ORDINAL EXPLANATION OF THE PERIODIC SYSTEM OF CHEMICAL-ELEMENTS

Textbooks often claim that quantum mechanics explained the periodic sy stem: namely, the actual configuration of electronic orbits that is re sponsible for the element's chemical properties can be described as th e one that minimizes the total energy, and the energy of each configur ation can be computed by using quantum mechanics. However, a careful a nalysis of this explanation reveals that, in addition to the basic equ ations of quantum mechanics, we need some heuristic rules that do not directly follow from quantum physics. One reason why additional heuris tics are necessary is that the corresponding numerical equations are e xtremely difficult to solve, and as we move to atoms with larger and l arger atomic numbers Z, they become even more difficult. Moreover, as Z grows, we must take relativistic effects into consideration, and thi s means going from partial differential equations to even more mathema tically difficult operator equations. In this paper, we show that if i nstead of the (often impossible) numerical optimization, we consider t he (available) ordinal information, we can then explain the observed p eriodic system.