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Principal Quantum Numbers
In quantum mechanics, the principal quantum number (''n'') of an electron in an atom indicates which electron shell or energy level it is in. Its values are natural numbers (1, 2, 3, ...). Hydrogen and Helium, at their lowest energies, have just one electron shell. Lithium through Neon (see periodic table) have two shells: two electrons in the first shell, and up to 8 in the second shell. Larger atoms have more shells. The principal quantum number is one of four quantum numbers assigned to each electron in an atom to describe the quantum state of the electron. The other quantum numbers for bound electrons are the total angular momentum of the orbit ''ℓ'', the angular momentum in the z direction ''ℓz'', and the spin of the electron ''s''. Overview and history As ''n'' increases, the electron is also at a higher energy and is, therefore, less tightly bound to the nucleus. For higher ''n'', the electron is farther from the nucleus, on average. For each value of ''n'', th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is the foundation of all quantum physics, which includes quantum chemistry, quantum field theory, quantum technology, and quantum information science. Quantum mechanics can describe many systems that classical physics cannot. Classical physics can describe many aspects of nature at an ordinary (macroscopic and Microscopic scale, (optical) microscopic) scale, but is not sufficient for describing them at very small submicroscopic (atomic and subatomic) scales. Classical mechanics can be derived from quantum mechanics as an approximation that is valid at ordinary scales. Quantum systems have Bound state, bound states that are Quantization (physics), quantized to Discrete mathematics, discrete values of energy, momentum, angular momentum, and ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magnetic Field
A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function (mathematics), function assigning a Euclidean vector, vector to each point of space, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bound State
A bound state is a composite of two or more fundamental building blocks, such as particles, atoms, or bodies, that behaves as a single object and in which energy is required to split them. In quantum physics, a bound state is a quantum state of a particle subject to a potential energy, potential such that the particle has a tendency to remain localized in one or more regions of space. The potential may be external or it may be the result of the presence of another particle; in the latter case, one can equivalently define a bound state as a state representing two or more particles whose interaction energy exceeds the total energy of each separate particle. One consequence is that, given a potential vanish at infinity, vanishing at infinity, negative-energy states must be bound. The energy spectrum of the set of bound states are most commonly discrete, unlike scattering states of Free particle, free particles, which have a continuous spectrum. Although not bound states in the stric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eigenvalues And Eigenvectors
In linear algebra, an eigenvector ( ) or characteristic vector is a vector that has its direction unchanged (or reversed) by a given linear transformation. More precisely, an eigenvector \mathbf v of a linear transformation T is scaled by a constant factor \lambda when the linear transformation is applied to it: T\mathbf v=\lambda \mathbf v. The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor \lambda (possibly a negative or complex number). Geometrically, vectors are multi-dimensional quantities with magnitude and direction, often pictured as arrows. A linear transformation rotates, stretches, or shears the vectors upon which it acts. A linear transformation's eigenvectors are those vectors that are only stretched or shrunk, with neither rotation nor shear. The corresponding eigenvalue is the factor by which an eigenvector is stretched or shrunk. If the eigenvalue is negative, the eigenvector's direction is reversed. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger, an Austrian physicist, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterization of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave. The equati ... [...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] |
Wave Function
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter), psi, respectively). Wave functions are complex number, complex-valued. For example, a wave function might assign a complex number to each point in a region of space. The Born rule provides the means to turn these complex probability amplitudes into actual probabilities. In one common form, it says that the squared modulus of a wave function that depends upon position is the probability density function, probability density of measurement in quantum mechanics, measuring a particle as being at a given place. The integral of a wavefunction's squared modulus over all the system's degrees of freedom must be equal to 1, a condition called ''normalization''. Since the wave function is complex-valued, only its relative phase and relative magnitud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Orbital
In quantum mechanics, an atomic orbital () is a Function (mathematics), function describing the location and Matter wave, wave-like behavior of an electron in an atom. This function describes an electron's Charge density, charge distribution around the Atomic nucleus, atom's nucleus, and can be used to calculate the probability of finding an electron in a specific region around the nucleus. Each orbital in an atom is characterized by a set of values of three quantum numbers , , and , which respectively correspond to electron's energy, its angular momentum, orbital angular momentum, and its orbital angular momentum projected along a chosen axis (magnetic quantum number). The orbitals with a well-defined magnetic quantum number are generally complex-valued. Real-valued orbitals can be formed as linear combinations of and orbitals, and are often labeled using associated Spherical harmonics#Harmonic polynomial representation, harmonic polynomials (e.g., ''xy'', ) which describe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bohr Model
In atomic physics, the Bohr model or Rutherford–Bohr model was a model of the atom that incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's nuclear Rutherford model, model, it supplanted the plum pudding model of J. J. Thomson only to be replaced by the quantum atomic model in the 1920s. It consists of a small, dense nucleus surrounded by orbiting electrons. It is analogy, analogous to the structure of the Solar System, but with attraction provided by Coulomb's law, electrostatic force rather than gravity, and with the electron energies quantized (assuming only discrete values). In the history of atomic physics, it followed, and ultimately replaced, several earlier models, including Joseph Larmor's Solar System model (1897), Jean Perrin's model (1901), the Cubical atom, cubical model (1902), Hantaro Nagaoka's Saturnian model (1904), the plum pudding model (1904), Arthur Haas's quantum model (1910), the Ru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Potassium
Potassium is a chemical element; it has Symbol (chemistry), symbol K (from Neo-Latin ) and atomic number19. It is a silvery white metal that is soft enough to easily cut with a knife. Potassium metal reacts rapidly with atmospheric oxygen to form flaky white potassium peroxide in only seconds of exposure. It was first isolated from potash, the ashes of plants, from which its name derives. In the periodic table, potassium is one of the alkali metals, all of which have a single valence electron in the outer electron shell, which is easily removed to create cation, an ion with a positive charge (which combines with anions to form salts). In nature, potassium occurs only in ionic salts. Elemental potassium reacts vigorously with water, generating sufficient heat to ignite hydrogen emitted in the reaction, and burning with a lilac-flame color, colored flame. It is found dissolved in seawater (which is 0.04% potassium by weight), and occurs in many minerals such as orthoclase, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boron
Boron is a chemical element; it has symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous form it is a brown powder. As the lightest element of the boron group it has three valence electrons for forming covalent bonds, resulting in many compounds such as boric acid, the mineral sodium borate, and the ultra-hard crystals of boron carbide and boron nitride. Boron is synthesized entirely by cosmic ray spallation and supernovas and not by stellar nucleosynthesis, so it is a low-abundance element in the Solar System and in the Earth's crust. It constitutes about 0.001 percent by weight of Earth's crust. It is concentrated on Earth by the water-solubility of its more common naturally occurring compounds, the borate minerals. These are mined industrially as evaporites, such as borax and kernite. The largest known deposits are in Turkey, the largest producer of boron minerals. Elemental boron is found in smal ... [...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] |
