Electronic configuration. Pauli exclusion principle

There are a number of rules that determine the way in which the electrons of an atom may be distributed, that is, that determine the electronic configuration of an atom. 

The most fundamental of these rules is the Pauli exclusion principle only two electrons can occupy any atomic orbital, and to do so these two must have opposite spins. These electrons of opposite spins are said to be paired. Electrons of like spin tend to get as far from each other as possible. This tendency is the most important of all the factors that determine the shapes and properties of molecules. 

The exclusion principle, advanced in 1925 by Wolfgang Pauli, Jr. (of the Institute for Theoretical Physics, Hamburg, Germany), has been called the cornerstone of chemistry. 

The first ten elements of the Periodic Table have the electronic configurations shown in Table 1.1. We see that an orbital becomes occupied only if the orbitals 

PpoUeni 13 (a) Show the electronic configurations for the next eight elements in the Periodic Table (from sodium through argon), (b) What relationship is there between ectronic configuration and periodic familj 7 (c) Between electronic configuration and chemical properties of the elements  

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We account for the ground-state electron configuration of an atom by using the building-up principle in conjunction with Fig. 1.41, the Pauli exclusion principle, and Hund s rule. 

Electron configurations of transition metal complexes are governed by the principles described in Chapters. The Pauli exclusion principle states that no two electrons can have identical descriptions, and Hund s rule requires that all unpaired electrons have the same spin orientation. These concepts are used in Chapter 8 for atomic configurations and in Chapters 9 and 10 to describe the electron configurations of molecules. They also determine the electron configurations of transition metal complexes. 

The last rule needed to generate electron configurations for all the atoms in the periodic table came from a German scientist named Friedrich Hund. Hund s rule can be expressed in several ways. The most precise definition is that atoms in a higher total spin state are more stable than those in a lower spin state. Thus, the sixth electron in carbon-12 must have the same spin as the fifth one. The Pauli exclusion principle then requires that it fill an empty p orbital. 

Fig. 6 The Huckel MOs of the three isomeric benzoquinodimethanes [8]. The bonding MOs of the ortho- and para-isomers are filled according to the Pauli exclusion principle. The electron configuration of the non-bonding MOs of the metaisomer is dictated by Hund s rule.

Watch the video clips at www.brightredbooks. net. These will help you understand how to use the Pauli exclusion principle, the aufbau principle and Hund s rule to write electronic configurations of atoms. 

Consider the electronic configuration of carbon again Is 2s 2pl Remember, there are three different p orbitals in the 2p subshell the p orbital lies on the x-axis the p orbital lies on the y-axis and the p orbital lies on the z-axis. The different p orbitals are degenerate. To obey Hund s rule, these degenerate orbitals must be filled singly before spin pairing occurs. To obey the Pauli exclusion principle, when an orbital is full with two electrons, these electrons must have opposite spins. This is not shown using spectroscopic notation, but is seen when orbital box notation is used. 

Each orbital can therefore contain no more than two electrons, with opposite spin quantum numbers. This rule, which affects the order in which electrons may fill orbitals, is known as the Pauli exclusion principle. Table 2.3 summarizes the configuration of electron orbitals for the first three shells. The orbitals are labeled with the numerical value of n and a letter corresponding to the value of l (s, p, d, f..). As you can see from Table 2.3, the n = 1 shell can hold up to two electrons, both in the s orbital, the n - 2 shell can hold up to eight electrons (2 in the s and 6 in the p orbital), the n - 3 can hold up to 18 electrons (2 s, 6 p, and 10 d), and the n 4 shell can hold up to 32 electrons (2 s, 6 p, 10 d, and 14 f). The lowest energy orbitals are occupied first. So for hydrogen, which has one electron, the electron resides in the Is orbital. For lithium, which has three electrons, two are in the Is orbital and the third is in the 2s orbital. For silicon (Z = 14), there are two electrons in Is, two electrons in 2s, six electrons in 2p, two electrons in 3s, and two electrons in 3p. 

The Pauli exclusion principle forbids cotain combinations of nt, and m, in determining the term symbols for the states of the nitrogen atom. Consider an excited nitrogen atom in which the electronic configuration is ls22522p13pI. What states now are possible ... 

N electrons with the same values of quantum numbers n,7 (LS coupling) or tijljji (jj coupling) are called equivalent. The corresponding configurations will be denoted as nlN (a shell) or nljN (a subshell). A number of permitted states of a shell of equivalent electrons are restricted by the Pauli exclusion principle, which requires antisymmetry of the wave function with respect to permutation of the coordinates of the electrons. 

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

By applying the Pauli Exclusion Principle, we can put each successive electron into the available lowest-energy orbital to yield the following electronic configurations for the first 30 elements in the periodic table (Table 2.3.1). 

Closely related to the Pauli exclusion principle is the third rule, Hund s rule, which states that when electrons occupy orbitals of equal energy (e.g., the five 3d orbitals), one electron enters each orbital until all the orbitals contain one electron. In this configuration, all electrons will have parallel spin (same direction). Second electrons then add to each orbital so that their spins are opposite to the first electrons in the orbital. Atoms with all outer orbitals half-filled are very stable. 

In the H2 molecule the lowest energy electron configuration is obtained by placing both electrons in the aR s molecular orbital with their spins paired so as to satisfy the Pauli exclusion principle. The Slater determinant for this arrangement is... 

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