Pauli principal

Avogadro s, 38, 146 Heisenberg uncertainty, 15 Le Chatelier s, 377, 468 Pauli exclusion, 34, 37 principal quantum number, 22... 

The Pauli and aufbau principles dictate where the cuts occur in the ribbon of elements. After two electrons have been placed in the 1. S orbital (He), the next electron must go in a less stable, n — 2 orbital (Li). After eight additional electrons have been placed in the 2 S and 2 p orbitals (Ne), the next electron must go in a less stable, = 3 orbital (Na). The ends of the rows in the periodic table are the points at which the next electron occupies an orbital of next higher principal quantum number. 

The mutual electrostatic repulsion of the electrons and the Pauli repulsion between electrons having the same spin. The Pauli repulsion contributes the principal part of the repulsion. It is based on the fact that two electrons having the same spin cannot share the same space. Pauli repulsion can only be explained by quantum mechanics, and it eludes simple model conceptions. 

The relative size of atomic orbitals, which is found to increase as their energy level rises, is defined by the principal quantum number, n, their shape and spatial orientation (with respect to the nucleus and each other) by the subsidiary quantum numbers, Z and m, respectively. Electrons in orbitals also have a further designation in terms of the spin quantum number, which can have the values +j or — j. One limitation that theory imposes on such orbitals is that each may accommodate not more than two electrons, these electrons being distinguished from each other by having opposed (paired) spins, t This follows from the Pauli exclusion principle, which states that no two electrons in any atom may have exactly the same set of quantum numbers. 

Pauli proposed the use of a fourth quantum number, which could have two values, thereby explaining why it is that electrons with identical energies behave differently in a strong magnetic field. If it is assumed that no two electrons in an atom may occupy the same atomic state, meaning that no two electrons can have the same four quantum numbers, then there might be two, but no more than two, 5 electrons for each principal quantum number. Six different... 

All electrons in atoms can be described by means of these four quantum numbers and, as first enunciated in 1926 by Pauli in his Exclusion Principle, each electron in an atom must have a unique set of the four quantum numbers. A summary of the electron shells and of the corresponding maximum numbers of orbitals, and electrons, is shown in Table 4.2 where each shell is defined by the value of the principal quantum number (K = 1, L = 2, etc. according to X-ray spectroscopy nomenclature). 

The filling of atomic orbitals follows an n + , n) orbital scheme known as the Madelung [75-77] or Klechkovskii [78] rule. In this orbital scheme, the electron occupies free states with the smallest value of the sum A = + of the principal quantum number n and the azimuthal quantum number ( according to the Pauli exclusion principle. In the presence of several states with identical N, the state with... 

The energy states of atoms are expressed in terms of four quantum numbers j it, the principal quantum number /, the azimuthal quantum number m, the magnetic quantum number and mt or s, the spin quantum number. According to Pauli s exclusion principle, no two electrons can have the same values for all the four quantum numbers. 

The Pauli exclusion principle provides an immediate explanation of the principal features of the periodic system of the elements, and also of the energy-level diagrams, such as that for beryllium shown in Figure 2-14. 

The positions of electrons around the nucleus are determined with the help of four quantum numbers. There is the principal quantum number (n), secondary quantum number (1), magnetic quantum number (m,) and spin quantum number (ms). Two electrons in an atom never have identical sets of the four quantum numbers. At least one of the four quantum numbers must be different. This is known as Pauli s principle. 

The set of quantum numbers n, /, / / and s define the state of an electron in an atom. From an examination of spectra, Wolfgang Pauli (1900-1958) enunciated what has become known as the Pauli Exclusion Principle. This states that there cannot be more than one electron in a given state defined by a particular set of values for n, /, / // and s. For a given principal quantum number n there are a total of 2n1 available electronic states. 

In this volume, principal consideration is given to the lighter elements, so that the Russell-Saunders (549) vector model of the atom is used. In this model a multielectron atom is assumed to have the quantum numbers n, L = lif Ml, 8 = siy (or n, L, J = L + S, Mj). This implies stronger and Si-Sj coupling than U-Si coupling. It follows from Pauli s principle that for a closed shell =... 

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