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A PERIODIC TABLE AND NEW PERIODIC FUNCTIONS1 Z. G. SZABO and B. LAKATOS Institute for Inorganic and Analytical Chemistry, University of Szeged, Szeged, Hungary
ALTHOUGH the periodic table is one of the fnndamental tools of both theoretical and descriptive inorganic chemistry, it is difficult to interpret the variations of chemical and physical properties of the elements in terms of the tables now in general use. The periodic law depends not only on the number of electrons of the neutral atom (atomic number) but also on electronic configuration as determined by quantum numbers, the Pauli exclusion principle, the stability sequence of atomic orbitals, and the ~ r i n c i ~of l e maximum multiplicity. table may be developed by arrangements of the s, p, and d electrons, which to a first approximation are the property-determininp- electrons. A theoretically correct
EDITOR'SNOTE: This paper is a condensation of one puhlished (in English) by the authors in Acta Chimica Amdemiae Seientiarum Hungaricae (Budapest) IV/2-4, pp. 129-49 (1954). Soholars whose particular interest is the emphasis of periodicity in the properties of elements are urged to consult the original paper for a more complete discussion. ~h~ itssistanee of D ~ L~~~~~~ . 5. ~ ~ and tD=. e Arthur N. Wrigley in the preparation of the present manuscript is gratefully acknowledged. % Asomewhat similar position was assigned to the inert gases in a chart described by C. A. KMUS in "Contemporary Develop York, ments in Chemistry," Columbia University press, N ~ W 1927.
VOLUME 34, NO. 9, SEPTEMBER, 1957
yet simple system may be obtained by rearranging the long periodic table in such a way that the inert gases are situated in the middle (I),?as shown in Figure 1. To the right of the inert gases come the elements in which an s-orbit becomes filled over a vacant d-orbit, followed by the elements in which the d-orbit becomes filled. At the left of the table are the elements that are filling an s-orbit, above a completed d-orbit, and those that are filling a p-orbit. As the best compromise between theory and simplicity, the lanthanides and actinides, which are filling f-orbits, are placed below the rest of the table. In the present periodic table, the filling of the individual orbits occurs in separate locations, a very important feature. since the fillins of different tvnes of orbits results in c&iderably different physical G d chemical properties for the elements concerned. In Mendeleev's time, with electronic stmcture unin known, the table was composed of periods rows. At the present time, ,periodicity of properties must be ascribed to the penodicity of the electronic ~ stmcture, and the filling of the shells is therefore preferahle as a basis for the table to the comnletion of periods, no matter how customary the may be, Theoretical and pedagogical advantages result, moreover, from the central position of the inert gases.
Figure 1.
P.riodic Table Ernphlsining E1ert..nis
DETAILED DESCRIPTION AND DISCUSSION OF THE TABLE
Periods begin with hydrogen or an alkali metal a t the middle of the table and terminate with an inert gas on the line below their inception. The principal quantum number of the outermost shell of an element is thus identical with the number of the period considered. The use of two rows for a period emphasizes the succession in the building of shells and the fact that a main shell is not usually completed by an inert gas but continues to he filled in the same row on the right of the table. After the filling of the d-orbit of a given principal quantum number, the filling of the s and p-orbits of the following principal quantum number takes place. Thus, each row represents the filling up of a shell. There are no main groups and subgroups in the present system, hut at the top of each column is shown the number of electrons in the subshell or subshells concerned, as indicated by magnetic and spin quantum numbers and the Pauli exclusion principle. The inert gases, which differ sharply from the other elements and which form a boundary in this table between elements filling s and p-orbits and those filling s- and d-orbits, are allotted the largest spaces. The elements filling their outermost s and p-fields are shown in standard size rectangles. The elements in which the shell next inside the outermost is being filled, the transition elements, are placed in smaller rectangles since they differ less from one another. Lastly, the elements in which the third-from-outermost shell is building up, the lanthanides and actinides, are shown in the smallest spaces, as resembling one another the most. Hund's rule of maximum multiplicity determines the number of unpaired electrons of an element. I n this
Configulation
form of the table, these can he shown separately for each column of elements. Both the number of unpaired electrons and the maximum valence characteristic of a column are shown in the two bottom rows of Figure 1. The expected electronic configuration of an element can easily be read from the table. Zr, for example, occurs in the same row as Rb, the fifth element in the alkalimetal column, and thus possesses two s-electrons in its Hth, or outermost shell. Being also the second of its row of transition elements, it should possess two d-electrons in its next-to-outermost, or fourth, shell. Thus the electronic configuration of Zr is that of Kr plus 5 9 , 4d2. Similarly that of Po consists of the core of Au plus 6s2,6p4. In some cases the actual configuration differs slightly from the expected (2). The gradual change in properties of the elements, borne out in the present table, makes possible their classification by dividing lines into seven groups: inert gases; nonmetallic elements; semimetallic elements; meta-metals; alkali and alkaline earth metals; transition metals; rare-earth metals (lanthanides, actinides). The heavy step-shaped line in the lefthand part of the table, besides separating different groups, also recalls Grimm's law of the hydrides. Above these steps covalent bonds are common; below, ionic bonds predominate. Elements immediately above the steps have nearly equal atomic radii, Goldschmidt ionic potentials, and electronegativities. Between the heavy and the dashed stepped lines lie the semimetals, unusual in their polymorphism, semiconductor properties, glass formation, etc. Incidentally the dashed line claims astatine as a semimetal instead of a halogen (S), in harmony with its coprecipitation as a sulfide (4) with tellurium (6),hut not as a silver salt (6). Similar step-wise relations discernible throughout the periodic system may be illustrated JOURNAL OF CHEMICAL EDUCATION
by the diagonal groups: BSi-As-Te-At, Na-Ca, Ca-Y, K-Sr, Rh-Ba, and Ti-Nb-W. For elements within the heavy lines, electropositive character increases from right to left and from top to bottom, except for interruption by the inert gases. For elements outside this group, electropositiveness increases from bottom to top and tends to increase with the number of unpaired electrons. The exclusion of beryllium and magnesium from the alkaline earths and their assignment to the semimetal and zinc groups, respectively, rest on electronic configuration and chemical properties: the two outer selectrons of these elements lie above totally completed shells, as with zinc hut not calcium; they form Grignard reagents but not saline hydrides. The central position of the inert gases accords with the tendency of other elements to attain an inert gas structure in ionically or covalently bound compounds or in the metallic state. Elements just to their left often gain enough electrons to form negative ions of inert gas configuration; those to their right may lose electrons to form analogous positive ions. Elements below the heavy stepped line tend to form ions with an outer shell of 18 or 18 2 electrons.
Figure 3.
Boiling Points of the S-P Element.
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ESTABLISHMENT OF PERIODIC FUNCTIONS
A special merit of this periodic table is that it facilitates the establishment of periodic functions that determine the physical properties of the elements. It is the fine distribution of electrons which establishes these functions. Past attempts to establish such functions have suffered (7, 8, Q), not only from unsatisfactory data in the literature but also from using atomic numher as the independent variable, whereas the physical constants are actually functions of the fine distribution of the electrons. In Figures 2, 3, and 4 are graphed the melting points, boiling points, and heats of sublimation of S-P elements as functions of their outermost s and p-electrons. One may generalize that for each family or column these physical constants are linearly related to the principal quantum number. The limited number of divergencies from this rule are due t o variations in molecular structure, lattice, and bond types. The constants of
Fimra 2.
Mcltinw Po:nts of the S-P Element.
VOLUME 34, NO. 9, SEPTEMBER, 1957
Figure 4.
H-t.
of Sublimation of the S-P Elnmmnt.
magnesium agree with extrapolated values of the zinc and not the calcium group. In the P-field, the straight lines connecting data of individual columns rise for the inert gas, halogen, oxygen, and nitrogen columns and thereafter display a downward tendency. For the Sfield, the slope is invariably downward. Sharp discontinuities, however, occur both in periodic functions and in the "column-lines" between BeMg, A1-Ga, Ge-Sn, and Sb-Bi, elemenbpairs divided in our periodic table by the heavy stepped line. The properties shown in the graph exhibit a t first one maximum followed by two maxima per period, explainable by the corresponding maxima in elemental bond strengths. The fourth-column maximum is due to the covalent lattices of these elements, while the other maximum results from the high bond energy (10) of the cubic, face-centered lattice of copper group elements. For the elements of the D-field the only physical data that could be utilized were the melting points. Within a column these are linear functions of the total quantum number (Figure 5), whereas the slopes of the plots of the individual columns (slopes of the dashed lines of Figure 5) are a function of the number of unpaired electrons (Figure 6). The maximum of the latter, hellshaped, curve a t the manganese group, coincides with the maximum number of unpaired electrons (and also with maximum electropositive character). The two sides of the bell-shaped curve are not symmetrical. This is probably related to the fact that on the two
in Meltin. Point (Saa Figure 5) Figure 6. The Slope of th. 1 n - e Within One Family as a Function of Number of d Electron*
sides different numbers of paired electrons correspond to the same number of unpaired electrons. While only unreliable data are available on the heats of sublimation and boiling points of D-field elements, it was interesting that with each new value from the recent literature these properties also began to display peri~dicity.~ The present periodic table is not only easily understood but also theoretically correct. It renders p o s sible the correct establishment of the property functions, dependent within a column on the principal quantum number. These functions, on the other hand, show the direction for further investigations and may perform in practice the same function in predicting values of physical properties as did the Mendeleev table in the discoverv of the eka-elements in earlier davs. a
See Acfa Chirn. Acad. Sci. Hung., 4, 145 (1954).
LITERATURE CITED SZABO, Z. G., AND B. LAKAMS, Research 5,590 (1952). DEBILNGER,U., "Chemisehe Physik der Metalle und Leeieruneen (Akademische Verlaasaesellschaft M. B. H.. -~eipzig),'i~D p.,44.
w.
ATEN, A. H. W., T. DOORGEEST, HOLLBTEIN, H. P. MOEKEN, Analyst, 77,774 (1952). CORSON, D. R.,K. R. MACKENZIE, E. SEGRE,Phys. Rev., 57, 459 (1940).
GARRISON, W. M., J. D . GILE, R. D. MAXWELL, J. G. HAM~LTON, Anal. Chem., 23,204 (1951). JOHNSON. G. L.. R. F. LEININGER, E. SEGRE.J. Chem. Phys.,'17, l(1949). HERDAN, G., Notwe (London), 162,215 (1948). SZABO,Z. G., B. LAKATOS, Natunoi88enschajten, 39. 486
(1952) - - - - ,. (9) Semo, Z. G., Magyar Tudornanyos Akademia Kemiai Twl. Oszl. K i i z l a a y e i . , 3, 153 (1953). (10) PRINT^, J. A,, J. M. DUMORE, L.TIAMTHOAN, Physica, 18, 307 (1952). \
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