Building-Up Principle and the Periodic Table

The chemical properties of an atom are related primarily to the electron configuration of its ground state. Table 8.1 lists the experimentally determined ground-state electron configurations of atoms Z = 1 to Z = 36. (A complete table appears in Appendix D.) 

Most of the configurations in Table 8.1 can be explained in terms of the building-up principle (or Aufbau principle), a scheme used to reproduce the electron configurations of the ground states of atoms by successively filling subshells with electrons in a specific order (the building-up order). Following this principle, you obtain the 

The quantum numbers and characteristics of orbitals were discussed in Section 7.5. 

A mnemonic diagram for the building-up order (diagonal rule] 

Now you can see how to reproduce the electron configurations of Table 8.1 using the building-up principle. Remember that the number of electrons in a neutral atom equals the atomic number Z. (The nuclear charge is +Z.) In the case of the simplest 

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The energy-ordering scheme (5-58) coupled with the Pauli or exclusion principle and Hund s rule leads us to a simple prescription for building up the electronic configurations of atoms. This aufbau principle is familiar to chemists and leads naturally to a correlation between electronic structure and the periodic table. The procedure is to place all the electrons of the atom into atomic orbitals, two to an orbital, starting at the... 

Between the years 1921 and 1923, Bohr returned to the problem of atomic structure and the periodic table. He announced a new improved version of the electronic periodic table, claiming it to be based on a principle of the old quantum theory, namely the adiabatic principle. His method, called the Aufbauprinzip, consisted in building up successive atoms by the addition of an extra electron to the previous atom. Bohr... 

The organization of the periodic table (Section B) can be explained now that we know about electron configurations (Box 1.2). The table is divided into s, p, d, and f blocks, named for the last subshell that is occupied according to the building-up principle (Fig. 1.34). Two elements are exceptions. Strictly, helium belongs in the s block, but it is shown in the p... 

The Aufbau principle provides the guideline for building up the elements. The periodic table classifies the elements according to their atomic numbers and thus also by the electronic configurations of their atoms. 

We thus have a simple model (the aufbau or building-up principle of Bohr [1] and Stoner [2]) which correctly predicts the periodic structure of Mendeleev s table of the elements. More precisely, one should state that Mendeleev s table is the experimental evidence which allows us to use an independent electron central field model and to associate each electron in a closed shell with a spherical harmonic of given n and i, because there is no physical reason why a particular l for an individual electron should be a valid quantum number angular momentum in classical mechanics is only conserved when there is spherical symmetry. 

The orbital concept and the Pauli exclusion principle allow us to understand the periodic table of the elements. An orbital is a one-electron spatial wave function. We have used orbiteils to obteiin approximate wave functions for many-electron atoms, writing the wave function as a Slater determinant of one-electron spin-orbitals. In the crudest approximation, we neglect all interelectronic repulsions and obtain hydrogenlike orbitals. The best possible orbitals are the Heu tree-Fock SCF functions. We build up the periodic table by feeding electrons into these orbitals, each of which can hold a pair of electrons with opposite spin. 

The elements with partially filled d and f subshells constitute a separate group within the Periodic Table, because their properties are quite distinct. Their fiindamental characteristic is that they do not follow the simple rule of the aufbau or building-up principle. For this reason, they are often left out of elementary discussions in courses on Quantum Mechanics, or merely referred to as complicated exceptions, whereas in fact they are a wonderfiil example of another class of elementary principles, namely the properties of short-range asymmetric wells. We shall refer to these elements as Q-elements, to distinguish them fi om the related class of rsne earths (R-elements) as defined elsewhere in this Handbook. 

Rule 1 The Aufbau ( Build-Up ) Principle. Orbitals fill in order of increasing energy, fi om lowest to highest. In this course, we are concerned primarily with the elements of the first, second, and third periods of the Periodic Table. Orbitals fill in the order Is,... 

The Building-Up Principle The periodic table can be constructed by increasing atomic number and adding electrons in a stepwise fashion. Specific guidelines (the Pauli exclusion principle and Hund s rule) help us write ground-state electron configurations of the elements, which tell us how electrons are distributed among the atomic orbitals. 

A useful way to determine electron configurations is based on the aufbau principle (German aufbauen, to build up ). We start at the beginning of the periodic table and add one proton to the nucleus and one electron to the lowest energy sublevel available. (Of course, one or more neutrons are also added to the nucleus.)... 

The Aufbau principle describes the theoretical, sequential building up of the elements in the periodic table by the stepwise addition of protons and electrons. 

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