Pauli exclusion principl

Pauli exclusion principle In any atom no two electrons can have all four quantum numbers the same. See exclusion principle. 

The resolution of this issue is based on the application of the Pauli exclusion principle and Femii-Dirac statistics. From the free electron model, the total electronic energy, U, can be written as... 

The state F) is such that the particle states a, b, c,..., q are occupied and each particle is equally likely to be in any one of the particle states. However, if two of the particle states a, b, c,...,q are the same then F) vanishes it does not correspond to an allowed state of the assembly. This is a characteristic of antisynmietric states and it is called the Pauli exclusion principle no two identical fennions can be in the same particle state. The general fimction for an assembly of bosons is... 

The sum over n. can now be perfonned, but this depends on the statistics that the particles in the ideal gas obey. Fenni particles obey the Pauli exclusion principle, which allows only two possible values n. = 0, 1. For Bose particles, n. can be any integer between zero and infinity. Thus the grand partition fiinction is... 

The average kinetic energy per particle at J= 0, is of the Fenni energy p. At constant A, the energy increases as the volume decreases smce fp Due to the Pauli exclusion principle, the Fenni energy gives... 

Themiodynamic stability requires a repulsive core m the interatomic potential of atoms and molecules, which is a manifestation of the Pauli exclusion principle operating at short distances. This means that the Coulomb and dipole interaction potentials between charged and uncharged real atoms or molecules must be supplemented by a hard core or other repulsive interactions. Examples are as follows. 

Because single-electron wave functions are approximate solutions to the Schroe-dinger equation, one would expect that a linear combination of them would be an approximate solution also. For more than a few basis functions, the number of possible lineal combinations can be very large. Fortunately, spin and the Pauli exclusion principle reduce this complexity. 

In addition to being negatively charged electrons possess the property of spin The spin quantum number of an electron can have a value of either +5 or According to the Pauli exclusion principle, two electrons may occupy the same orbital only when... 

Pauli exclusion principle (Section 1 1) No two electrons can have the same set of four quantum numbers An equivalent expression is that only two electrons can occupy the same orbital and then only when they have opposite spins PCC (Section 15 10) Abbreviation for pyndimum chlorochro mate C5H5NH" ClCr03 When used in an anhydrous medium PCC oxidizes pnmary alcohols to aldehydes and secondary alcohols to ketones... 

Because of the quantum mechanical Uncertainty Principle, quantum mechanics methods treat electrons as indistinguishable particles. This leads to the Pauli Exclusion Principle, which states that the many-electron wave function—which depends on the coordinates of all the electrons—must change sign whenever two electrons interchange positions. That is, the wave function must be antisymmetric with respect to pair-wise permutations of the electron coordinates. 

Again, for the filled orbitals L = 0 and 5 = 0, so we have to consider only the 2p electrons. Since n = 2 and f = 1 for both electrons the Pauli exclusion principle is in danger of being violated unless the two electrons have different values of either or m. For non-equivalent electrons we do not have to consider the values of these two quantum numbers because, as either n or f is different for the electrons, there is no danger of violation. 

Intrinsic Semiconductors. For semiconductors in thermal equiHbrium, (Ai( )), the average number of electrons occupying a state with energy E is governed by the Fermi-Dirac distribution. Because, by the Pauli exclusion principle, at most one electron (fermion) can occupy a state, this average number is also the probabiHty, P E), that this state is occupied (see Fig. 2c). In equation 2, K... 

Electrons act as if they were spinning around an axis, in much the same way that the earth spins. This spin can have two orientations, denoted as up T and down i. Only two electrons can occupy an orbital, and they must be of opposite spin, a statement called the Pauli exclusion principle. 

Pauli exclusion principle (Section 1.3) No more than two electrons can occupy the same orbital, and those two must have spins of opposite sign. 

The four quantum numbers that characterize an electron in an atom have now been considered. There is an important rule, called the Pauli exclusion principle, that relates to these numbers. It requires that no two electrons in an atom can have the same set of four quan-... 

The Pauli exclusion principle has an implication that is not obvious at first glance. It requires that only two electrons can fit into an orbital, since there are only two possible values of m,. Moreover, if two electrons occupy the same orbital, they must have opposed spins. Otherwise they would have the same set of four quantum numbers. 

Hund s rule, like the Pauli exclusion principle, is based on experiment It is possible to determine the number of unpaired electrons in an atom. With solids, this is done by studying their behavior in a magnetic field. If there are unpaired electrons present the solid will be attracted into the field. Such a substance is said to be paramagnetic. If the atoms in the solid contain only paired electrons, it is slightly repelled by the field. Substances of this type are called diamagnetic. With gaseous atoms, the atomic spectrum can also be used to establish the presence and number of unpaired electrons. 

Pascal An SI unit of pressure the pressure exerted by the force of 1 newton on an area of 1 square meter, 104,635 Paschen series, 138 Pasteur, Louis, 601 Pauli exclusion principle, 141-143 Pauling, Linus, 185 Pentyl propionate, 596t Peptide linkage The—C—N—group... 

Pauli exclusion principle, 141-143 permissible values, 142t principle energy levels, 140 sublevels, 140-141 Quartz, 242... 

The fundamental laws which determine the behavior of an electronic system are the Schrodinger equation (Eq. II. 1) and the Pauli exclusion principle expressed in the form of the antisymmetry requirement (Eq. II.2). We note that even the latter auxiliary condition introduces a certain correlation between the movements of the electrons. 

In formulating the second-quantized description of a system of noninteracting fermions, we shall, therefore, have to introduce distinct creation and annihilation operators for particle and antiparticle. Furthermore, since all the fermions that have been discovered thus far obey the Pauli Exclusion principle we shall have to make sure that the formalism describes a many particle system in terms of properly antisymmetrized amplitudes so that the particles obey Fermi-Dirac statistics. For definiteness, we shall in the present section consider only the negaton-positon system, and call the negaton the particle and the positon the antiparticle. 

The wave function, constructed from the atomic orbitals must be antisymmetric with respect to interchange of electrons in order to satisfy the Pauli exclusion principle, having different spin quantum numbers (a and J3) for two electrons which are in the same orbital. 

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