We describe how both nuclear and atomic periodic tables happen to have common arrangements over many elements. Thus, it is possible to make a nuclear periodic table based on proton magic number nuclei, corresponding to the noble-gas (rare-gas) elements. Protons and neutrons in a nucleus form shell structures of nucleon orbitals, analogous to the shell structure of electron orbitals around a nucleus in an atom. (3) Comparison between nuclear and atomic periodic tables of elements. We will explain how valence tendencies, clearly expressed in Mendeleev’s short-period table, are recovered in the 3D helical table based on the modern long form, if the element symbols are arranged on three concentric tubes. (2) Three-dimensional (3D) periodic table that expresses Mendeleev’s periodic law. We introduce the work of Pfeiffer ( 1920), who was a student and an assistant to Werner. However, it is much less known who introduced the arrangement of the rare-earth elements in a separate table below the main table for conciseness and convenience. For the evolution of the long-form table we use today, Werner’s pioneering work in 1905 is known (van Spronsen 1969). (1) Long- form periodic tables by Werner and by Pfeiffer. In this article, we discuss the following three topics. With the discoveries of new classes of elements and accurate determination of their chemical and physical properties, along with the development of quantum mechanics that introduced fundamental concepts in elements, numerous efforts have been made to improve the periodic tables of elements (van Spronsen 1969 Mazurs 1974 Imyanitov 2016 Pyykkö 2019 Scerri 2020). Mendeleev’s periodic table is based on the “periodic law” which states that the chemical and physical properties of elements and their compounds are periodic functions of the atomic weight (Mendeleev 1869, 1871). It expresses the periodic properties of the building blocks of nature in a concise table. Periodic table of the chemical elements is undoubtedly considered as one of the greatest scientific achievements of humanity. We show that the resulting alignments of the elements in both the atomic and nuclear periodic tables are common over about two thirds of the tables because of a fortuitous coincidence in their magic numbers. Here, the nuclear shell structure leads to a new arrangement of the elements with the proton magic-number nuclei treated like noble-gas atoms. Finally we introduce a topic on the recently proposed nuclear periodic table based on the proton magic numbers (Hagino and Maeno in Found Chem 22:267–273, 2020). , 2001), which combines the s- and p-blocks into one tube, can recover features of Mendeleev’s periodic law. In particular, we explain how the 3D periodic table “Elementouch” (Maeno in Periodic-table-of-the-elements stationery. As the second topic, we compare various three-dimensional (3D) helical periodic tables that resolve some of the shortcomings of the long-form periodic tables in this respect. Although long-form tables more precisely represent electron orbitals around a nucleus, they lose some of the features of Mendeleev’s short-form table to express similarities of chemical properties of elements when forming compounds. Today’s widely used periodic table essentially inherits Pfeiffer’s arrangements. 8:984–991, 1920), who refined Werner’s work and rearranged the rare-earth elements in a separate table below the main table for convenience. As the first topic, we describe the work of Pfeiffer (Naturwiss. The periodic table currently used worldwide is of a long form pioneered by Werner in 1905. It was Mendeleev who proposed a periodic table based on the extensive periodic law and predicted a number of unknown elements at that time. A large variety of periodic tables of the chemical elements have been proposed.
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