Narrow Results

An interdisciplinary analysis is presented in this paper on the relationship between the bifurcation behavior of chaotic systems, specifically Chua's circuit, and the quantized energy level of atoms. We show that it is possible to associate special capacitance values in Chua's circuits with the electronic energy levels E_n of atoms calculated from Bohr's Law. In particular, these particular capacitance values correspond to the bifurcation points α_n of Chua's circuits. We found a functional relation associating a specific Chua's circuit to the Hydrogen atom and obtained a map of "Atom" to " Chua's Circuit". This map can be extended to other elements in the Periodic Table, thereby demonstrating an almost universal relation between the two different physical systems. With this map we can calculate the energy levels of different atoms from bifurcation diagrams (or vice-versa) and express the analytical relations in terms of the two variables α_n and E_n.

Textbooks often claim that quantum mechanics explained the periodic system: namely, the actual configuration of electronic orbits that is responsible for the element's chemical properties can be described as the one that minimizes the total energy, and the energy of each configuration can be computed by using quantum mechanics.

However, a careful analysis of this explanation reveals that, in addition to the basic equations of quantum mechanics, we need some heuristic rules that do not directly follow from quantum physics. One reason why additional heuristics are necessary is that the corresponding numerical equations are extremely difficult to solve, and as we move to atoms with larger and larger atomic numbers Z, they become even more difficult. Moreover, as Z grows, we must take relativistic effects into consideration, and this means going from partial differential equations to even more mathematically difficult operator equations.

In this paper, we show that if instead of the (often impossible) numerical optimization, we consider the (available) ordinal information, we can then explain the observed periodic system.

There is now a considerable body of published work on the epistemology of modern chemistry, especially with regard to the nature of quantum chemistry. In addition, the question of the metaphysical underpinnings of chemistry has received a good deal of attention. The present article concentrates on metaphysical considerations including the question of whether elements and groups of elements are natural kinds. It is also argued that an appeal to the metaphysical nature of elements can help clarify the re-emerging controversies among chemists regarding the placement of the elements hydrogen and helium in the periodic system and the question of whether there exists a best form of the periodic table.

The debate about the relative epistemic weights carried in favour of a theory by predictions of new phenomena as opposed to accommodations of already known phenomena has a long history. We readdress the issue through a detailed re-examination of a particular historical case that has often been discussed in connection with it—that of Mendeleev and the prediction by his periodic law of the three 'new' elements, gallium, scandium and germanium. We find little support for the standard story that these predictive successes were outstandingly important in the success of Mendeleev's scheme. Accommodations played an equal role—notably that of argon, the first of the 'noble gases' to be discovered; and the methodological situation in this chemical example turns out to be in interesting ways different from that in other cases—invariably from physics—that have been discussed in this connection. The historical episode when accurately analysed provides support for a different account of the relative weight of prediction and accommodation—one that is further articulated here.

This article concerns various foundational aspects of the periodic system of the elements. These issues include the dual nature of the concept of an "element" to include element as a "basic substance" and as a "simple substance." We will discuss the question of whether there is an optimal form of the periodic table, including whether the left-step table fulfils this role. We will also discuss the derivation or explanation of the [n + ℓ, n] or Madelung rule for electron-shell filling and whether indeed it is important to attempt to derive this rule from first principles. In particular, we examine the views of two chemists, Henry Bent and Eugen Schwarz, who have independently addressed many of these issues.