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Gamow Factor
The Gamow factor, Sommerfeld factor or Gamow–Sommerfeld factor, named after its discoverer George Gamow or after Arnold Sommerfeld, is a probability factor for two nuclear particles' chance of overcoming the Coulomb barrier in order to undergo nuclear reactions, for example in nuclear fusion. By classical physics, there is almost no possibility for protons to fuse by crossing each other's Coulomb barrier at temperatures commonly observed to cause fusion, such as those found in the sun. When George Gamow instead applied quantum mechanics to the problem, he found that there was a significant chance for the fusion due to tunneling. The probability of two nuclear particles overcoming their electrostatic barriers is given by the following equation: : P_g(E) = e^ where E_g is the Gamow energy, : E_g \equiv 2 m_r c^2 (\pi \alpha Z_a Z_b)^2 Here, m_r = \frac is the reduced mass of the two particles. The constant \alpha is the fine structure constant, c is the speed of light, and Z_a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Gamow
George Gamow (March 4, 1904 – August 19, 1968), born Georgiy Antonovich Gamov ( uk, Георгій Антонович Гамов, russian: Георгий Антонович Гамов), was a Russian-born Soviet and American polymath, theoretical physicist and cosmologist. He was an early advocate and developer of Lemaître's Big Bang theory. He discovered a theoretical explanation of alpha decay by quantum tunneling, invented the liquid drop model and the first mathematical model of the atomic nucleus, and worked on radioactive decay, star formation, stellar nucleosynthesis and Big Bang nucleosynthesis (which he collectively called nucleocosmogenesis), and molecular genetics. In his middle and late career, Gamow directed much of his attention to teaching and wrote popular books on science, including '' One Two Three... Infinity'' and the ''Mr Tompkins'' series of books (1939–1967). Some of his books are still in print more than a half-century after their original publicat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maxwell–Boltzmann Distribution
In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used for describing particle speeds in idealized gases, where the particles move freely inside a stationary container without interacting with one another, except for very brief collisions in which they exchange energy and momentum with each other or with their thermal environment. The term "particle" in this context refers to gaseous particles only (atoms or molecules), and the system of particles is assumed to have reached thermodynamic equilibrium.''Statistical Physics'' (2nd Edition), F. Mandl, Manchester Physics, John Wiley & Sons, 2008, The energies of such particles follow what is known as Maxwell–Boltzmann statistics, and the statistical distribution of speeds is derived by equating particle energies with kinetic energy. Mathematica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radium
Radium is a chemical element with the symbol Ra and atomic number 88. It is the sixth element in group 2 of the periodic table, also known as the alkaline earth metals. Pure radium is silvery-white, but it readily reacts with nitrogen (rather than oxygen) upon exposure to air, forming a black surface layer of radium nitride (Ra3N2). All isotopes of radium are radioactive, the most stable isotope being radium-226 with a half-life of 1600 years. When radium decays, it emits ionizing radiation as a by-product, which can excite fluorescent chemicals and cause radioluminescence. Radium, in the form of radium chloride, was discovered by Marie and Pierre Curie in 1898 from ore mined at Jáchymov. They extracted the radium compound from uraninite and published the discovery at the French Academy of Sciences five days later. Radium was isolated in its metallic state by Marie Curie and André-Louis Debierne through the electrolysis of radium chloride in 1911. In nature, radium is found ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundamental physical constant. In the SI system of units, the value of the elementary charge is exactly defined as e = coulombs, or 160.2176634 zeptocoulombs (zC). Since the 2019 redefinition of SI base units, the seven SI base units are defined by seven fundamental physical constants, of which the elementary charge is one. In the centimetre–gram–second system of units (CGS), the corresponding quantity is . Robert A. Millikan and Harvey Fletcher's oil drop experiment first directly measured the magnitude of the elementary charge in 1909, differing from the modern accepted value by just 0.6%. Under assumptions of the then-disputed atomic theory, the elementary charge had also been indirectly inferred to ~3% accuracy from black ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coulomb Constant
The Coulomb constant, the electric force constant, or the electrostatic constant (denoted , or ) is a proportionality constant in electrostatics equations. In SI base units it is equal to .Derived from ''k''e = 1/(4''πε''0) – It was named after the French physicist Charles-Augustin de Coulomb (1736–1806) who introduced Coulomb's law. Value of the constant The Coulomb constant is the constant of proportionality in Coulomb's law, :\mathbf = k_\text\frac\mathbf_r where is a unit vector in the -direction. In SI: : k_\text = \frac, where \varepsilon_0 is the vacuum permittivity. This formula can be derived from Gauss' law, : Taking this integral for a sphere, radius , centered on a point charge, the electric field points radially outwards and is normal to a differential surface element on the sphere with constant magnitude for all points on the sphere. : Noting that for some test charge , :\begin \mathbf &= \frac\frac\mathbf_r = k_\text\frac\mathbf_r \\ pt\th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coulomb's Law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventionally called ''electrostatic force'' or Coulomb force. Although the law was known earlier, it was first published in 1785 by French physicist Charles-Augustin de Coulomb, hence the name. Coulomb's law was essential to the development of the theory of electromagnetism, maybe even its starting point, as it made it possible to discuss the quantity of electric charge in a meaningful way. The law states that the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them. Coulomb studied the repulsive force between bodies having electrical charges of the same sign: Coulomb also ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Harmonics
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations in many scientific fields. Since the spherical harmonics form a complete set of orthogonal functions and thus an orthonormal basis, each function defined on the surface of a sphere can be written as a sum of these spherical harmonics. This is similar to periodic functions defined on a circle that can be expressed as a sum of circular functions (sines and cosines) via Fourier series. Like the sines and cosines in Fourier series, the spherical harmonics may be organized by (spatial) angular frequency, as seen in the rows of functions in the illustration on the right. Further, spherical harmonics are basis functions for irreducible representations of SO(3), the group of rotations in three dimensions, and thus play a central role in the group theoretic discussion of SO(3). Spherical harmonics originate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, 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 a wave function, the quantum-mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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