FOUR-DIMENSIONAL PYRAMIDAL STRUCTURE OF THE PERIODIC PROPERTIES OF ATOMS AND CHEMICAL ELEMENTS

The recent results show that the dependence of the elements’ properties on the nuclei charge has a four-dimensional structure. The geometrical interpretation of this structure results in a fourdimensional pyramidal representation of the periodic properties of elements, which havetraditionally been presented on a plane since Mendeleyev’s times.

1. INTRODUCTION. The question whether there is a third dimension in the periodicproperties of the elements has been under discussion since 1939. Pauling was first to introduceelectronegativity index into the periodic system 1, while Allen suggested the configurationenergy 2. However as Maddox pointed out 3, neither Pauling nor Allen ever discussed an idea onthe existence of three-dimensional invariants and symmetries in the table of elements.The three-dimensional structure that displayed the periodicity of the elemental propertiesand had the shape of a step pyramid was introduced only in 1992 4. However, it has beenrecently proven 5 that the structure of the set of all elements has not only the third, but also eventhe fourth dimension. Below, the four-dimensional properties of the Periodic table are discussed.2. THE STRUCTURE OF ELECTRONIC SHELLS FILLING AS A FUNCTION OF THENUCLEI CHARGE. The correspondence of the four-dimensional pyramid of the elementalproperties originates from the geometrical interpretation of Hund’s empirical rule 6: the termwith the highest value of the spin S (within the given electronic configuration) and with thehighest possible value of the orbital moment L (with the given S) has the lowest energy 7. Theorder of the increase in energy of atomic orbitals has been experimentally proven and wellestablished 8:1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p < 8s(1)If one splits the set of inequalities (1) and substitutes inequality symbols by arrows, the order oforbitals filling as the function of the nuclei charge can be presented in the following form

Открыть: 4D-PYRAMID-OF-ATOMS-AND-ELEMENTS-PAPER

Four dimensional pyramid of atoms and elemets (fig 8b Scientific Israel - Technological Advantages vol. 7, No.1,2 , pp. 134-150 (2006) is represented below