one adds three corrective terms to the Hamiltonian, the leading order relativistic correction to the kinetic energy, the correction due to the spin-orbit coupling, and the Darwinian term. These corrections can also be obtained from the limit of the Dirac equation, since Diracs theory naturally incorporates relativity. Classically, the energy term of the Hamiltonian is T = p 22 m where p is the momentum. However, when considering a more accurate theory of nature via, R is the distance of the electron from the nucleus. The spin-orbit correction can be understood by shifting from the frame of reference into one where the electron is stationary. In this case the orbiting nucleus functions as a current loop. However, the electron itself has a magnetic moment due to its angular momentum. The two magnetic vectors, B → and μ → s couple together so there is a certain energy cost depending on their relative orientation. Remark, On the = and = energy level, which the fine structure said their level are the same, if we take the g-factor to be 2.0031904622, then, the calculated energy level will be different by using 2 as g-factor. Only using 2 as the g-factor, we can match the level in the 1st order approximation of the relativistic correction. When using the higher order approximation for the term, the 2.0031904622 g-factor may agree with each other. However, if we use the g-factor as 2.0031904622, the result does not agree with the formula, there is one last term in the non-relativistic expansion of the Dirac equation. This is because the function of an electron with l >0 vanishes at the origin. For example, it gives the 2s-orbit the same energy as the 2p-orbit by raising the 2s-state by 9. 057×10−5 eV, the Darwin term changes the effective potential at the nucleus
10.
Magnetic moment
–
The magnetic moment of a magnet is a quantity that determines the torque it will experience in an external magnetic field. A loop of current, a bar magnet, an electron, a molecule. The magnetic moment may be considered to be a vector having a magnitude, the direction of the magnetic moment points from the south to north pole of the magnet. The magnetic field produced by the magnet is proportional to its magnetic moment, more precisely, the term magnetic moment normally refers to a systems magnetic dipole moment, which produces the first term in the multipole expansion of a general magnetic field. The dipole component of a magnetic field is symmetric about the direction of its magnetic dipole moment. The magnetic moment is defined as a vector relating the aligning torque on the object from an applied magnetic field to the field vector itself. The relationship is given by, τ = μ × B where τ is the acting on the dipole and B is the external magnetic field. This definition is based on how one would measure the magnetic moment, in principle, the unit for magnetic moment is not a base unit in the International System of Units. As the torque is measured in newton-meters and the field in teslas. This has equivalents in other units, N·m/T = A·m2 = J/T where A is amperes. In the CGS system, there are different sets of electromagnetism units, of which the main ones are ESU, Gaussian. The ratio of these two non-equivalent CGS units is equal to the speed of light in space, expressed in cm·s−1. All formulae in this article are correct in SI units, they may need to be changed for use in other unit systems. For example, in SI units, a loop of current with current I and area A has magnetic moment IA, the preferred classical explanation of a magnetic moment has changed over time. Before the 1930s, textbooks explained the moment using hypothetical magnetic point charges, since then, most have defined it in terms of Ampèrian currents. The sources of magnetic moments in materials can be represented by poles in analogy to electrostatics, consider a bar magnet which has magnetic poles of equal magnitude but opposite polarity. Each pole is the source of force which weakens with distance. Since magnetic poles always come in pairs, their forces partially cancel each other because while one pole pulls and this cancellation is greatest when the poles are close to each other i. e. when the bar magnet is short
11.
Azimuthal quantum number
–
The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. The azimuthal quantum number is the second of a set of numbers which describe the unique quantum state of an electron. It is also known as the angular momentum quantum number, orbital quantum number or second quantum number. Connected with the states of the atoms electrons are four quantum numbers, n, ℓ, mℓ. These specify the complete, unique quantum state of an electron in an atom. The wavefunction of the Schrödinger equation reduces to three equations that when solved, lead to the first three quantum numbers, therefore, the equations for the first three quantum numbers are all interrelated. The azimuthal quantum number arose in the solution of the part of the wave equation as shown below. Generally, the coordinate system works best with spherical models, the cylindrical system with cylinders. The quantum number ℓ is always an integer,0,1,2,3. While many introductory textbooks on quantum mechanics will refer to L by itself, when referring to angular momentum, it is better to simply use the quantum number ℓ. Atomic orbitals have distinctive shapes denoted by letters, in the illustration, the letters s, p, and d describe the shape of the atomic orbital. Their wavefunctions take the form of spherical harmonics, and so are described by Legendre polynomials, one mnemonic to remember the sequence S. P. D. F. G. H. is Sober Physicists Dont Find Giraffes Hiding In Kitchens Like My Nephew. A few other mnemonics are Smart People Dont Fail, Silly People Drive Fast, silly professors dance funny, Scott picks dead flowers, son pieno di figa, each of the different angular momentum states can take 2 electrons. This is because the quantum number mℓ runs from −ℓ to ℓ in integer units. Each distinct n, ℓ, mℓ orbital can be occupied by two electrons with opposing spins, giving 2 electrons overall, orbitals with higher ℓ than given in the table are perfectly permissible, but these values cover all atoms so far discovered. Generally speaking, the number of electrons in the nth energy level is 2n2. The angular momentum quantum number, ℓ, governs the number of planar nodes going through the nucleus, a planar node can be described in an electromagnetic wave as the midpoint between crest and trough, which has zero magnitude. In an s orbital, no nodes go through the nucleus, in a p orbital, one node traverses the nucleus and therefore ℓ has the value of 1
12.
Atomic nucleus
–
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
13.
Hydrogen atom
–
A hydrogen atom is an atom of the chemical element hydrogen. The electrically neutral atom contains a positively charged proton and a single negatively charged electron bound to the nucleus by the Coulomb force. Atomic hydrogen constitutes about 75% of the mass of the universe. In everyday life on Earth, isolated hydrogen atoms are extremely rare, instead, hydrogen tends to combine with other atoms in compounds, or with itself to form ordinary hydrogen gas, H2. Atomic hydrogen and hydrogen atom in ordinary English use have overlapping, yet distinct, for example, a water molecule contains two hydrogen atoms, but does not contain atomic hydrogen. Attempts to develop an understanding of the hydrogen atom have been important to the history of quantum mechanics. The most abundant isotope, hydrogen-1, protium, or light hydrogen, contains no neutrons and is just a proton, protium is stable and makes up 99. 9885% of naturally occurring hydrogen by absolute number. Deuterium contains one neutron and one proton, deuterium is stable and makes up 0. 0115% of naturally occurring hydrogen and is used in industrial processes like nuclear reactors and Nuclear Magnetic Resonance. Tritium contains two neutrons and one proton and is not stable, decaying with a half-life of 12.32 years, because of the short half life, Tritium does not exist in nature except in trace amounts. Higher isotopes of hydrogen are only created in artificial accelerators and reactors and have half lives around the order of 10−22 seconds, the formulas below are valid for all three isotopes of hydrogen, but slightly different values of the Rydberg constant must be used for each hydrogen isotope. Hydrogen is not found without its electron in ordinary chemistry, as ionized hydrogen is highly chemically reactive. When ionized hydrogen is written as H+ as in the solvation of classical acids such as hydrochloric acid, in that case, the acid transfers the proton to H2O to form H3O+. Ionized hydrogen without its electron, or free protons, are common in the interstellar medium, experiments by Ernest Rutherford in 1909 showed the structure of the atom to be a dense, positive nucleus with a light, negative charge orbiting around it. This immediately caused problems on how such a system could be stable, classical electromagnetism had shown that any accelerating charge radiates energy described through the Larmor formula. If this were true, all atoms would instantly collapse, however seem to be stable. Furthermore, the spiral inward would release a smear of electromagnetic frequencies as the orbit got smaller, instead, atoms were observed to only emit discrete frequencies of radiation. The resolution would lie in the development of quantum mechanics, in 1913, Niels Bohr obtained the energy levels and spectral frequencies of the hydrogen atom after making a number of simple assumptions in order to correct the failed classical model. The assumptions included, Electrons can only be in certain, discrete circular orbits or stationary states, thereby having a set of possible radii
14.
Albert A. Michelson
–
Albert Abraham Michelson was an American physicist known for his work on the measurement of the speed of light and especially for the Michelson–Morley experiment. In 1907 he received the Nobel Prize in Physics and he became the first American to receive the Nobel Prize in sciences. Michelson was born in Strzelno, Province of Posen in Prussia into a Jewish family and he moved to the US with his parents in 1855, at the age of two. He grew up in the towns of Murphys Camp, California and Virginia City, Nevada. His family was Jewish by birth but non-religious, and Michelson himself was a lifelong agnostic and he spent his high school years in San Francisco in the home of his aunt, Henriette Levy, who was the mother of author Harriet Lane Levy. President Ulysses S. Grant awarded Michelson a special appointment to the U. S. Naval Academy in 1869, during his four years as a midshipman at the Academy, Michelson excelled in optics, heat, climatology and drawing. After graduating in 1873 and two years at sea, he returned to the Naval Academy in 1875 to become an instructor in physics, in 1879, he was posted to the Nautical Almanac Office, Washington, to work with Simon Newcomb. In the following year he obtained leave of absence to continue his studies in Europe and he visited the Universities of Berlin and Heidelberg, and the Collège de France and École Polytechnique in Paris. In 1877, he married Margaret Hemingway, daughter of a wealthy New York stockbroker and lawyer and they had two sons and a daughter. Michelson was fascinated with the sciences, and the problem of measuring the speed of light in particular, while at Annapolis, he conducted his first experiments of the speed of light, as part of a class demonstration in 1877. After two years of studies in Europe, he resigned from the Navy in 1881, in 1883 he accepted a position as professor of physics at the Case School of Applied Science in Cleveland, Ohio and concentrated on developing an improved interferometer. In 1887 he and Edward Morley carried out the famous Michelson–Morley experiment which failed to detect evidence of the existence of the luminiferous ether and he later moved on to use astronomical interferometers in the measurement of stellar diameters and in measuring the separations of binary stars. In 1899, he married Edna Stanton and they raised one son and three daughters. He also won the Copley Medal in 1907, the Henry Draper Medal in 1916, a crater on the Moon is named after him. Michelson died in Pasadena, California at the age of 78, the University of Chicago Residence Halls remembered Michelson and his achievements by dedicating Michelson House in his honor. Case Western Reserve has dedicated a Michelson House to him, clark University named a theatre after him. Michelson Laboratory at Naval Air Weapons Station China Lake in Ridgecrest, there is a display in the publicly accessible area of the Lab which includes facsimiles of Michelsons Nobel Prize medal, the prize document, and examples of his diffraction gratings. Michelson published his result of 299,910 ±50 km/s in 1879 before joining Newcomb in Washington DC to assist with his measurements there, thus began a long professional collaboration and friendship between the two
15.
Wolfgang Pauli
–
Wolfgang Ernst Pauli was an Austrian-born Swiss and American theoretical physicist and one of the pioneers of quantum physics. The discovery involved spin theory, which is the basis of a theory of the structure of matter, Pauli was born in Vienna to a chemist Wolfgang Joseph Pauli and his wife Bertha Camilla Schütz, his sister was Hertha Pauli, the writer and actress. Paulis middle name was given in honor of his godfather, physicist Ernst Mach, Paulis paternal grandparents were from prominent Jewish families of Prague, his great-grandfather was the Jewish publisher Wolf Pascheles. Paulis father converted from Judaism to Roman Catholicism shortly before his marriage in 1899, Paulis mother, Bertha Schütz, was raised in her own mothers Roman Catholic religion, her father was Jewish writer Friedrich Schütz. Pauli was raised as a Roman Catholic, although eventually he and he is considered to have been a deist and a mystic. Pauli attended the Döblinger-Gymnasium in Vienna, graduating with distinction in 1918, only two months after graduation, he published his first paper, on Albert Einsteins theory of general relativity. He attended the Ludwig-Maximilians University in Munich, working under Arnold Sommerfeld, Sommerfeld asked Pauli to review the theory of relativity for the Encyklopädie der mathematischen Wissenschaften. Two months after receiving his doctorate, Pauli completed the article and it was praised by Einstein, published as a monograph, it remains a standard reference on the subject to this day. From 1923 to 1928, he was a lecturer at the University of Hamburg, during this period, Pauli was instrumental in the development of the modern theory of quantum mechanics. In particular, he formulated the principle and the theory of nonrelativistic spin. In 1928, he was appointed Professor of Theoretical Physics at ETH Zurich in Switzerland where he made significant scientific progress and he held visiting professorships at the University of Michigan in 1931, and the Institute for Advanced Study in Princeton in 1935. He was awarded the Lorentz Medal in 1931, at the end of 1930, shortly after his postulation of the neutrino and immediately following his divorce and the suicide of his mother, Pauli experienced a personal crisis. He consulted psychiatrist and psychotherapist Carl Jung who, like Pauli, Jung immediately began interpreting Paulis deeply archetypal dreams, and Pauli became one of the depth psychologists best students. He soon began to criticize the epistemology of Jungs theory scientifically, a great many of these discussions are documented in the Pauli/Jung letters, today published as Atom and Archetype. Jungs elaborate analysis of more than 400 of Paulis dreams is documented in Psychology, the German annexation of Austria in 1938 made him a German citizen, which became a problem for him in 1939 after the outbreak of World War II. In 1940, he tried in vain to obtain Swiss citizenship, Pauli moved to the United States in 1940, where he was employed as a professor of theoretical physics at the Institute for Advanced Study. In 1946, after the war, he became a citizen of the United States and subsequently returned to Zurich. In 1949, he was granted Swiss citizenship, in 1958, Pauli was awarded the Max Planck medal
16.
Electromagnetism
–
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as fields, magnetic fields. The other three fundamental interactions are the interaction, the weak interaction, and gravitation. The word electromagnetism is a form of two Greek terms, ἤλεκτρον, ēlektron, amber, and μαγνῆτις λίθος magnētis lithos, which means magnesian stone. The electromagnetic force plays a role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of forces between individual atoms and molecules in matter, and is a manifestation of the electromagnetic force. Electrons are bound by the force to atomic nuclei, and their orbital shapes. The electromagnetic force governs the processes involved in chemistry, which arise from interactions between the electrons of neighboring atoms, there are numerous mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric potential, although electromagnetism is considered one of the four fundamental forces, at high energy the weak force and electromagnetic force are unified as a single electroweak force. In the history of the universe, during the epoch the unified force broke into the two separate forces as the universe cooled. Originally, electricity and magnetism were considered to be two separate forces, Magnetic poles attract or repel one another in a manner similar to positive and negative charges and always exist as pairs, every north pole is yoked to a south pole. An electric current inside a wire creates a corresponding magnetic field outside the wire. Its direction depends on the direction of the current in the wire. A current is induced in a loop of wire when it is moved toward or away from a field, or a magnet is moved towards or away from it. While preparing for a lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation. As he was setting up his materials, he noticed a compass needle deflected away from north when the electric current from the battery he was using was switched on. At the time of discovery, Ørsted did not suggest any explanation of the phenomenon. However, three later he began more intensive investigations
17.
Dipole
–
In electromagnetism, there are two kinds of dipoles, An electric dipole is a separation of positive and negative charges. The simplest example of this is a pair of electric charges of equal magnitude but opposite sign, a permanent electric dipole is called an electret. A magnetic dipole is a circulation of electric current. A simple example of this is a loop of wire with some constant current through it. Dipoles can be characterized by their moment, a vector quantity. For the current loop, the dipole moment points through the loop. In addition to current loops, the electron, among other fundamental particles, has a dipole moment. That is because it generates a field that is identical to that generated by a very small current loop. However, the magnetic moment is not due to a current loop. It is also possible that the electron has a dipole moment although it has not yet been observed. A permanent magnet, such as a bar magnet, owes its magnetism to the magnetic dipole moment of the electron. The two ends of a bar magnet are referred to as poles, and may be labeled north and south, the dipole moment of the bar magnet points from its magnetic south to its magnetic north pole. The north pole of a bar magnet in a compass points north, however, that means that Earths geomagnetic north pole is the south pole of its dipole moment and vice versa. The only known mechanisms for the creation of magnetic dipoles are by current loops or quantum-mechanical spin since the existence of magnetic monopoles has never been experimentally demonstrated, the term comes from the Greek δίς, twice and πόλος, axis. A physical dipole consists of two equal and opposite point charges, in the sense, two poles. Its field at large distances depends almost entirely on the moment as defined above. A point dipole is the limit obtained by letting the separation tend to 0 while keeping the dipole moment fixed, the field of a point dipole has a particularly simple form, and the order-1 term in the multipole expansion is precisely the point dipole field. Although there are no magnetic monopoles in nature, there are magnetic dipoles in the form of the quantum-mechanical spin associated with particles such as electrons
18.
Spin (physics)
–
In quantum mechanics and particle physics, spin is an intrinsic form of angular momentum carried by elementary particles, composite particles, and atomic nuclei. Spin is one of two types of angular momentum in mechanics, the other being orbital angular momentum. In some ways, spin is like a vector quantity, it has a definite magnitude, all elementary particles of a given kind have the same magnitude of spin angular momentum, which is indicated by assigning the particle a spin quantum number. The SI unit of spin is the or, just as with classical angular momentum, very often, the spin quantum number is simply called spin leaving its meaning as the unitless spin quantum number to be inferred from context. When combined with the theorem, the spin of electrons results in the Pauli exclusion principle. Wolfgang Pauli was the first to propose the concept of spin, in 1925, Ralph Kronig, George Uhlenbeck and Samuel Goudsmit at Leiden University suggested an physical interpretation of particles spinning around their own axis. The mathematical theory was worked out in depth by Pauli in 1927, when Paul Dirac derived his relativistic quantum mechanics in 1928, electron spin was an essential part of it. As the name suggests, spin was originally conceived as the rotation of a particle around some axis and this picture is correct so far as spin obeys the same mathematical laws as quantized angular momenta do. On the other hand, spin has some properties that distinguish it from orbital angular momenta. Although the direction of its spin can be changed, a particle cannot be made to spin faster or slower. The spin of a particle is associated with a magnetic dipole moment with a g-factor differing from 1. This could only occur if the internal charge of the particle were distributed differently from its mass. The conventional definition of the quantum number, s, is s = n/2. Hence the allowed values of s are 0, 1/2,1, 3/2,2, the value of s for an elementary particle depends only on the type of particle, and cannot be altered in any known way. The spin angular momentum, S, of any system is quantized. The allowed values of S are S = ℏ s = h 4 π n, in contrast, orbital angular momentum can only take on integer values of s, i. e. even-numbered values of n. Those particles with half-integer spins, such as 1/2, 3/2, 5/2, are known as fermions, while particles with integer spins. The two families of particles obey different rules and broadly have different roles in the world around us, a key distinction between the two families is that fermions obey the Pauli exclusion principle, that is, there cannot be two identical fermions simultaneously having the same quantum numbers
19.
G-factor (physics)
–
A g-factor is a dimensionless quantity that characterizes the magnetic moment and gyromagnetic ratio of an atom, a particle or nucleus. Protons, neutrons, nuclei and other composite baryonic particles have magnetic moments arising from their spin, conventionally, the associated g-factors are defined using the nuclear magneton, and thus implicitly using the protons mass rather than the particles mass as for a Dirac particle. There are three magnetic moments associated with an electron, one from its angular momentum, one from its orbital angular momentum. In atomic physics, the electron spin g-factor is often defined as the value or negative of ge. The z-component of the moment then becomes μ z = − g s μ B m s The value gs is roughly equal to 2.002319. The reason it is not precisely two is explained by quantum electrodynamics calculation of the magnetic dipole moment. For an infinite mass nucleus, the value of gL is exactly equal to one, the value of gJ is related to gL and gs by a quantum-mechanical argument, see the article Landé g-factor. That the muon g-factor is not quite the same as the electron g-factor is mostly explained by quantum electrodynamics and these are entirely a result of the mass difference between the particles. However, not all of the difference between the g-factors for electrons and muons is exactly explained by the Standard Model. The muon g-factor can, in theory, be affected by physics beyond the Standard Model, so it has been measured very precisely, in particular at the Brookhaven National Laboratory. In the E821 collaboration final report in November 2006, the measured value is 2.0023318416. This is a difference of 3.4 standard deviations, suggesting that beyond-the-Standard-Model physics may be having an effect, the Brookhaven muon storage ring has been transported to Fermilab where the g−2 experiment will use it to make more precise measurements of muon g-factor. The electron g-factor is one of the most precisely measured values in physics, anomalous magnetic dipole moment Electron magnetic moment CODATA recommendations 2006
20.
Angular momentum
–
In physics, angular momentum is the rotational analog of linear momentum. It is an important quantity in physics because it is a conserved quantity – the angular momentum of a system remains constant unless acted on by an external torque. The definition of momentum for a point particle is a pseudovector r×p. This definition can be applied to each point in continua like solids or fluids, unlike momentum, angular momentum does depend on where the origin is chosen, since the particles position is measured from it. The angular momentum of an object can also be connected to the angular velocity ω of the object via the moment of inertia I. However, while ω always points in the direction of the rotation axis, Angular momentum is additive, the total angular momentum of a system is the vector sum of the angular momenta. For continua or fields one uses integration, torque can be defined as the rate of change of angular momentum, analogous to force. Applications include the gyrocompass, control moment gyroscope, inertial systems, reaction wheels, flying discs or Frisbees. In general, conservation does limit the motion of a system. In quantum mechanics, angular momentum is an operator with quantized eigenvalues, Angular momentum is subject to the Heisenberg uncertainty principle, meaning only one component can be measured with definite precision, the other two cannot. Also, the spin of elementary particles does not correspond to literal spinning motion, Angular momentum is a vector quantity that represents the product of a bodys rotational inertia and rotational velocity about a particular axis. Angular momentum can be considered an analog of linear momentum. Thus, where momentum is proportional to mass m and linear speed v, p = m v, angular momentum is proportional to moment of inertia I. Unlike mass, which only on amount of matter, moment of inertia is also dependent on the position of the axis of rotation. Unlike linear speed, which occurs in a line, angular speed occurs about a center of rotation. Therefore, strictly speaking, L should be referred to as the angular momentum relative to that center and this simple analysis can also apply to non-circular motion if only the component of the motion which is perpendicular to the radius vector is considered. In that case, L = r m v ⊥, where v ⊥ = v sin θ is the component of the motion. It is this definition, × to which the moment of momentum refers
21.
Electric current
–
An electric current is a flow of electric charge. In electric circuits this charge is carried by moving electrons in a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionised gas. The SI unit for measuring a current is the ampere. Electric current is measured using a device called an ammeter, electric currents cause Joule heating, which creates light in incandescent light bulbs. They also create magnetic fields, which are used in motors, inductors and generators, the particles that carry the charge in an electric current are called charge carriers. In metals, one or more electrons from each atom are loosely bound to the atom and these conduction electrons are the charge carriers in metal conductors. The conventional symbol for current is I, which originates from the French phrase intensité de courant, current intensity is often referred to simply as current. The I symbol was used by André-Marie Ampère, after whom the unit of current is named, in formulating the eponymous Ampères force law. The notation travelled from France to Great Britain, where it became standard, in a conductive material, the moving charged particles which constitute the electric current are called charge carriers. In other materials, notably the semiconductors, the carriers can be positive or negative. Positive and negative charge carriers may even be present at the same time, a flow of positive charges gives the same electric current, and has the same effect in a circuit, as an equal flow of negative charges in the opposite direction. Since current can be the flow of positive or negative charges. The direction of current is arbitrarily defined as the same direction as positive charges flow. This is called the direction of current I. If the current flows in the direction, the variable I has a negative value. When analyzing electrical circuits, the direction of current through a specific circuit element is usually unknown. Consequently, the directions of currents are often assigned arbitrarily
22.
Angular momentum coupling
–
In quantum mechanics, the procedure of constructing eigenstates of total angular momentum out of eigenstates of separate angular momenta is called angular momentum coupling. For instance, the orbit and spin of a particle can interact through spin–orbit interaction. In both cases the angular momenta are no longer constants of motion, but the sum of the two angular momenta usually still is. Angular momentum coupling in atoms is of importance in atomic spectroscopy, Angular momentum coupling of electron spins is of importance in quantum chemistry. Also in the shell model angular momentum coupling is ubiquitous. In astronomy, spin-orbit coupling reflects the law of conservation of angular momentum. This is more known as orbital resonance. Often, the physical effects are tidal forces. Conservation of angular momentum is the principle that the angular momentum of a system has a constant magnitude. Angular momentum is a property of a system that is a constant of motion in two situations, The system experiences a spherically symmetric potential field. The system moves in isotropic space, in both cases the angular momentum operator commutes with the Hamiltonian of the system. By Heisenbergs uncertainty relation this means that the momentum and the energy can be measured at the same time. An example of the first situation is an atom whose electrons only experiences the Coulomb force of its atomic nucleus, if we ignore the electron-electron interaction, the orbital angular momentum l of each electron commutes with the total Hamiltonian. In this model the atomic Hamiltonian is a sum of energies of the electrons. The individual electron angular momenta li commute with this Hamiltonian and that is, they are conserved properties of this approximate model of the atom. An example of the situation is a rigid rotor moving in field-free space. A rigid rotor has a well-defined, time-independent, angular momentum and these two situations originate in classical mechanics. The third kind of conserved angular momentum, associated with spin, however, all rules of angular momentum coupling apply to spin as well
23.
Tensor
–
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors. Elementary examples of such include the dot product, the cross product. Geometric vectors, often used in physics and engineering applications, given a coordinate basis or fixed frame of reference, a tensor can be represented as an organized multidimensional array of numerical values. The order of a tensor is the dimensionality of the array needed to represent it, or equivalently, for example, a linear map is represented by a matrix in a basis, and therefore is a 2nd-order tensor. A vector is represented as a 1-dimensional array in a basis, scalars are single numbers and are thus 0th-order tensors. Because they express a relationship between vectors, tensors themselves must be independent of a choice of coordinate system. The precise form of the transformation law determines the type of the tensor, the tensor type is a pair of natural numbers, where n is the number of contravariant indices and m is the number of covariant indices. The total order of a tensor is the sum of two numbers. The concept enabled an alternative formulation of the differential geometry of a manifold in the form of the Riemann curvature tensor. There are several approaches to defining tensors, although seemingly different, the approaches just describe the same geometric concept using different languages and at different levels of abstraction. For example, an operator is represented in a basis as a two-dimensional square n × n array. The numbers in the array are known as the scalar components of the tensor or simply its components. They are denoted by giving their position in the array, as subscripts and superscripts. For example, the components of an order 2 tensor T could be denoted Tij , whether an index is displayed as a superscript or subscript depends on the transformation properties of the tensor, described below. The total number of required to identify each component uniquely is equal to the dimension of the array. However, the term generally has another meaning in the context of matrices. Just as the components of a change when we change the basis of the vector space. Each tensor comes equipped with a law that details how the components of the tensor respond to a change of basis
24.
Irreducible representation
–
Every finite-dimensional unitary representation on a Hermitian vector space V is the direct sum of irreducible representations. The structure analogous to a representation in the resulting theory is a simple module. Let ρ be a representation i. e. a homomorphism ρ, G → G L of a group G where V is a space over a field F. If we pick a basis B for V, ρ can be thought of as a function from a group into a set of invertible matrices, however, it simplifies things greatly if we think of the space V without a basis. A linear subspace W ⊂ V is called G -invariant if ρ w ∈ W for all g ∈ G, the restriction of ρ to a G -invariant subspace W ⊂ V is known as a subrepresentation. A representation ρ, G → G L is said to be if it has only trivial subrepresentations. If there is a proper non-trivial invariant subspace, ρ is said to be reducible, Group elements can be represented by matrices, although the term represented has a specific and precise meaning in this context. A representation of a group is a mapping from the elements to the general linear group of matrices. The representations D and D are said to be equivalent representations, K, although some authors just write the numerical label without brackets. The dimension of D is the sum of the dimensions of the blocks, d i m = d i m + d i m + … + d i m If this is not possible, then the representation is indecomposable. Identifying the irreducible representations therefore allows one to label the states, predict how they will split under perturbations and this allows them to derive relativistic wave equations. The theory of groups and quantum mechanics, a. D. Boardman, D. E. OConner, P. A. Young. Symmetry and its applications in science, Group theory in quantum mechanics, an introduction to its present usage. Group Theory in Quantum Mechanics, An Introduction to Its Present Usage, manchester Physics Series, John Wiley & Sons. Weinberg, S, The Quantum Theory of Fields,1, Cambridge university press, molecular Quantum Mechanics, An introduction to quantum chemistry. Group theoretical discussion of wave equations. On Unitary Representations Of The Inhomogeneous Lorentz Group, commission on Mathematical and Theoretical Crystallography, Summer Schools on Mathematical Crystallography. Some Notes on Young Tableaux as useful for irreps of su. Hunt, Representations of Lorentz and Poincaré groups
25.
Del
–
Del, or nabla, is an operator used in mathematics, in particular, in vector calculus, as a vector differential operator, usually represented by the nabla symbol ∇. When applied to a function defined on a domain, it denotes its standard derivative as defined in calculus. When applied to a field, del may denote the gradient of a scalar field, strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember. These formal products do not necessarily commute with other operators or products, del is used as a shorthand form to simplify many long mathematical expressions. It is most commonly used to simplify expressions for the gradient, divergence, curl, directional derivative, and Laplacian. In particular, if a hill is defined as a function over a plane h. The magnitude of the gradient is the value of this steepest slope, when operating on a vector it must be distributed to each component. The Laplacian is ubiquitous throughout modern mathematical physics, appearing for example in Laplaces equation, Poissons equation, the equation, the wave equation. Del can also be applied to a field with the result being a tensor. The tensor derivative of a vector field v → is a 9-term second-rank tensor – that is, a 3×3 matrix – but can be denoted simply as ∇ ⊗ v →, where ⊗ represents the dyadic product. This quantity is equivalent to the transpose of the Jacobian matrix of the field with respect to space. The divergence of the field can then be expressed as the trace of this matrix. Because of the diversity of vector products one application of del already gives rise to three major derivatives, the gradient, divergence, and curl and this is part of the value to be gained in notationally representing this operator as a vector. Though one can often replace del with a vector and obtain an identity, making those identities mnemonic. Whereas a vector is an object with both a magnitude and direction, del has neither a magnitude nor a direction until it operates on a function. For that reason, identities involving del must be derived with care, schey, H. M. Div, Grad, Curl, and All That, An Informal Text on Vector Calculus. Earliest Uses of Symbols of Calculus, NA Digest, Volume 98, Issue 03. A survey of the use of ∇ in vector analysis Tai
26.
Selection rule
–
In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in atomic nuclei, the selection rules may differ according to the technique used to observe the transition. In the following, mainly atomic and molecular transitions are considered, if the value of this integral is zero the transition is forbidden. In practice, the integral itself does not need to be calculated to determine a selection rule and it is sufficient to determine the symmetry of transition moment function, ψ1 ∗ μ ψ2. If the symmetry of this function spans the totally symmetric representation of the point group to which the atom or molecule belongs then its value is not zero and the transition is allowed. The transition moment integral is zero if the transition moment function, ψ1 ∗ μ ψ2, is anti-symmetric or odd, the symmetry of the transition moment function is the direct product of the parities of its three components. The symmetry characteristics of each component can be obtained from standard character tables, rules for obtaining the symmetries of a direct product can be found in texts on character tables. The Laporte rule is a selection rule formally stated as follows, In a centrosymmetric environment, the Laporte rule applies to electric dipole transitions, so the operator has u symmetry. P orbitals also have u symmetry, so the symmetry of the transition moment function is given by the triple product u×u×u, likewise, d orbitals have g symmetry, so the triple product g×u×g also has u symmetry and the transition is forbidden. The wave function of an electron is the product of a space-dependent wave function. Spin is directional and can be said to have odd parity and it follows that transitions in which the spin direction changes are forbidden. In formal terms, only states with the total spin quantum number are spin-allowed. In crystal field theory, d-d transitions that are spin-forbidden are much weaker than spin-allowed transitions, both can be observed, in spite of the Laporte rule, because the actual transitions are coupled to vibrations that are anti-symmetric and have the same symmetry as the dipole moment operator. In vibrational spectroscopy, transitions are observed between different vibrational states, in a fundamental vibration, the molecule is excited from its ground state to the first excited state. The symmetry of the wave function is the same as that of the molecule. It is, therefore, a basis for the totally symmetric representation in the point group of the molecule. It follows that, for a transition to be allowed. In infrared spectroscopy, the transition moment operator transforms as either x and/or y and/or z, the excited state wave function must also transform as at least one of these vectors
27.
Electron paramagnetic resonance
–
Electron paramagnetic resonance or electron spin resonance spectroscopy is a method for studying materials with unpaired electrons. The basic concepts of EPR are analogous to those of nuclear magnetic resonance, EPR spectroscopy is particularly useful for studying metal complexes or organic radicals. EPR was first observed in Kazan State University by Soviet physicist Yevgeny Zavoisky in 1944, and was developed independently at the same time by Brebis Bleaney at the University of Oxford. Every electron has a moment and spin quantum number s =12, with magnetic components m s = +12 and m s = −12.0023 for the free electron. Therefore, the separation between the lower and the state is Δ E = g e μ B B0 for unpaired free electrons. This equation implies that the splitting of the levels is directly proportional to the magnetic fields strength. An unpaired electron can move between the two levels by either absorbing or emitting a photon of energy h ν such that the resonance condition. This leads to the equation of EPR spectroscopy, h ν = g e μ B B0. Furthermore, EPR spectra can be generated by varying the photon frequency incident on a sample while holding the magnetic field constant or doing the reverse. In practice, it is usually the frequency that is kept fixed, a collection of paramagnetic centers, such as free radicals, is exposed to microwaves at a fixed frequency. At this point the electrons can move between their two spin states. The upper spectrum below is the absorption for a system of free electrons in a varying magnetic field. The lower spectrum is the first derivative of the absorption spectrum, the latter is the most common way to record and publish EPR spectra. For the microwave frequency of 9388.2 MHz, the predicted resonance occurs at a field of about B0 = h ν / g e μ B =0.3350 teslas =3350 gausses. For example, for the field of 3350 G shown at the right, in practice, EPR samples consist of collections of many paramagnetic species, and not single isolated paramagnetic centers. At 298 K, X-band microwave frequencies give n upper / n lower ≈0.998, therefore, transitions from the lower to the higher level are more probable than the reverse, which is why there is a net absorption of energy. With k f and P being constants, N min ~ −1, i. e. N min ~ ν − α, in practice, α can change varying from 0.5 to 4.5 depending on spectrometer characteristics, resonance conditions, and sample size. A great sensitivity is obtained with a low detection limit N min
28.
Radical (chemistry)
–
In chemistry, a radical is an atom, molecule, or ion that has an unpaired valence electron. Most radicals are reasonably stable only at low concentrations in inert media or in a vacuum. A notable example of a radical is the hydroxyl radical. Two other examples are triplet oxygen and triplet carbene which have two unpaired electrons, free radicals may be created in a number of ways, including synthesis with very dilute or rarefied reagents, reactions at very low temperatures, or breakup of larger molecules. The latter can be affected by any process that puts energy into the parent molecule, such as ionizing radiation, heat, electrical discharges, electrolysis. Radicals are intermediate stages in many chemical reactions, free radicals play an important role in combustion, atmospheric chemistry, polymerization, plasma chemistry, biochemistry, and many other chemical processes. In living organisms, the free radicals superoxide and nitric oxide and their reaction products regulate many processes, such as control of vascular tone and they also play a key role in the intermediary metabolism of various biological compounds. Such radicals can even be messengers in a process dubbed redox signaling, a radical may be trapped within a solvent cage or be otherwise bound. The qualifier free was then needed to specify the unbound case, following recent nomenclature revisions, a part of a larger molecule is now called a functional group or substituent, and radical now implies free. However, the old nomenclature may still appear in some books, the term radical was already in use when the now obsolete radical theory was developed. Louis-Bernard Guyton de Morveau introduced the phrase radical in 1785 and the phrase was employed by Antoine Lavoisier in 1789 in his Traité Élémentaire de Chimie, a radical was then identified as the root base of certain acids. Historically, the radical in radical theory was also used for bound parts of the molecule. These are now called functional groups, for example, methyl alcohol was described as consisting of a methyl radical and a hydroxyl radical. In a modern context the first organic free radical identified was triphenylmethyl radical and this species was discovered by Moses Gomberg in 1900 at the University of Michigan USA. In 1933 Morris Kharash and Frank Mayo proposed that free radicals were responsible for anti-Markovnikov addition of hydrogen bromide to allyl bromide. It should be noted that the electron of the breaking bond also moves to pair up with the attacking radical electron. Free radicals also take part in addition and radical substitution as reactive intermediates. Chain reactions involving free radicals can usually be divided into three distinct processes and these are initiation, propagation, and termination
29.
Transition metal
–
Many scientists describe a transition metal as any element in the d-block of the periodic table, which includes groups 3 to 12 on the periodic table. In actual practice, the lanthanide and actinide series are also considered transition metals and are called inner transition metals. Cotton and Wilkinson expand the brief IUPAC definition by specifying which elements are included, as well as the elements of groups 4 to 11, they add scandium and yttrium in group 3 which have a partially filled d subshell in the metallic state. These last two elements are included even though they do not seem to possess the properties which are so characteristic of the transition metals in general. Lanthanum and actinium in Group 3 are however classified as lanthanides and actinides respectively and these elements are now known as the d-block. In the d-block the atoms of the elements have between 1 and 10 d electrons, Sc and Y in Group 3 are also generally recognized as transition metals. However the elements La–Lu and Ac–Lr and Group 12 attract different definitions from different authors, many chemistry textbooks and printed periodic tables classify La and Ac as Group 3 elements and transition metals, since their atomic ground-state configurations are s2d1 like Sc and Y. The elements Ce-Lu are considered as the series and Th-Lr as the actinide series. The two series together are classified as elements, or as inner transition elements. Some inorganic chemistry textbooks include La with the lanthanides and Ac with the actinides, a third classification defines the f-block elements as La-Yb and Ac-No, while placing Lu and Lr in Group 3. This is based on the Aufbau principle for filling electron subshells, in which 4f is filled before 5d, zinc, cadmium, and mercury are generally excluded from the transition metals as they have the electronic configuration d10s2, with no incomplete d shell. In the oxidation state +2 the ions have the electronic configuration d10, however, these elements can exist in other oxidation states, including the +1 oxidation state, as in the diatomic ion Hg2+2. The group 12 elements Zn, Cd and Hg may therefore, under certain rules, however, it is often convenient to include these elements in a discussion of the transition elements. Another example occurs in the Irving-Williams series of stability constants of complexes, although meitnerium, darmstadtium, and roentgenium are within the d-block and are expected to behave as transition metals, this has not yet been experimentally confirmed. The general electronic configuration of the elements is d1, 10n s1,2. The period 6 and 7 transition metals also add f1,14 electrons and this rule is however only approximate – it only holds for some of the transition elements, and only then in their neutral ground state. The d-sub-shell is the next-to-last sub-shell and is denoted as d -sub-shell, the number of s electrons in the outermost s sub-shell is generally one or two except palladium, with no electron in that s-sub shell in its ground state. The s-sub-shell in the shell is represented as the ns sub-shell
30.
Pioneer plaque
–
The plaques show the nude figures of a human male and female along with several symbols that are designed to provide information about the origin of the spacecraft. The Pioneer 10 and 11 spacecraft were the first human-built objects to escape velocity from the Solar System. The plaques were attached to the antenna support struts in a position that would shield them from erosion by interstellar dust. He approached Carl Sagan, who had lectured about communication with extraterrestrial intelligences at a conference in Crimea, Sagan was enthusiastic about the idea of sending a message with the Pioneer spacecraft. NASA agreed to the plan and gave him three weeks to prepare a message, together with Frank Drake he designed the plaque, and the artwork was prepared by Sagans then wife Linda Salzman Sagan. Both plaques were manufactured at Precision Engravers, San Carlos, California, the first plaque was launched with Pioneer 10 on March 2,1972, and the second followed with Pioneer 11 on April 5,1973. Material,6061 T6 gold-anodized aluminum Width,229 mm Height,152 mm Thickness,1.27 mm Mean depth of engraving,0.381 millimeters Mass, approx. 0.120 kilograms At the top left of the plate is a representation of the hyperfine transition of hydrogen. The spin-flip transition of a hydrogen atom’s electron has a frequency of about 1420.405 MHz, light at this frequency has a vacuum wavelength of 21.106 cm. Below the symbol, the small vertical line—representing the binary digit 1—specifies a unit of length as well as a unit of time, both units are used as measurements in the other symbols. On the right side of the plaque, a man and a woman are shown in front of the spacecraft, between the brackets that indicate the height of the woman, the binary representation of the number 8 can be seen. In units of the wavelength of the transition of hydrogen this means 8 ×21 cm =168 cm. The right hand of the man is raised as a sign of good will, although this gesture may not be understood, it offers a way to show the opposable thumb and how the limbs can be moved. Originally Sagan intended the humans to be holding hands. The original drawings of the figures were based on drawings by Leonardo da Vinci, one can see that the womans genitals are not really depicted, only the Mons pubis is shown. It has been claimed that Sagan, having time to complete the plaque, suspected that NASA would have rejected a more intricate drawing. Carl Sagan said that the decision to not include the line on the womans genitalia which would be caused by the intersection of the labia majora was due to two reasons. First, Greek sculptures of women do not include that line, second, Carl Sagan believed that a design with such an explicit depiction of a womans genitalia would be considered too obscene to be approved by NASA
31.
Interstellar medium
–
In astronomy, the interstellar medium is the matter that exists in the space between the star systems in a galaxy. This matter includes gas in ionic, atomic, and molecular form, as well as dust and it fills interstellar space and blends smoothly into the surrounding intergalactic space. The energy that occupies the same volume, in the form of radiation, is the interstellar radiation field. The interstellar medium is composed of phases, distinguished by whether matter is ionic, atomic, or molecular. The interstellar medium is composed primarily of hydrogen followed by helium with trace amounts of carbon, oxygen, the thermal pressures of these phases are in rough equilibrium with one another. Magnetic fields and turbulent motions also provide pressure in the ISM, in all phases, the interstellar medium is extremely tenuous by terrestrial standards. In cool, dense regions of the ISM, matter is primarily in molecular form, in hot, diffuse regions of the ISM, matter is primarily ionized, and the density may be as low as 10−4 ions per cm3. Compare this with a density of roughly 1019 molecules per cm3 for air at sea level. By mass, 99% of the ISM is gas in any form, and 1% is dust. Of the gas in the ISM, by number 91% of atoms are hydrogen and 9% are helium, with 0. 1% being atoms of elements heavier than hydrogen or helium, by mass this amounts to 70% hydrogen, 28% helium, and 1. 5% heavier elements. The hydrogen and helium are primarily a result of primordial nucleosynthesis, the ISM plays a crucial role in astrophysics precisely because of its intermediate role between stellar and galactic scales. Stars form within the densest regions of the ISM, molecular clouds, and replenish the ISM with matter and energy through planetary nebulae, stellar winds, and supernovae. This interplay between stars and the ISM helps determine the rate at which a galaxy depletes its gaseous content, voyager 1 reached the ISM on August 25,2012, making it the first artificial object from Earth to do so. Interstellar plasma and dust will be studied until the end in 2025. Table 1 shows a breakdown of the properties of the components of the ISM of the Milky Way, field, Goldsmith & Habing put forward the static two phase equilibrium model to explain the observed properties of the ISM. Their modeled ISM consisted of a dense phase, consisting of clouds of neutral and molecular hydrogen. McKee & Ostriker added a third phase that represented the very hot gas which had been shock heated by supernovae. These phases are the temperatures where heating and cooling can reach a stable equilibrium and their paper formed the basis for further study over the past three decades
32.
Carl Sagan
–
Carl Edward Sagan was an American astronomer, cosmologist, astrophysicist, astrobiologist, author, science popularizer, and science communicator in astronomy and other natural sciences. He is best known for his work as a science popularizer and his best known scientific contribution is research on extraterrestrial life, including experimental demonstration of the production of amino acids from basic chemicals by radiation. Sagan argued the now accepted hypothesis that the surface temperatures of Venus can be attributed to. Sagan published more than 600 scientific papers and articles and was author, co-author or editor of more than 20 books. He wrote many science books, such as The Dragons of Eden, Brocas Brain and Pale Blue Dot. The most widely watched series in the history of American public television, the book Cosmos was published to accompany the series. He also wrote the science fiction novel Contact, the basis for a 1997 film of the same name and his papers, containing 595,000 items, are archived at The Library of Congress. Sagan always advocated scientific skeptical inquiry and the method, pioneered exobiology. He spent most of his career as a professor of astronomy at Cornell University and he married three times and had five children. After suffering from myelodysplasia, Sagan died of pneumonia at the age of 62, Carl Sagan was born in Brooklyn, New York. His father, Samuel Sagan, was an immigrant garment worker from Kamianets-Podilskyi, then Russian Empire and his mother, Rachel Molly Gruber, was a housewife from New York. Carl was named in honor of Rachels biological mother, Chaiya Clara, in Sagans words and he had a sister, Carol, and the family lived in a modest apartment near the Atlantic Ocean, in Bensonhurst, a Brooklyn neighborhood. According to Sagan, they were Reform Jews, the most liberal of North American Judaisms four main groups, both Sagan and his sister agreed that their father was not especially religious, but that their mother definitely believed in God, and was active in the temple. During the depths of the Depression, his father worked as a theater usher, according to biographer Keay Davidson, Sagans inner war was a result of his close relationship with both of his parents, who were in many ways opposites. Sagan traced his later analytical urges to his mother, a woman who had extremely poor as a child in New York City during World War I. As a young woman she had held her own ambitions, but they were frustrated by social restrictions, her poverty, her status as a woman and a wife. Davidson notes that she therefore worshipped her only son, Carl and he would fulfill her unfulfilled dreams. However, he claimed that his sense of wonder came from his father, in his free time he gave apples to the poor or helped soothe labor-management tensions within New Yorks garment industry