Rest mass

It was stated above that the Schrodinger equation cannot be solved exactly for any molecular systems. However, it is possible to solve the equation exactly for the simplest molecular species, Hj (and isotopically equivalent species such as ITD" ), when the motion of the electrons is decoupled from the motion of the nuclei in accordance with the Bom-Oppenheimer approximation. The masses of the nuclei are much greater than the masses of the electrons (the resting mass of the lightest nucleus, the proton, is 1836 times heavier than the resting mass of the electron). This means that the electrons can adjust almost instantaneously to any changes in the positions of the nuclei. The electronic wavefunction thus depends only on the positions of the nuclei and not on their momenta. Under the Bom-Oppenheimer approximation the total wavefunction for the molecule can be written in the following form ... 

Where b is Planck s constant and m and are the effective masses of the electron and hole which may be larger or smaller than the rest mass of the electron. The effective mass reflects the strength of the interaction between the electron or hole and the periodic lattice and potentials within the crystal stmcture. In an ideal covalent semiconductor, electrons in the conduction band and holes in the valence band may be considered as quasi-free particles. The carriers have high drift mobilities in the range of 10 to 10 cm /(V-s) at room temperature. As shown in Table 4, this is the case for both metallic oxides and covalent semiconductors at room temperature. 

In terms of the electron rest mass and the electron charge we find... 

One of the consequences of the constant speed of light is that the mass of a particle which moves at a substantial fraction of c increases over the rest mass. 

Ruhe,/. rest quiescence repose, quiet, peace, -lage,/. position of rest, -masse,/, rest mass. 

Historical Background.—Relativistic quantum mechanics had its beginning in 1900 with Planck s formulation of the law of black body radiation. Perhaps its inception should be attributed more accurately to Einstein (1905) who ascribed to electromagnetic radiation a corpuscular character the photons. He endowed the photons with an energy and momentum hv and hv/c, respectively, if the frequency of the radiation is v. These assignments of energy and momentum for these zero rest mass particles were consistent with the postulates of relativity. It is to be noted that zero rest mass particles can only be understood within the framework of relativistic dynamics. 

In order to arrive at an equation for a relativistic particle of rest mass m and spin s we can proceed in essentially the same way. If in the relation between energy and momentum for a relativistic particle 3... 

Matter Anything with an at-rest mass greater than zero. 

Photon A particle with energy but no at-rest mass. It represents a quantum of electromagnetic radiation. 

Following the hypothesis of electron spin by Uhlenbeck and Goudsmit, P. A. M. Dirac (1928) developed a quantum mechanics based on the theory of relativity rather than on Newtonian mechanics and applied it to the electron. He found that the spin angular momentum and the spin magnetic moment of the electron are obtained automatically from the solution of his relativistic wave equation without any further postulates. Thus, spin angular momentum is an intrinsic property of an electron (and of other elementary particles as well) just as are the charge and rest mass. 

Annihilation (Positron-Electron)—An interaction between a positive and a negative electron in which they both disappear their rest mass, being converted into electromagnetic radiation (called annihilation radiation) with two 0.51 MeV gamma photons emitted at an angle of 180° to each other. 

Electron—A stable elementary particle having an electric charge equal to 1.60210xl0 19 C (Coulombs) and a rest mass equal to 9.1091xl0 31 kg. A positron is a positively charged "electron" (see Positron). 

Neutrino (V)—A neutral particle of infinitesimally small rest mass emitted during beta plus or beta minus decay. This particle accounts for conservation of energy in beta plus and beta minus decays. It plays no role in damage from radiation. 

Proton—Elementary nuclear particle with a positive electric charge equal numerically to the charge of the electron and a rest mass of 1.007 mass units. 

A list of selected reactions used for the study of light isotopes in a material (atomic number < 20) is given by Demortier (2000). The Q value of a nuclear reaction represents the difference between the total rest mass of the interacting particles and those of emitted ones ... 

In 1923 de Broglie made the bold suggestion that matter, like light, has a dual nature in that it sometimes behaves like particles and sometimes like waves. He suggested that material (i.e., non-zero-rest mass) particles with a momentum p = mv should have wave properties and a corresponding wavelength given by... 

The units we use in daily life, such as kilogram (or pound) and meter (or inch) are tailored to the human scale. In the world of quantum mechanics, however, these units would lead to inconvenient numbers. For example, the mass of the electron is 9.1095 X J0 31 kg and the radius of the first circular orbit of the hydrogen atom in Bohr s theory, the Bohr radius, is 5.2918 X 10 11 m. Atomic units, usually abbreviated as au, are introduced to eliminate the need to work with these awkward numbers, which result from the arbitrary units of our macroscopic world. The atomic unit of length is equal to the length of the Bohr radius, that is, 5.2918 X 10 n m, and is called the bohr. Thus 1 bohr = 5.2918 X 10"11 m. The atomic unit of mass is the rest mass of the electron, and the atomic unit of charge is the charge of an electron. Atomic units for these and some other quantities and their values in SI units are summarized in the accompanying table. 

Name Symbol Identity Nuclear Rest Mass (amu)... 

The E in this equation is the energy of the process. The m is the mass of the matter that is converted to energy—the change in rest mass. Note well that it is not the total mass of the reactant nucleus, but only the mass of the matter that is converted to energy. Sometimes the equation is written as... 

The mass of matter at rest is referred to as rest mass. When matter is put into motion, its mass increases corresponding to its increased energy. The extra mass is given by... 

When a nuclear event takes place, some rest mass is converted to extra mass of the product particles because of their high speed or to the mass of photons of light. While the total mass is conserved in the process, some rest mass (that is, some matter) is converted to energy. 

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