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Hund's Rules
In atomic physics and quantum chemistry, Hund's rules refers to a set of rules that German physicist Friedrich Hund formulated around 1925, which are used to determine the term symbol that corresponds to the ground state of a multi-electron atom. The first rule is especially important in chemistry, where it is often referred to simply as Hund's Rule. The three rules are: # For a given electron configuration, the term with maximum multiplicity has the lowest energy. The multiplicity is equal to 2S + 1 \ , where S is the total spin angular momentum for all electrons. The multiplicity is also equal to the number of unpaired electrons plus one. Therefore, the term with lowest energy is also the term with maximum S \, and maximum number of unpaired electrons with equal spin angular momentum (either +1/2 or -1/2). # For a given multiplicity, the term with the largest value of the total orbital angular momentum quantum number L \, has the lowest energy. # For a given term ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pauli Exclusion Principle
In quantum mechanics, the Pauli exclusion principle (German: Pauli-Ausschlussprinzip) states that two or more identical particles with half-integer spins (i.e. fermions) cannot simultaneously occupy the same quantum state within a system that obeys the laws of quantum mechanics. This principle was formulated by Austrian physicist Wolfgang Pauli in 1925 for electrons, and later extended to all fermions with his spin–statistics theorem of 1940. In the case of electrons in atoms, the exclusion principle can be stated as follows: in a poly-electron atom it is impossible for any two electrons to have the same two values of ''all'' four of their quantum numbers, which are: ''n'', the principal quantum number; ', the azimuthal quantum number; ''m'', the magnetic quantum number; and ''ms'', the spin quantum number. For example, if two electrons reside in the same orbital, then their values of ''n'', ', and ''m'' are equal. In that case, the two values of ''m''s (spin) pair must be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sulfur
Sulfur ( American spelling and the preferred IUPAC name) or sulphur ( Commonwealth spelling) is a chemical element; it has symbol S and atomic number 16. It is abundant, multivalent and nonmetallic. Under normal conditions, sulfur atoms form cyclic octatomic molecules with the chemical formula S8. Elemental sulfur is a bright yellow, crystalline solid at room temperature. Sulfur is the tenth most abundant element by mass in the universe and the fifth most common on Earth. Though sometimes found in pure, native form, sulfur on Earth usually occurs as sulfide and sulfate minerals. Being abundant in native form, sulfur was known in ancient times, being mentioned for its uses in ancient India, ancient Greece, China, and ancient Egypt. Historically and in literature sulfur is also called brimstone, which means "burning stone". Almost all elemental sulfur is produced as a byproduct of removing sulfur-containing contaminants from natural gas and petroleum.. Downloahere Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Good Quantum Number
In quantum mechanics, the eigenvalue q of an observable O is said to be a good quantum number if the observable O is a constant of motion. In other words, the quantum number is good if the corresponding observable commutes with the Hamiltonian. If the system starts from the eigenstate with an eigenvalue q, it remains on that state as the system evolves in time, and the measurement of O always yields the same eigenvalue q. Good quantum numbers are often used to label initial and final states in experiments. For example, in particle colliders: # Particles are initially prepared in approximate momentum eigenstates; the particle momentum being a good quantum number for non-interacting particles. # The particles are made to collide. At this point, the momentum of each particle is undergoing change and thus the particles’ momenta are not a good quantum number for the interacting particles during the collision. # A significant time after the collision, particles are measured in momentum ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Momentum Operator
In quantum mechanics, the angular momentum operator is one of several related operators analogous to classical angular momentum. The angular momentum operator plays a central role in the theory of atomic and molecular physics and other quantum problems involving rotational symmetry. Being an observable, its eigenfunctions represent the distinguishable physical states of a system's angular momentum, and the corresponding eigenvalues the observable experimental values. When applied to a mathematical representation of the state of a system, yields the same state multiplied by its angular momentum value if the state is an eigenstate (as per the eigenstates/eigenvalues equation). In both classical and quantum mechanical systems, angular momentum (together with linear momentum and energy) is one of the three fundamental properties of motion.Introductory Quantum Mechanics, Richard L. Liboff, 2nd Edition, There are several angular momentum operators: total angular momentum (usually den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of its atomic nucleus. For ordinary nuclei composed of protons and neutrons, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every atom of that element. The atomic number can be used to uniquely identify ordinary chemical elements. In an ordinary uncharged atom, the atomic number is also equal to the number of electrons. For an ordinary atom which contains protons, neutrons and electrons, the sum of the atomic number ''Z'' and the neutron number ''N'' gives the atom's atomic mass number ''A''. Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes) and the mass defect of the nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in daltons (making a quantity called the " relative isotopic mass"), is within 1% ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Titanium
Titanium is a chemical element; it has symbol Ti and atomic number 22. Found in nature only as an oxide, it can be reduced to produce a lustrous transition metal with a silver color, low density, and high strength, resistant to corrosion in sea water, aqua regia, and chlorine. Titanium was discovered in Cornwall, Great Britain, by William Gregor in 1791 and was named by Martin Heinrich Klaproth after the Titans of Greek mythology. The element occurs within a number of minerals, principally rutile and ilmenite, which are widely distributed in the Earth's crust and lithosphere; it is found in almost all living things, as well as bodies of water, rocks, and soils. The metal is extracted from its principal mineral ores by the Kroll and Hunter processes. The most common compound, titanium dioxide (TiO2), is a popular photocatalyst and is used in the manufacture of white pigments. Other compounds include titanium tetrachloride (TiCl4), a component of smoke screens and cata ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triplet State
In quantum mechanics, a triplet state, or spin triplet, is the quantum state of an object such as an electron, atom, or molecule, having a quantum spin ''S'' = 1. It has three allowed values of the spin's projection along a given axis ''m''S = −1, 0, or +1, giving the name "triplet". Spin, in the context of quantum mechanics, is not a mechanical rotation but a more abstract concept that characterizes a particle's intrinsic angular momentum. It is particularly important for systems at atomic length scales, such as individual atoms, protons, or electrons. A triplet state occurs in cases where the spins of two unpaired electrons, each having spin ''s'' = , align to give ''S'' = 1, in contrast to the more common case of two electrons aligning oppositely to give ''S'' = 0, a spin singlet. Most molecules encountered in daily life exist in a singlet state because all of their electrons are paired, but molecular oxygen is an exception. At room temperature, O2 exists in a triplet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spectroscopic Notation
Spectroscopic notation provides a way to specify atomic ionization states, atomic orbitals, and molecular orbitals. Ionization states Spectroscopists customarily refer to the spectrum arising from a given ionization state of a given element by the element's symbol followed by a Roman numeral. The numeral I is used for spectral lines associated with the neutral element, II for those from the first ionization state, III for those from the second ionization state, and so on. For example, "He I" denotes lines of neutral helium, and "C IV" denotes lines arising from the third ionization state, C3+, of carbon. This notation is used for example to retrieve data from thNIST Atomic Spectrum Database Atomic and molecular orbitals Before atomic orbitals were understood, spectroscopists discovered various distinctive series of spectral lines in atomic spectra, which they identified by letters. These letters were later associated with the azimuthal quantum number, ''ℓ''. The let ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Silicon
Silicon is a chemical element; it has symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic lustre, and is a tetravalent metalloid (sometimes considered a non-metal) and semiconductor. It is a member of group 14 in the periodic table: carbon is above it; and germanium, tin, lead, and flerovium are below it. It is relatively unreactive. Silicon is a significant element that is essential for several physiological and metabolic processes in plants. Silicon is widely regarded as the predominant semiconductor material due to its versatile applications in various electrical devices such as transistors, solar cells, integrated circuits, and others. These may be due to its significant band gap, expansive optical transmission range, extensive absorption spectrum, surface roughening, and effective anti-reflection coating. Because of its high chemical affinity for oxygen, it was not until 1823 that Jöns Jakob Berzelius was first able to p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Quantum Number
In atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number ( or ) distinguishes the orbitals available within a given subshell of an atom. It specifies the component of the orbital angular momentum that lies along a given axis, conventionally called the ''z''-axis, so it describes the orientation of the orbital in space. The spin magnetic quantum number specifies the ''z''-axis component of the spin angular momentum for a particle having spin quantum number . For an electron, is , and is either + or −, often called "spin-up" and "spin-down", or α and β. The term ''magnetic'' in the name refers to the magnetic dipole moment associated with each type of angular momentum, so states having different magnetic quantum numbers shift in energy in a magnetic field according to the Zeeman effect. The four quant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
