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Bohr Radius
The Bohr radius () is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is The number in parentheses denotes the uncertainty of the last digits. Definition and value The Bohr radius is defined as a_0 = \frac = \frac , where * \varepsilon_0 is the permittivity of free space, * \hbar is the reduced Planck constant, * m_ is the mass of an electron, * e is the elementary charge, * c is the speed of light in vacuum, and * \alpha is the fine-structure constant. The CODATA value of the Bohr radius (in SI units) is History In the Bohr model for atomic structure, put forward by Niels Bohr in 1913, electrons orbit a central nucleus under electrostatic attraction. The original derivation posited that electrons have orbital angular momentum in integer multiples of the reduced Planck ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Niels Bohr
Niels Henrik David Bohr (, ; ; 7 October 1885 – 18 November 1962) was a Danish theoretical physicist who made foundational contributions to understanding atomic structure and old quantum theory, quantum theory, for which he received the Nobel Prize in Physics in 1922. Bohr was also a philosopher and a promoter of scientific research. Bohr developed the Bohr model of the atom, in which he proposed that energy levels of electrons are discrete and that the electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level (or orbit) to another. Although the Bohr model has been supplanted by other models, its underlying principles remain valid. He conceived the principle of Complementarity (physics), complementarity: that items could be separately analysed in terms of contradictory properties, like behaving as a Wave–particle duality, wave or a stream of particles. The notion of complementarity dominated Bohr's thinking in both science and philoso ... [...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] |
Compton Wavelength
The Compton wavelength is a quantum mechanical property of a particle, defined as the wavelength of a photon whose energy is the same as the rest energy of that particle (see mass–energy equivalence). It was introduced by Arthur Compton in 1923 in his explanation of the scattering of photons by electrons (a process known as Compton scattering). The standard Compton wavelength of a particle of mass is given by \lambda = \frac, where is the Planck constant and is the speed of light. The corresponding frequency is given by f = \frac, and the angular frequency is given by \omega = \frac. The CODATA value for the Compton wavelength of the electron is Other particles have different Compton wavelengths. Reduced Compton wavelength The reduced Compton wavelength \lambda\!\!\!\bar ( barred lambda) of a particle is defined as its Compton wavelength divided by : : \lambda\!\!\!\bar = \frac = \frac, where is the reduced Planck constant. Role in equations for massive pa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
HyperPhysics
''HyperPhysics'' is an educational website about physics topics. The information architecture of the website is based on HyperCard, the platform on which the material was originally developed, and a thesaurus organization, with thousands of controlled links and usual trees organizing topics from general to specific. It also exploits concept maps to facilitate smooth navigation. ''HyperPhysics'' is hosted by Georgia State University and authored by Georgia State faculty member Dr. Rod Nave. In the early 2000s, various teaching and education facilitators made use of ''HyperPhysics'' material through projects and organizations, and also publishers which use SciLinks. References External links * * *{{Cite journal , last=Wild , first=Sarah , date=2023-02-07 , title=HyperPhysics, the popular online physics resource, turns 25 , url=https://pubs.aip.org/physicstoday/Online/41812/HyperPhysics-the-popular-online-physics-resource , journal=Physics Today ''Physics Today'' is the mem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean, mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would expect to get in reality. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by Integral, integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Units
The atomic units are a system of natural units of measurement that is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They were originally suggested and named by the physicist Douglas Hartree. Atomic units are often abbreviated "a.u." or "au", not to be confused with similar abbreviations used for astronomical units, arbitrary units, and absorbance units in other contexts. Motivation In the context of atomic physics, using the atomic units system can be a convenient shortcut, eliminating symbols and numbers and reducing the order of magnitude of most numbers involved. For example, the Hamiltonian operator in the Schrödinger equation for the helium atom with standard quantities, such as when using SI units, is : \hat = - \frac \nabla_1^2 - \frac \nabla_2^2 - \frac - \frac + \frac , but adopting the convention associated with atomic units that transforms quantities into dimensionl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned with the way in which electrons are arranged around the nucleus and the processes by which these arrangements change. 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 nuclear power and nuclear weapons, due to the synonymous use of ''atomic'' and ''nuclear'' in standard English. Physicists distinguish between atomic physics—which deals with the atom as a system consisting of a nucleus and electrons—and nuclear physics, which studies nuclear reactions and special properties of atomic nuclei. As with many scientific fields, strict delineation can be highly contrived and atomic physics is often considered in the w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperfine Structure
In atomic physics, hyperfine structure is defined by small shifts in otherwise degenerate electronic energy levels and the resulting splittings in those electronic energy levels of atoms, molecules, and ions, due to electromagnetic multipole interaction between the nucleus and electron clouds. In atoms, hyperfine structure arises from the energy of the nuclear magnetic dipole moment interacting with the magnetic field generated by the electrons and the energy of the nuclear electric quadrupole moment in the electric field gradient due to the distribution of charge within the atom. Molecular hyperfine structure is generally dominated by these two effects, but also includes the energy associated with the interaction between the magnetic moments associated with different magnetic nuclei in a molecule, as well as between the nuclear magnetic moments and the magnetic field generated by the rotation of the molecule. Hyperfine structure contrasts with '' fine structure'', which resu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. It was first measured precisely for the hydrogen atom by Albert A. Michelson and Edward W. Morley in 1887, laying the basis for the theoretical treatment by Arnold Sommerfeld, introducing the fine-structure constant. Background Gross structure The ''gross structure'' of line spectra is the structure predicted by the quantum mechanics of non-relativistic electrons with no spin. For a hydrogenic atom, the gross structure energy levels only depend on the principal quantum number ''n''. However, a more accurate model takes into account relativistic and spin effects, which break the degeneracy of the energy levels and split the spectral lines. The scale of the fine structure splitting relative to the gross structure energies is on the order of (''Zα'')2, where ''Z'' is the atomic number ... [...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] |
Reduced Mass
In physics, reduced mass is a measure of the effective inertial mass of a system with two or more particles when the particles are interacting with each other. Reduced mass allows the two-body problem to be solved as if it were a one-body problem. Note, however, that the mass determining the gravitational force is ''not'' reduced. In the computation, one mass ''can'' be replaced with the reduced mass, if this is compensated by replacing the other mass with the sum of both masses. The reduced mass is frequently denoted by \mu ( mu), although the standard gravitational parameter is also denoted by \mu (as are a number of other physical quantities). It has the dimensions of mass, and SI unit kg. Reduced mass is particularly useful in classical mechanics. Equation Given two bodies, one with mass ''m''1 and the other with mass ''m''2, the equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of mass \m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrogen
Hydrogen is a chemical element; it has chemical symbol, symbol H and atomic number 1. It is the lightest and abundance of the chemical elements, most abundant chemical element in the universe, constituting about 75% of all baryon, normal matter. Under standard conditions, hydrogen is a gas of diatomic molecules with the chemical formula, formula , called dihydrogen, or sometimes hydrogen gas, molecular hydrogen, or simply hydrogen. Dihydrogen is colorless, odorless, non-toxic, and highly combustible. Stars, including the Sun, mainly consist of hydrogen in a plasma state, while on Earth, hydrogen is found as the gas (dihydrogen) and in molecular forms, such as in water and organic compounds. The most common isotope of hydrogen (H) consists of one proton, one electron, and no neutrons. Hydrogen gas was first produced artificially in the 17th century by the reaction of acids with metals. Henry Cavendish, in 1766–1781, identified hydrogen gas as a distinct substance and discovere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
