The Periodic Law in Mathematical Form.

Periodic table of the elements and the Thomas–Fermi atom

“…It is in order to understand these that we try to improve and systematize our understanding of atoms. This is where the periodic system comes in; it has been called "without doubt the most important generalization in chemistry" (Hakala [29]). Attempts to construct a table for diatomic molecules have been made (Hefferlin et al [30]) with some success.…”

Using the similarity theory and dimensional analysis to quantify the periodic dependence of the properties of chemical elements

“…At the same time, the numerous studies of this kind and the wide variety of approaches used indicate that this problem has not yet been adequately resolved. [30][31][32][33][34] It has been repeatedly noted 6 that a serious obstacle that makes it difficult to establish the quantitative form of the periodic law is the diversity and heterogeneity of various physical and chemical properties of elements. Indeed, if the argument of the desired quantitative form of the periodic dependence, of course, should be the charge of the atomic nucleus (i.e.…”

“…At the same time, the numerous studies of this kind and the wide variety of approaches used indicate that this problem has not yet been adequately resolved. 30–34…”

Mendeleev Table: a Proof of Madelung Rule and Atomic Tietz Potential

“…Then the [n + l, n]-rule with help of four actions of arithmetic and well known formulas k=n k=1 k = (1/2)n(n + 1), k=n k=1 k 2 = (1/6)n(n + 1)(2n + 1), leads to the Klechkovski-Hakala formulas [11,15] Z n+l = K(n + l) + 1, n+l Z = K(n + l + 1), Z n,l = K(n + l + 1) − 2(l + 1) 2 + 1, n,l Z = K(n + l + 1) − 2l 2 , Z n = K(n + 1) − 1, n Z = K(2n) − 2(n − 1) 2 = (1/6) (2n − 1) 3 + 11(2n − 1) , Z l = K(2l + 1) + 1 = (1/6) (2l + 1) 3 + (5 − 2l) , Z nr = K(n r + 2) − 1.…”