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Relativistic Quantum Chemistry
Relativistic quantum chemistry combines relativistic mechanics with quantum chemistry to calculate elemental properties and structure, especially for the heavier elements of the periodic table. A prominent example is an explanation for the color of gold: due to relativistic effects, it is not silvery like most other metals. The term ''relativistic effects'' were developed in light of the history of quantum mechanics. Initially, quantum mechanics was developed without considering the theory of relativity. Relativistic effects are those discrepancies between values calculated by models that consider relativity and those that do not. Relativistic effects are important for heavier elements with high atomic numbers, such as lanthanides and actinides. Relativistic effects in chemistry can be considered to be perturbations, or small corrections, to the non-relativistic theory of chemistry, which is developed from the solutions of the Schrödinger equation. These corrections affect the ele ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relativistic Mechanics
In physics, relativistic mechanics refers to mechanics compatible with special relativity (SR) and general relativity (GR). It provides a non-quantum mechanical description of a system of particles, or of a fluid, in cases where the velocities of moving objects are comparable to the speed of light ''c''. As a result, classical mechanics is extended correctly to particles traveling at high velocities and energies, and provides a consistent inclusion of electromagnetism with the mechanics of particles. This was not possible in Galilean relativity, where it would be permitted for particles and light to travel at ''any'' speed, including faster than light. The foundations of relativistic mechanics are the postulates of special relativity and general relativity. The unification of SR with quantum mechanics is relativistic quantum mechanics, while attempts for that of GR is quantum gravity, an unsolved problem in physics. As with classical mechanics, the subject can be divided into " ... [...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 line spectra 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 and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arnold Sommerfeld
Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretical physics. He served as doctoral supervisor for many Nobel Prize winners in physics and chemistry (only J. J. Thomson's record of mentorship is comparable to his). He introduced the second quantum number ( azimuthal quantum number) and the third quantum number ( magnetic quantum number). He also introduced the fine-structure constant and pioneered X-ray wave theory. Early life and education Sommerfeld was born in 1868 to a family with deep ancestral roots in Prussia. His mother Cäcilie Matthias (1839–1902) was the daughter of a Potsdam builder. His father Franz Sommerfeld (1820–1906) was a physician from a leading family in Königsberg, where Arnold's grandfather had resettled from the hinterland in 1822 for a career as Cour ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bohr Model
In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar System, but with attraction provided by electrostatic forces in place of gravity. It came after the solar system Joseph Larmor model (1897), the solar system Jean Perrin model (1901), the cubical model (1902), the Hantaro Nagaoka Saturnian model (1904), the plum pudding model (1904), the quantum Arthur Haas model (1910), the Rutherford model (1911), and the nuclear quantum John William Nicholson model (1912). The improvement over the 1911 Rutherford model mainly concerned the new quantum physical interpretation introduced by Haas and Nicholson, but forsaking any attempt to align with classical physics radiation. The model's key success lay in explaining the Rydberg formula for the spectral emission lines of atomic hydrogen. While ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fine-structure Constant
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles. It is a dimensionless quantity, independent of the system of units used, which is related to the strength of the coupling of an elementary charge ''e'' with the electromagnetic field, by the formula . Its numerical value is approximately , with a relative uncertainty of The constant was named by Arnold Sommerfeld, who introduced it in 1916 Equation 12a, ''"rund 7·" (about ...)'' when extending the Bohr model of the atom. quantified the gap in the fine structure of the spectral lines of the hydrogen atom, which had been measured precisely by Michelson and Morley in 1887. Definition In terms of other fundamental physical constants, may be defined as: \alpha = \frac = \frac , where * is the elementary c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reduced Planck's Constant
The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalence, the relationship between mass and frequency. Specifically, a photon's energy is equal to its frequency multiplied by the Planck constant. The constant is generally denoted by h. The reduced Planck constant, or Dirac constant, equal to the constant divided by 2 \pi, is denoted by \hbar. In metrology it is used, together with other constants, to define the kilogram, the SI unit of mass. The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value The constant was first postulated by Max Planck in 1900 as part of a solution to the ultraviolet catastrophe. At the end of the 19th century, accurate measurements of the spectrum of black body radiation existed, but the distribution ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bohr Radius
The Bohr radius (''a''0) 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 parenthesis denotes the uncertainty of the last digits. Definition and value The Bohr radius is defined as a_0 = \frac = \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] |
Velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a physical vector quantity; both magnitude and direction are needed to define it. The scalar absolute value ( magnitude) of velocity is called , being a coherent derived unit whose quantity is measured in the SI ( metric system) as metres per second (m/s or m⋅s−1). For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in speed, direction or both, then the object is said to be undergoing an ''acceleration''. Constant velocity vs acceleration To have a ''constant velocity'', an object must have a constant speed in a constant direction. Constant dire ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron Rest Mass
The electron mass (symbol: ''m''e) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy-equivalent of about or about Terminology The term "rest mass" is sometimes used because in special relativity the mass of an object can be said to increase in a frame of reference that is moving relative to that object (or if the object is moving in a given frame of reference). Most practical measurements are carried out on moving electrons. If the electron is moving at a relativistic velocity, any measurement must use the correct expression for mass. Such correction becomes substantial for electrons accelerated by voltages of over . For example, the relativistic expression for the total energy, ''E'', of an electron moving at speed v is :E = \gamma m_\text c^2 , where the Lorentz factor is \gamma = 1/\sqrt . In this expression ''m''e is the "re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Electron
The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron's mass is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum ( spin) of a half-integer value, expressed in units of the reduced Planck constant, . Being fermions, no two electrons can occupy the same quantum state, per the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: They can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mass In Special Relativity
The word "mass" has two meanings in special relativity: ''invariant mass'' (also called rest mass) is an invariant quantity which is the same for all observers in all reference frames, while the relativistic mass is dependent on the velocity of the observer. According to the concept of mass–energy equivalence, invariant mass is equivalent to ''rest energy'', while relativistic mass is equivalent to ''relativistic energy'' (also called total energy). The term "relativistic mass" tends not to be used in particle and nuclear physics and is often avoided by writers on special relativity, in favor of referring to the body's relativistic energy. In contrast, "invariant mass" is usually preferred over rest energy. The measurable inertia and the warping of spacetime by a body in a given frame of reference is determined by its relativistic mass, not merely its invariant mass. For example, photons have zero rest mass but contribute to the inertia (and weight in a gravitational field) of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorentz Factor
The Lorentz factor or Lorentz term is a quantity expressing how much the measurements of time, length, and other physical properties change for an object while that object is moving. The expression appears in several equations in special relativity, and it arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz. It is generally denoted (the Greek lowercase letter gamma). Sometimes (especially in discussion of superluminal motion) the factor is written as (Greek uppercase-gamma) rather than . Definition The Lorentz factor is defined as :\gamma = \frac = \frac = \frac , where: *''v'' is the relative velocity between inertial reference frames, *''c'' is the ''speed of light in a vacuum'', * is the ratio of ''v'' to ''c'', *''t'' is coordinate time, * is the proper time for an observer (measuring time intervals in the observer's own frame). This is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
