Multielectron atoms Pauli exclusion principle

The Pauli Exclusion Principle states that no two electrons of any single atom may simultaneously occupy a slate described by only a single set of quantum numbers. Five such numbers arc needed to describe fully the quantum-mechanical conditions of an electron. For j-j coupling this set is generally ti. I., v. j. iij. and for l.-S it is /t. /. j. u(. nr,. From die coupling of the angular momentum associated with the latter sets a full description of the multielectron stale, described by it, L. S, J. Mis determined. 

Electron Spin and the Pauli Exclusion Principle Orbital Energy Levels in Multielectron Atoms Electron Configurations of Multielectron Atoms Electron Configurations and the Periodic Table... 

The importance of the spin quantum number comes when electrons occupy specific orbitals in multielectron atoms. According to the Pauli exclusion principle,... 

Note that the complete wavefunction as written in Eq. (2.47) changes sign if the labels of the electrons (1 and 2) are interchanged. W. PauU pointed out that the wavefunctions of all multielectronic systems have this property. The overall wavefunction invariably is antisymmetric for an interchange of the coordinates (both positional and spin) of any two electrons. This assertion rests on experimental measurements of atomic and molecular absorption spectra absorption bands predicted on the basis of antisymmetric electrOTiic wavefunctirais are seen experimentally, whereas bands predicted on the basis of symmetric electronic wave-functions are not observed. Its most important implication is the Pauli exclusion principle, which says that a given spatial wavefunction can hold no more than two electrons. This follows if an electron can be described completely by specifying its spatial and spin wavefunctions and electrons have only two possible spin wave-functions (a and fi). 

Results of various calculations were presented. In the orbital approximation, the energies of the orbitals in multielectron atoms depend on the angular momentum quantum number as well as on the principal quantum number, increasing as / increases. The ground state of a multielectron atom is identified by the Aufbau principle, choosing orbitals that give the lowest sum of the orbital energies consistent with the Pauli exclusion principle. 

Putting electrons into orbitals in multielectron atoms is governed by three rules, the Aufbau principle, the Pauli exclusion principle, and Hund s rule. The Aufbau, or building-up, principle tells us to put the electrons in the lowest-energy orbital that is available. The Pauli principle restricts the contents of the orbital to two electrons, with spins, s, +1/2 and -1/2. Hund s rule of maximum multiplicity (the law of antisocial electrons... ) means that where there is more than one orbital of equivalent energy, the electrons distribute between them in order to keep apart. 

The electron configuration for the molecule is obtained by placing the electrons into the MOs in a particular order. This is analogous to the conceptual model we used for multielectron atoms. The only difference here is that we are filling MOs, not AOs. Not surprisingly, rules we used for atoms, such as the Pauli exclusion principle and Hund s rule, also apply to molecules. That is, the maximum number of electrons per... 

In atoms with more than one electron, wave functions should include the coordinates of each particle, and a new term representing the electrostatic interactions between electrons. Even for the case of only two electrons, such a wave equation is so complex that it has never been solved exactly. To analyse multielectron atoms some approximations have to be made. The most practical one is to assume that the electron considered moves in an electrical potential that is a combination of all other electrons and the nucleus, and that this potential has spherical symmetry. This approximation has proven very useful, as it allows a description of energy states in a similar manner to that employed for the H atom by using a comparable set of four quantum numbers. An important, additional condition appears no two electrons can have the same set of quantum numbers in other words, no more than one electron can occupy the same energy state. This is Pauli s exclusion principle. 

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