D. I. Mendeleev’s Periodic System of Elements and Some Questions of Atomic Physics

I. P. Selinov

1. D. I. Mendeleev’s Periodic System of Elements

1951

As is known, Mendeleev’s periodic law consists in the fact that in the sequence of chemical elements arranged in order of increasing number of electrons \(Z\) in the atomic shell of neutral atoms (determined by the charge of the atomic nucleus \(Ze\)), analogous features in the form and properties of the compounds of the elements and in the properties of simple substances recur periodically. This law is conditioned by the layered structure of the atomic shell, as a result of which, as the number of electrons in the atomic shell increases, a similar structure of the peripheral electron layers is periodically repeated.

Mendeleev’s periodic law is usually expressed in the form of the periodic system of elements, which gives a rational (“natural”) systematics of the atoms of chemical elements. Reflecting the principal regularity in the properties of the elements, the periodic system is continuously being enriched in its details. There is no doubt that in a few years it will differ from the system published in Tables I and II in that it will have been supplemented by a number of new isotopes and also, possibly, by several “transuranium” elements obtained as a result of neutron synthesis or by bombardment of the isotopes Pu, Am, and other heavy elements with light nuclei (\(C^{13}\), \(O^{16}\), etc.). Therefore, for scientific and educational purposes it is necessary periodically to publish Mendeleev’s system, systematically supplemented with new scientific data.

The periodic system of elements in Tables I and II is given in the form of the so-called “short” Mendeleev system, which,

as has rightly been noted,\(^{1,2}\) most adequately expresses the periodic law and therefore is the most widespread in scientific and educational literature. The advantage of the “short” system, in the author’s opinion, is due chiefly to the fact that it consists, in essence, of eight groups, including in Group VIII the so-called “zero group” of inert elements. With such a construction of the system the sequence of filling with electrons in the atoms of the elements of the principal subgroups of the first peripheral shell, in which the maximum number of electrons is eight, is clearly expressed. Thus, the group number of the system acquires a definite physical meaning; it corresponds to the number of \(s\)- and \(p\)-electrons in the peripheral shell in the atoms of the elements of the principal subgroups and to the maximum number, for most elements, of valence electrons in the elements of both the principal and the secondary subgroups.

Proceeding from this, it seems advisable to change, as has been done in certain Russian and foreign monographs,\(^{3}\) the old numbering of the groups and to count the inert elements, whose electrons in the atoms form in the peripheral shell a closed shell of eight electrons, not as the zero group but as the eighth group. As for the triads of elements which D. I. Mendeleev called “transitional,” placing them in a separate independent group is rather artificial.\(^{1}\) The properties of these elements have a number of similar features both with the elements preceding them and with the elements located after them: Cu, Ag, and Au (which D. I. Mendeleev even placed\(^{4}\) in parentheses together with the triads of transitional elements Fe, Co, Ni, etc.). Therefore the triads of elements may be placed either to the right or to the left of the eight principal groups of the system of elements. Table II gives a system of elements in which, as in the variant of the system proposed by S. A. Shchukarev,\(^{5}\) the triads of transitional elements are placed on the left. In Table I they are placed on the right and denoted by the letters \(b, c, d\). In the author’s opinion, the form of the periodic system of elements shown in Tables I and II, although less customary than the periodic system with a zero group and the rare-earth elements placed below the table, nevertheless essentially reflects more adequately the structure of the electronic shell of atoms.

In particular, in Tables I and II the complete analogy between the 6th and the unfinished 7th periods is clearly visible.

This regularity in Mendeleev’s system became obvious only after the discovery of the actinoids;\(^{6}\) whereas earlier, before the discovery of the fission of heavy nuclei, the transuranium elements were considered for the most part as transitional elements (Eka-Os, Eka-Ir, Eka-Pt) and, consequently, it was believed, contrary to the analogous structure of the 2nd and 3rd, as well as the 4th and 5th periods in the system, that the filling

of the electron shells in the 7th period proceeds in the reverse order as compared with the 6th period. This erroneous assumption arose because the quantum theory of the structure of the electron shells of atoms could not give an unambiguous answer to the question of the sequence in which the electron layers in the shells of these atoms are filled, and also because the regularities that were becoming apparent in Mendeleev’s system were not taken into account to a sufficient degree.

Table I

Periodic System of the Chemical Elements

D. I. Mendeleev

Atomic weight, determined from radioactive-decay data.

The latter circumstance was also favored by the fact that, after the discovery of most of the rare-earth elements, in almost all variants of the “short” system of elements, including those proposed by the author,^7 the rare-earth elements, as something anomalous, were placed outside the system of elements, whereas in essence they are an organic part of the system and therefore are arrang-

are also arranged symmetrically in two neighboring periods, as are the triads of elements. As is evident from Tables I–II, the inclusion of the lanthanoids and actinoids in the system makes it possible to present more clearly the regularity in the magnitude and alternation of the periods of the system, a regularity determined by the sequence in which the electron shells in the atoms of the chemical elements are filled.

At the present time the literature contains various versions of the periodic system of the elements that include obsolete and inaccurate data, in particular incorrectly depicting the position of the actinoid group.^8 Therefore it seems highly necessary that the chemical or physico-mathematical division of the Academy of Sciences of the USSR approve a number of versions (an interesting version of the system has been proposed by Prof. S. A. Shchukarev) of the modern system of the elements. The approved versions of the system could be used in educational and scientific literature, as well as for the publication of a multicolored wall chart * (as, for example,^9).

In considering the system of the elements it should be noted that, for some elements, different names and symbols are still in use. At the chemical conference in Amsterdam in 1949, a choice was made among the various names of certain elements. It was decided to call: beryllium \(_4\mathrm{Be}\), not glucinium \(_4\mathrm{Gl}\); niobium \(_{41}\mathrm{Nb}\), not columbium \(_{41}\mathrm{Cb}\); lutetium \(_{71}\mathrm{Lu}\), not cassiopium \(_{71}\mathrm{Cp}\); tungsten \(_{74}\mathrm{W}\), not wolfram \(_{74}\mathrm{W}\). However, for a number of elements different symbols and names have still been preserved; for example: the element with \(Z=86\) is called niton \(_{86}\mathrm{Nt}\), radon \(_{86}\mathrm{Rn}\), or emanation \(_{86}\mathrm{Em}\). At one time the International Committee on Radioactivity adopted the name radon instead of emanation; however, because one of the isotopes of emanation is denoted by the symbol Rn, the name “emanation” is nevertheless retained in a number of modern tables.^21 In the writing of symbols, various designations are also encountered: argon is denoted A and Ar, thulium Tu and Tm, iodine I and J. In Tables I and II the designation I has been adopted as being closer to the first letter of the Greek word \(Ioeidēs\), from which the name of the element derives. This same symbol (I) denotes iodine in one of the last tables compiled by Mendeleev.^4

At this same conference of 1949, new names and symbols were adopted for elements obtained artificially: \(43\mathrm{Tc}\), \(61\mathrm{Pm}\), \(85\mathrm{At}\), \(87\mathrm{Fr}\), \(93\mathrm{Np}\), \(94\mathrm{Pu}\), \(95\mathrm{Am}\), \(96\mathrm{Cm}\). However, in the author’s opinion, the names technetium (artificial) and astatine (unstable) cannot be considered successful, since the production, as a result of nuclear reactions, of unstable elements is not specific only to these elements. In the same way, the 61st element and the transuranium elements are obtained.

* In the last 10–15 years, no large multicolored Mendeleev table has been published in the USSR.

PERIODIC SYSTEM OF CHEMICAL ELEMENTS OF D. I. MENDELEEV (1951)

Table II

Explanatory notes to the table

Electron configuration in the peripheral shells of the atom.
Atomic weight: an asterisk marks atomic weights obtained from isotope abundances and isotope masses; for radioactive elements \((Z>83)\), the mass number or the mass of the longest-lived isotope is given.
Symbol of the element; the symbols Eka-Tm, Eka-Yb, etc. denote as yet unknown elements—homologues of Tm, Yb, etc.
\(Z\)—the ordinal number of the element; \(Z\) is equal to the number of electrons in the neutral atom and to the number of protons in the nucleus, determining the nuclear charge.
Large numerals are the mass numbers of beta-stable, stable, and alpha-radioactive isotopes.
Smaller numerals are the mass numbers of beta-radioactive isotopes, transforming with emission of electrons \((\beta^-)\), positrons \((\beta^+)\), or by capture of an electron from the atomic shell \((K)\); underlining denotes a long-lived isotope contained in the natural mixture of isotopes of the element.
The middle line of mass numbers indicates isotopes for which it has been established or assumed that the binding energy of protons and neutrons in the nucleus is greater than in other isobaric nuclei. Presumed members are placed in parentheses.

Example cell shown:

Periodic system

Right-hand auxiliary columns

Labels in the auxiliary columns:

The periodic system of the elements has been compiled from data published up to April 1951. The groups in Mendeleev’s “short” system are denoted by Roman numerals.

The main (a) and secondary (b) subgroups of the elements are denoted by Latin letters. The symbols of the elements of the side subgroups are shifted to the right relative to the symbols of the elements of the main subgroups, and the atomic number for these elements is placed after the symbol.

In the elements of the main subgroups the first peripheral layer in the atomic shell is filled with electrons. In the elements of the secondary groups the second, deeper layer is filled. The elements with atomic numbers \(Z=58—(103)\), in which an even deeper, third layer is being filled, are close in their chemical properties to lanthanum and actinium; therefore the lines separating them (in order to show the chemical similarity of these elements and the fact that they are all located, in essence, in two elongated cells of lanthanum and actinium) are drawn as dotted lines. It should be noted here that for Ra and Th the relative positions of the \(5f\)- and \(6d\)-levels remain still unknown. Therefore, since it is impossible sharply to delimit the \(5f\)- and \(6d\)-states in the atoms of the first elements among the actinides, these elements are in a certain respect related both to yttrium and, correspondingly, to the elements of groups IV, V, and VI.

The triads of elements with \(Z=26—28;\ 44—46;\ 76—78\) have properties transitional between those of the elements of groups VII and I, and are placed on the left, since in this way a more symmetrical arrangement is obtained both of the elements of the secondary subgroups and of the rare-earth elements, which are divided in half.

The first period occupies a special place in the system, since it contains only two elements, because the first shell, unlike the following ones, consists of only two electrons. Therefore H and He do not occupy a dual position in the system and correspond both to elements located at the beginning of a period and to elements terminating a period.

After the first period, each of the two periods with the same \(n\) (the principal quantum number in the last filled shell)—the second and third, the fourth and fifth, the sixth and, probably, the seventh—has the same number (\(n\)) of filled shells in the atoms of the last element in the period, the same sequence of filling of the peripheral shells, and the same number of elements in the period (this number being equal to the number of electrons in the last filled shell).

The table gives all known isotopes (except radioisotopes with undetermined mass number); moreover, if the mass numbers of the isotopes occur consecutively, a dash is used for brevity, for example for Xe: 128—132 instead of 128, 129, 130, 131, 132.

In the middle line of mass numbers (\(M\)) are placed the principal central isotopes of the element, having a relatively greater binding energy than the other isotopes in the cluster, and determining, in the main, the increase of the atomic weights of the elements with increasing atomic number (\(Z\)). For elements with even \(Z\), the central isotopes will be \(\beta\)-stable isotopes, as well as the following \(\beta^-\)-radioactive isotopes with even \(M\) (having a greater binding energy than their stable isobars): long-lived \(^{87}\mathrm{Rb}\), \(^{187}\mathrm{Re}\), and those located on the \(\beta^+\)-radioactivity boundary, \(\beta^-\)-radioactive isotopes that are most long-lived among their neighbors—Tc and Pm (elements without \(\beta\)-stable isotopes). The central isotopes of elements with odd \(Z\), or the isotopes of odd-odd elements lying between them, are in turn shifted between the fragments of the \(M\) line of the preceding and following elements, since, for elements with \(Z=30\) elements, they have a smaller binding energy than their neighbors, and in the squares of the periodic isotopes of neighboring elements placed to the right are in the upper line.

Since in elements \(Z>60\) an alternation of four pairs of neighboring elements with even \(Z\) and even \(M\) with even central isotopes \(M^{\mathrm{even}}\) and one pair of elements with two isotopes \(M^{\mathrm{even}}\), for example \(^{163}\mathrm{Dy}\), \(^{165}\mathrm{Dy}\), \(^{167}\mathrm{Er}\), \(^{169}\mathrm{Tm}\), etc., is observed, extrapolating this pattern to the hundredth element, one may outline how this is done in the table, as well as the hypothetical values of the mass numbers of the \(\beta\)-stable and \(\beta\)-radioactive isotopes. Points near the numbers indicate that the other isotopes of these elements with smaller \(M\) and larger \(M\) than the isotopes shown in the table will be, respectively, \(\beta^-\)-radioactive (lower line) and \(\alpha\)-, \(K\)-capture-radioactive (upper line).

It would be more correct to give a similar name not to elements 43 and 85, but to elements 43 and 61, since only these elements, of all the elements up to \(Z=83\), have no stable isotopes.

Scientists who studied astatine called this element, after Mendeleev, who had predicted its existence, eka-iodine, and in their investigations used the similarity of the properties of eka-iodine to those of iodine. It would therefore be fair to name it, in honor of the great scientist whose system of elements serves as the principal method in the search for and identification of new elements, “mendelevium.” This name is just as justified as the name of the 96th element, which, in honor of the scientists who discovered artificial radioactivity, was named curium.

In view of the uncertainty in the names of certain chemical elements, it is necessary that this question be discussed by the appropriate body of the Academy of Sciences of the USSR, and that standardized names and transcriptions of the symbols of all elements of Mendeleev’s system be adopted. The need has matured for the organization of a Soviet scientific institution in the form of a commission on atomic constants and terms under the Academy of Sciences of the USSR. Such an institution should periodically approve the values of atomic constants, publish annual summaries of new values of atomic weights, tables of stable and radioactive isotopes, nuclear reactions, and other atomic and nuclear characteristics, and also organize discussion and, when necessary, submit for approval by the Academy of Sciences of the USSR proposals on new units, names, and terms, the need for which arises with the development of science.

2. ATOMIC WEIGHTS OF ELEMENTS AND THE UNIFIED SCALE OF ATOMIC WEIGHTS

In the periodic system of the elements it is customary to give atomic weights obtained as a result of chemical investigations, according to the summaries annually published by the Committee on Atomic Weights \(^{10}\). However, for a number of elements, mass-spectrographic investigations undoubtedly give more accurate values of the atomic weights. For example, as is evident from Table 11, iridium has two stable isotopes, \(\mathrm{Ir}^{191}\) and \(\mathrm{Ir}^{193}\). From the values of the relative abundances of these isotopes one obtains an atomic weight of iridium equal to 192.2; therefore it may be considered proven that the value of the chemical atomic weight of iridium (equal to 193.1), published in the tables of atomic weights of the Committee on Atomic Weights \(^{10}\), is erroneous. Likewise, the chemical values of the atomic weights of gold and thulium, each of which has only one stable isotope, are undoubtedly too high. It would therefore be more correct to give a summary of the best

values of atomic weights measured both by chemical and by mass-spectrographic methods. In Tables I and II, for several elements in which the discrepancies[^10] between the values of the chemical atomic weights and the mass-spectrographic data are especially large (the latter being more accurate), not the chemical but the mass-spectrographic values of the atomic weights are given.

For radioactive elements having no long-lived isotopes, the concept of the atomic weight of an element, i.e. the average weight of a natural mixture of stable or long-lived (with period \(>10^8\) years) isotopes, is inapplicable. Therefore, for an element having no stable isotopes, instead of the atomic weight, Tables I and II give the mass number of the longest-lived isotope. For elements for which it is not yet known which isotope has the greatest period (for example, \(\mathrm{Tc}^{97}\) or \(\mathrm{Tc}^{99}\)), or for which the discovery of new isotopes with large periods may be expected (\(\mathrm{Pu}\), \(\mathrm{Cm}\), \(\mathrm{Bk}\), \(\mathrm{Cf}\)), the atomic weight is not given (Table I), or the presumed mass number of the longest-lived isotope is indicated in parentheses (Table II). Atomic weights obtained from isotopic data, in contrast to atomic weights taken from the tables,[^10] are marked in Tables I and II with an asterisk.

The values of atomic weights are given in the tables on the “chemical” scale of atomic weights, in which \(1/16\) of the atomic weight of oxygen is taken as the unit. In the so-called “physical” scale of F. W. Aston, \(1/16\) of the atomic weight of the most abundant oxygen isotope \(\mathrm{O}^{16}\) is taken as the unit. Stas’s scale of atomic weights (the so-called “chemical” scale) is inconvenient in that the unit is taken to be the atomic weight of a mixture of the stable isotopes of oxygen, which may vary somewhat as a result of small fluctuations in the abundances of the isotopes in oxygen of different origin. Moreover, as research develops, the very values of the relative abundances of the isotopes are subject to change. Therefore the chemical unit of atomic weights is not strictly constant, and the conversion factor (according to the latest data equal to \(1.0002783 \pm 0.0000005\)[^12]) between the chemical and physical scales may somewhat change its value. The inconvenience of the existence of two scales of atomic weights has repeatedly been noted in the literature,[^13] and it would be highly desirable in the near future to introduce a single scale of atomic weights that does not have the shortcomings indicated above.

The new scale of atomic weights should meet the following requirements:

1. As the unit there should be chosen the atomic weight of an element consisting of only one stable isotope, and therefore completely independent of the origin of the element. In this case the isotopic atomic weight will coincide with the atomic weight of the element.

1. In order that the atomic weights of all isotopes be close to the mass numbers, it is necessary that the mass defect of the stable isotope of the chosen element have a mean value between the extreme values of the mass-defect curve. For this reason one cannot choose, for example, hydrogen \({}_{1}\mathrm{H}^{1}\), since the atomic weights of isotopes of heavy elements in hydrogen units would be almost one and a half times smaller than the mass number.

2. The chosen element must be convenient for mass-spectrographic measurements, and the mass of its stable isotope must have been measured sufficiently well.

3. This element must give a large number of chemical compounds with various elements.

4. The introduction of a new scale must not substantially change the atomic weights accepted in chemical practice, calculated with respect to the atomic weight of oxygen equal to 16.000.

Only one element satisfies all these conditions—fluorine. It has been proved that fluorine consists of one stable isotope, \(\mathrm{F}^{19}\), while the isotopes of adjacent mass numbers \(\mathrm{F}^{17}\), \(\mathrm{F}^{18}\), \(\mathrm{F}^{20}\) are radioactive with short periods. Therefore fluorine cannot have more than one stable or long-lived isotope.

The mass of the stable isotope of fluorine has been measured with great accuracy and is equal to 19.00435, i.e., the mass defect of the atomic nucleus of fluorine is close to the mass defect of the oxygen isotope \(\mathrm{O}^{16}\), and therefore the values of isotope masses calculated with respect to fluorine will differ little from the values of the masses in oxygen units. Mass-spectrographic measurements of heavy isotopes show that in many cases a direct comparison of isotope masses with the mass of \(\mathrm{O}^{16}\) is difficult, and the masses of isotopes are determined relative to the masses of other isotopes. Therefore the fluorine isotope \(\mathrm{F}^{19}\), as a unit of mass, is just as convenient as \(\mathrm{O}^{16}\).

Fluorine, like oxygen, forms compounds with almost all elements, and the chemistry of fluorine has in recent years undergone considerable development.

The chemical atomic weight of fluorine is 19.00, i.e., within the limits of error it is expressed in oxygen units by an integer. As a result, the “chemical” atomic weights of the elements practically do not change in the transition to the fluorine scale of atomic weights.

Proceeding from these considerations, it seems expedient to adopt as the unit both for the atomic weights of elements and for the atomic weights of isotopes \(1/19\) of the atomic weight of fluorine. The conversion factor for the transition from isotope masses calculated with respect to the oxygen isotope \(\mathrm{O}^{16}=16.0000\) to masses on the fluorine scale \((\mathrm{F}^{19}=19.0000)\) is equal to 0.99976.

3. ISOTOPES AND ATOMIC WEIGHTS OF CHEMICAL ELEMENTS

The atomic weight of a chemical element is the mean value of the atomic weights of the stable and long-lived isotopes of the given element, obtained from the values of the mass numbers, relative abundances, and mass defects of these isotopes. Therefore, when giving the atomic weights of elements in a table, it is also desirable to give (as has been done in Table II) the isotopes of the elements.

A comparison of the atomic weights of elements with the mass numbers and abundances of isotopes shows that the change in atomic weights with increasing atomic number is governed by regularities in the course of the mass numbers and in the abundances of isotopes. This is clearly seen, for example, from the differences of the rounded atomic weights of the elements from oxygen to chlorine:

Such alternation is due to the fact that: 1) the mass numbers of these elements go consecutively, with no isobars; 2) elements with odd $Z$ have one stable isotope; and 3) elements with even $Z$ have three isotopes, with the lightest isotope being the most abundant.$^{14}$

In the decades that have passed since the discovery of the periodic system of the elements, a large number of works were published in which the authors attempted to find regularities in the changes of the atomic weights of chemical elements. However, only at the present time, in connection with the development of the physics of the atomic nucleus, has it become possible to explain$^{14,15}$ these laws by reducing them to regularities in the course of the mass numbers and in the distribution of the relative abundances of isotopes. It turned out that the number of central isotopes (the middle line of the mass numbers in Table II) for most elements with even $Z$ is equal to three or five, and for elements with odd $Z$—to one or two (a second stable isotope appears in elements of odd $Z$ in those cases when the isobaric central isotope $M^{\text{even}}$ of a neighboring element with even $Z$ proves to be radioactive).

In the first case (i.e., with three central isotopes in an element with even $Z$), the increase in the mass number in analogous central isotopes upon passing from one element $Z^{\text{even}}$ to the next element $Z^{\text{even}}$, or from an element $Z^{\text{odd}}$ to the following $Z^{\text{odd}}$, will be equal to four (for example, in the elements $Z^{\text{odd}}$: ${}_{11}\mathrm{Na}^{23}$—${}_{13}\mathrm{Al}^{27}$—${}_{15}\mathrm{P}^{31}$ and ${}_{67}\mathrm{Ho}^{165}$—${}_{69}\mathrm{Tu}^{169}$); in the second case (with five central isotopes in elements with even $Z$) it

is equal to six (for example, \({}_{69}\mathrm{Tm}^{169}—{}_{71}\mathrm{Lu}^{175}—{}_{73}\mathrm{Ta}^{181}\)). Corresponding to this, the difference in the atomic weights of neighboring elements of the same parity, \(Z^{\mathrm{even}}\) or \(Z^{\mathrm{odd}}\), will be close (as is seen from Table II) to four and six. These two types of structure of the pleiads of \(\beta\)-stable isotopes \(Z^{\mathrm{even}}\) are due to the fact that the increase in the number of protons and neutrons in the majority of nuclei (except the very light ones) of the central isotopes proceeds in two ways: by the successive addition of two protons and two neutrons \((\Delta M=4)\) or of two protons and four neutrons \((\Delta M=6)^{15}\). This type of alternation may be regarded as being caused by the alternation in the nucleus of normal energy levels with pairs of protons and neutrons, which form repeating groups consisting of one biproton and one bineutron level \(2p2n\), or of one biproton and two bineutron levels \(2p4n\), which may be called helion groups, or helions, and denoted respectively by \(\alpha'\) and \(\alpha''\). The regularities in the construction and alternation of the two types of helion groups, as well as the regularities associated with the construction of these groups in the abundance of isotopes, determine the observed course of the atomic weights of the elements with increasing \(Z^{15}\). The peripheral \(\beta\)-stable isotopes (the upper and lower lines of mass numbers in Table II) are isobars of the central isotopes, and therefore the regularities in the increase of the atomic weights of the elements depend on them only very little. However, the anomalously great abundance of peripheral isotopes in some elements leads to the long-known anomalies in the course of the atomic weights of the chemical elements, which consist in the fact that the atomic weights increase with increasing \(Z\) for all elements except the following pairs: \({}_{18}\mathrm{Ar}—{}_{19}\mathrm{K}\); \({}_{27}\mathrm{Co}—{}_{28}\mathrm{Ni}\); \({}_{52}\mathrm{Te}—{}_{53}\mathrm{I}\).

The cause of these anomalies consists in the anomalously great abundance of the peripheral isotopes: \(\mathrm{A}^{40}\), \(\mathrm{Ni}^{58}\), \(\mathrm{Te}^{128}\), and \(\mathrm{Te}^{130}\). The first anomaly is probably due to the addition to the argon isotope \(\mathrm{A}^{40}\) of the products of radioactive decay of the long-lived isotope \(\mathrm{K}^{40}\), and also to the tendency toward a relative increase in the number of neutrons, observed at the end of the first period in the system of isotopes\({}^{15}\). The second anomaly is due to the fact that in nickel, unlike all other elements (except zinc), the lightest peripheral isotope (\(\mathrm{Ni}^{58}\)) is the most abundant isotope, which is possibly connected with the end of a semiperiod at this point in the system of isotopes\({}^{15}\). The third anomaly is associated with the addition to the peripheral isotopes of tellurium (\(\mathrm{Te}^{128}\), \(\mathrm{Te}^{130}\)) with normal abundance of products of the process of fission of heavy nuclei occurring in nature. This addition, owing to the low abundance of tellurium in nature, substantially changes the relative abundances of the isotopes of tellurium (and also xenon), but has practically no influence on

the abundance of isotopes in most other elements, which are considerably more widespread in nature than tellurium and xenon[^15]. In radioactive elements, as is also evident from the table, anomalies are observed in the course of the atomic weights or, more precisely, mass numbers (in S. A. Shchukarev’s terminology—nucleon numbers) of the longest-lived isotopes in neighboring elements with even and odd \(Z\). This is due to the fact that in several radioactive elements with even \(Z\) the longest period is possessed by peripheral \(\beta\)-stable isotopes \(M^{\text{even}}\) with the largest mass number, whereas in the elements with odd \(Z\) following them the longest period is possessed by the central \(\beta\)-stable isotope. Therefore the atomic weight of thorium is greater than that of protactinium, and that of uranium is greater than that of neptunium.

4. PERIODIC REGULARITIES IN THE ELECTRON SHELL OF THE ATOM AND IN ATOMIC NUCLEI

In the properties of atomic nuclei there are certain periodic regularities which it is interesting to compare with the periods of D. I. Mendeleev’s system. In the properties of isotopes one may note a dual periodicity with respect to \(Z\), with periods 2 and 20. The first periodicity, manifested in the sharp difference after nitrogen in the structure of the pleiads of \(\beta\)-stable isotopes in elements with \(Z^{\text{odd}}\) (one or two isotopes \(M^{\text{odd}}\)) and in elements with \(Z^{\text{even}}\) (from three to ten isotopes of both even and odd mass numbers), can be explained by the formation in the nucleus of heliogroups of the type \(\alpha'\) and \(\alpha''\).

The second periodicity in the system of atomic nuclei consists in the fact[^14] that, mainly after \(\Delta Z = 20\), analogous features recur in the structure of the pleiads and in the abundances of isotopes, dividing the whole system of atomic nuclei into five periods: 1) \({}_{0}n^{1}\)—\({}_{20}\mathrm{Ca}^{40}\), 2) \({}_{20}\mathrm{Ca}^{41}\)—\({}_{40}\mathrm{Zr}^{90}\), 3) \({}_{40}\mathrm{Zr}^{91}\)—\({}_{60}\mathrm{Nd}^{142}\), 4) \({}_{60}\mathrm{Nd}^{143}\)—\({}_{84}\mathrm{Po}^{208,210}\), 5) \({}_{84}\mathrm{Po}^{209}\)—… Isotopes having the same number of neutrons (20, 50, 82, and 124 or 126) as the last central isotopes in the periods possess relatively greater stability than neighboring isotopes with a different number of neutrons. In recent years a large number of experimental and theoretical works have been published indicating a number of features in the system of isotopes associated with the number of neutrons in nuclei equal to 20, 50, 82, 124, or 126. The somewhat greater length of the fourth period is due to the superposition in this part of the system of the regularity of the alternation \(4\alpha''\) and \(1\alpha'\), characteristic of half-periods at the end of the system of isotopes. According to the observed regularities, the number of neutrons corresponding to the end of the fourth period is probably equal to 124 or 126. It is customary to assume that this number is equal to 126; however, after the discovery of the longest-lived \(\beta\)-stable isotope

polonium \({}_{84}\mathrm{Po}^{208}\) (analogous to \({}_{20}\mathrm{Ca}^{40}\), \({}_{40}\mathrm{Zr}^{90}\), \({}_{60}\mathrm{Nd}^{142}\) in position in the isotope system), one may also suppose that this value is equal to 124 (the number of neutrons in the nucleus \({}_{84}\mathrm{Po}^{208}\)). A repetition of a number of features characterizing the end of a period may be expected at the end of the fifth period in the isotope system near the element with \(Z = 104\) (or 108).

Thus, a comparison of the periodic regularities in the system of atomic nuclei with the periods of the Mendeleev system shows that they are close, but do not coincide. Therefore the attempts of various authors to identify the periodicity in the properties of atomic nuclei with the periodicity in the electron shell, as a careful comparison with the available experimental data shows, do not correspond to reality.

The difference between the regularities in the Mendeleev system and the periodic regularities in the nucleus is due to the fact that, alongside regularities and properties common to the electron shell and the atomic nucleus (certain quantum-mechanical regularities, the Pauli principle, Coulomb repulsive forces between electrons in the shell and protons in the nucleus), qualitatively different forces act in the atomic nucleus (nuclear attractive forces) than in the electron shell, and it consists not of electrons but of two types of particles: protons and neutrons. As a result of the difference in the composition and in the forces acting in the electron shell and in atomic nuclei, the processes of genesis of the electron shell and of genesis of the nucleus have a somewhat different character. Apparently, the nucleus also has a layered structure, but, unlike in the electron shell, a new layer begins to be filled in the nucleus only when the preceding one has been filled. It is interesting to note that the study of the formation of nuclear shells by means of the Thomas–Fermi statistical method also leads to the conclusion of a “strict order” in the filling of shells, since each subsequent shell begins to be filled only after all the preceding ones have been filled. This latter circumstance is apparently connected with the fact that, in contrast to electrons, predominantly attractive forces act between nucleons.\(^{16}\)

The equal magnitude (apart from the somewhat longer fourth period) of the periods (with respect to \(Z\)) in the isotope system can be explained by the assumption that, just as in atoms the filled outer layers in the electron shell consist of an identical number of electrons, equal to eight (apart from the first layer \(1\mathrm{H}—2\mathrm{He}\), which has two electrons), so in the nucleus the layers consist of an identical number of helions, equal to ten (apart from the fourth period, which has 12 helions), and consequently have the same number of protons (20). At the same time, the total number of neutrons and nucleons in the periods will be different because of the different number of helions of type \(\alpha'\) and \(\alpha''\). This accounts for the irregular—

nuclear differences between the numbers of neutrons (20, 50, 82 and 124 or 126) in the nuclei at the ends of periods.

In conclusion it must be added that these assumptions of the author concerning the helion structure of the nucleus are still rather hypothetical, since the periodic regularities in the properties of nuclei have been studied less than those in the properties of atoms. As a result, a number of authors have put forward other assumptions about the nature of periodicity in the system of isotopes. For example, A. P. Znoiko^22 attempts, in contrast to what has been set forth here, to identify the periodicity in the system of isotopes with the magnitudes of the periods in Mendeleev’s system. Further experimental investigations will undoubtedly make it possible to establish, with greater reliability, the regularities in the structure of atomic nuclei and the character of periodicity in the system of isotopes.

If one assumes that atomic nuclei, like atomic shells, have a “layered” structure, then the periodic law may be given the following, more general formulation. With an increase in the number of structural elements—nucleons, and also, possibly, helions (in the atomic nucleus) and electrons (in the atomic shell)—analogous features are periodically repeated both in the structure and properties of nuclei and in the structure and properties of atoms; moreover, these features and the periodicity in nuclei and in atoms have a different character, although they possess a number of similar traits.

5. THE DISCOVERY OF NEW RADIOACTIVE ELEMENTS AND THE PROBLEM OF THE LIMITS OF THE PERIODIC SYSTEM OF ELEMENTS

Thus, the periodic law in its general form expresses the regularities of development and interrelation of definite forms of matter: atoms and atomic nuclei. The periodic system provides a classification of definite forms of matter, and its limits are determined by the number of possible kinds of atoms and atomic nuclei in nature. The successes of atomic-nuclear physics make it possible to approach the solution of a number of questions connected with the periodic system to which chemistry could not give an answer. Thus, at the present time one can draw a number of conclusions about the lower and upper limits of the periodic system, about the total number of stable and long-lived elements in nature, and study the properties of artificially created elements that do not exist under natural conditions on Earth.

The question of the lower limit of the periodic system and of the number of elements from the first element (hydrogen) to the 98th or 100th element (centurium) may be considered solved. It has been proved that the nuclei of atoms consist of protons and neutrons, and consequently there are no atoms having positively charged nuclei with a charge smaller than the charge of the proton (the nucleus of the hydrogen isotope \({}_{1}\mathrm{H}^{1}\)); nor can there be chemical elements whose number of electrons

in an atom is smaller than that of hydrogen, which has one electron. Therefore the periodic system of D. I. Mendeleev, which gives a systematics of the atoms of the chemical elements, begins with hydrogen. As for the “elementary particles,” they are qualitatively different forms of matter than atoms and atomic nuclei, and therefore obey laws distinct from the periodic law of D. I. Mendeleev established for the atoms of the chemical elements. The principal task of the physics of elementary particles is precisely to elucidate those qualitatively new features and regularities that are specific to these forms of matter.

A remarkable achievement of science is also the elimination from the periodic system of the elements of the “blank spots”—the unfilled cells of the system. Not only have all elements existing in nature with atomic numbers from 1 to 100 been discovered, but it has also been shown that no new elements can be found in this interval. The reasons have also been explained for the unsuccessful searches on Earth for elements with atomic numbers 43, 61, and 85, and the erroneousness has been proved of a number of earlier reports of the discovery of these elements, to which the authors gave various names (for example, from the names of states in the USA: illinium, virginium, and alabamium), and which were mistakenly included in many old tables of Mendeleev’s periodic system. The absence on Earth of chemical elements with \(Z = 43\) and 61 is due, according to the helion hypothesis, to the fact that they are situated at the beginning of periods of the isotope system, and in these positions the formation is energetically almost equally favorable both of a helion group of the type \(2n2p\) and of the type \(4n2p\). For example, for Mo—Ru it is equally probable that the nucleons are built up according to the type \(2n2p\) \(\left({}_{42}\mathrm{Mo}^{95},\ {}_{42}\mathrm{Mo}^{96},\ {}_{43}\mathrm{Tc}^{97},\ {}_{44}\mathrm{Ru}^{98}\right)\) and according to the type \(4n2p\) \(\left({}_{42}\mathrm{Mo}^{95},\ {}_{42}\mathrm{Mo}^{96},\ {}_{42}\mathrm{Mo}^{97},\ {}_{42}\mathrm{Mo}^{98},\ {}_{43}\mathrm{Tc}^{99},\ {}_{44}\mathrm{Ru}^{100}\right)\). As a result, the masses of neighboring isobars are close (for example, \(\mathrm{Mo}^{97}\) and \(\mathrm{Tc}^{97}\), \(\mathrm{Tc}^{99}\) and \(\mathrm{Ru}^{99}\)), differ little from one another, and \(\mathrm{Tc}^{97}\) and \(\mathrm{Tc}^{99}\) prove to be \(\beta\)-radioactive with a small decay energy and a long period. If the half-lives of these isotopes are less than \(10^{8}\) years, then during the time that has elapsed since the formation of the elements they have decayed and therefore cannot occur in the Earth’s crust*). As for the other isotopes of these elements, their periods must be shorter, since, according to the regularities in the distribution of isotope periods, the periods of \(\beta\)-radioactive isotopes decrease with distance from the region of the central isotopes.

*) The period of the long-lived isotope \(\mathrm{Tc}^{97}\) is still not known exactly, and therefore the question of the absence of these elements in natural conditions in nature will be finally resolved when the period of these isotopes has been measured. It may be assumed, by analogy with \(\mathrm{Pm}^{145}\), which has a longer half-life (\(\simeq 30\) years) than \(\mathrm{Pm}^{147}\), that \(\mathrm{Tc}^{97}\) has a somewhat longer period than \(\mathrm{Tc}^{99}\).

Since atoms lighter than hydrogen cannot exist and all gaps in the periodic system are filled, the number of elements in Mendeleev’s system can be increased only by completing the system in the direction of elements with \(Z\) greater than those of the known elements. In 1950 two new elements with atomic numbers 97 and 98 were obtained; they were named (by analogy with the origin of the names of their chemical homologues: terbium and dysprosium) according to the place of their production: berkelium or berkelium (bercelium, Bk) (in English, barklium)—from the city of Berkeley, and californium (californium, Cf)—from the university and the state of California. The element with atomic number 97 was obtained by Thompson, Ghiorso, and Seaborg\({}^{17}\) by bombarding the 95th element—americium—with high-energy \(\alpha\)-particles in the reaction

\[ {}_{95}\mathrm{Am}^{241}+\alpha \rightarrow {}_{97}\mathrm{Bk}^{243}+2n. \]

In its chemical properties berkelium has stable oxidation states III and IV; like other transuranium elements, it belongs to the actinoids and is an analogue of terbium. The isotope of berkelium found has a half-life \(T=4.6\) hours and transforms by emission of an \(\alpha\)-particle (0.1%) into \(\mathrm{Am}^{239}\) (\(T=15\) h.) or by capture of a \(K\)-electron (99.9%) into \(\mathrm{Cm}^{243}\) (\(T\cong100\) years). The emitted \(\alpha\)-particles have energies: \(6.20\) MeV (17%); \(6.55\) (53%); \(6.72\) (30%).

The same authors, together with Street,\({}^{18}\) obtained the element with atomic number 98. Californium was obtained on the same cyclotron as berkelium, by irradiating curium with \(\alpha\)-particles of energy 35 MeV. The isotope of californium is obtained, apparently, by the reaction \({}_{96}\mathrm{Cm}^{242}+\alpha \rightarrow {}_{98}\mathrm{Cf}^{244}+2n\). The isotope \({}_{98}\mathrm{Cf}^{244}\) has a half-life of 45 minutes and emits \(\alpha\)-rays with an energy of about 7.1 MeV.

The isotope \({}_{98}\mathrm{Cf}^{244}\) probably (according to the systematics of isotopes) also transforms by capture of a \(K\)-electron. In its chemical properties californium, like berkelium, belongs to the actinoids and, as the authors indicate, using Mendeleev’s terminology, is eka-dysprosium. Californium has a stable oxidation state III, and higher oxidation states IV and V have not been observed. The predominance of the oxidation state III is in agreement with the lowering of the stable oxidation state among the lanthanoids and actinoids\({}^{19}\) with increasing \(Z\).

At the beginning of 1951 a report was published\({}^{20}\) on the production of isotopes of californium: \(\mathrm{Cf}^{244}\) and \(\mathrm{Cf}^{246}\) by bombarding uranium with carbons (nuclei of the isotope \(\mathrm{C}^{12}\) of high energy) according to the reactions:

\[ {}_{92}\mathrm{U}^{238}+{}_{6}\mathrm{C}^{12}\rightarrow{}_{98}\mathrm{Cf}^{244}+6n \]

\[ {}_{92}\mathrm{U}^{238}+{}_{6}\mathrm{C}^{12}\rightarrow{}_{98}\mathrm{Cf}^{246}+4n. \]

The new isotope \(Cf^{246}\) has a half-life of 35 hours and emits \(\alpha\)-rays with an energy of \(6.75 \pm 0.05\) MeV. Earlier, in 1950, astatine had been obtained from gold by means of a reaction of the same type.

At the beginning of 1951, indirect reports appeared (see, for example, Atomes No. 58, 1951) of the discovery, by bombarding plutonium with carbon ions, of isotopes of two new elements: with \(Z = 99\), named atheneum (from the Latin Athenae—Athens, symbol probably An), and with \(Z = 100\), named centurium (from the Latin centum—one hundred, symbol Ct); however, the scientific works confirming the discovery of these elements have not yet been published. The use of light nuclei (\(He^4\), \(C^{12}\), \(O^{16}\), etc.) of high energy for bombarding the heaviest isotopes of the periodic system (alongside the reactions of neutron synthesis carried out in a nuclear reactor) will undoubtedly make it possible in the near future to obtain a number of “transcenturium” elements with \(Z > 100\) and thereby to extend Mendeleev’s periodic system.

At the present time it may be considered that all stable or long-lived (with \(T > 10^8\) years) elements in nature have been discovered. The regular decrease in the periods of the isotopes of the transuranium elements beyond uranium explains the absence in nature of long-lived elements after uranium.

Tables I and II show the probable structure of the unfinished seventh period and indicate the properties, according to Mendeleev’s law, of the as yet undiscovered elements. However, from these tables one cannot conclude that the periodic system ends with the 118th element, at which the seventh period is completed. The upper limit of Mendeleev’s system is determined by the fact that, in connection with the decrease in binding energy as the number of nucleons in the nucleus increases, nuclei must ultimately be obtained that are unstable with respect to the emission of neutrons and protons (analogously to \(He^5\) and \(Li^5\) among light nuclei), i.e., the energy released upon the addition of one more nucleon to the nucleus is \(\leq 0\), and therefore any further complication of nuclei is impossible. Thus the number of different kinds of free nuclei, both \(\beta\)-stable and \(\beta\)-radioactive, in the universe is not very large (of the order of a thousand nuclei), and the number of possible chemical elements is probably not much greater than one hundred. However, the question of the upper limit of the system of elements, determined by the nucleonic instability of nuclei, still remains open, and in order to clarify it the production of new radioactive nuclei is necessary.

It is also possible that, in fact, the boundary of Mendeleev’s system lies below the boundary of the nucleonic instability of nuclei and is determined by the very short periods of \(\alpha\)-decay or spontaneous fission in the nuclei of the last elements in Mendeleev’s system.

References Cited

1. E. Rabinovich and E. Tilo, The Periodic System of the Elements. 1933.

2. B. M. Kedrov, Chemical concepts in the light of the Mendeleev legacy, § 5 (in the collection: D. I. Mendeleev’s Periodic Law and Its Philosophical Significance, 1947).

3. See, for example, Landolt-Börnstein, Zahlenwerte und Funktionen, 1950, p. 11.

4. D. I. Mendeleev, article “Elements.” Encyclopedic Dictionary, Brockhaus and Efron, 1904.

5. S. A. Shchukarev, The present state of D. I. Mendeleev’s periodic law; Proceedings of the Jubilee Mendeleev Congress, vol. II, 1937.

6. Article “Actinides,” Great Soviet Encyclopedia, 2nd ed., vol. 2, 1950.

7. G. Semat, Introduction to Atomic Physics, Appendix III, transl. from English, IL, 1948; F. W. Aston, Mass-Spectra and Isotopes, Appendix II, transl. from English, IL, 1948.

8. Scientific and Technical Foundations of Nuclear Power Engineering, ed. K. Goodman, transl. from English, vol. I, p. 316; IL, 1948; Putilov et al., A Handbook of Physics for Teachers, 1951.

9. Henry P. Hubbard, Periodic Charts of the Atoms, 1947.

10. Report of Committee on Atomic Weight, J. Am. Chem. Soc. 70, 3531 (1948); 71, 1141 (1949), 72, 1431 (1950).

11. S. Petrovich, Tables on the physics of the atomic nucleus, table B, Appendix to the Russian translation of W. Riezler, Introduction to Nuclear Physics, IL, 1948.

12. Nier, Phys. Rev. 77, 789 (1950).

13. See, for example, Scientific and Technical Foundations of Nuclear Power Engineering, ed. K. Goodman, transl. from English, vol. I, p. 7, IL, 1948.

14. I. P. Selinov, Periodic system of isotopes, ZhETF 4, 666 (1934); Phys. Zeits. d. Sowjetunion 7, 82 (1935).

15. I. P. Selinov, Appendix 2 in Ya. I. Frenkel’s book Principles of the Theory of Atomic Nuclei, 1950; I. P. Selinov, The problem of the systematics of atomic nuclei and the search for new radioisotopes (unpublished work awarded a prize at the All-Union competition of young specialists organized by the Central Committee of the Komsomol and the Academy of Sciences of the USSR in 1938).

16. D. Ivanenko and V. Rodichev, DAN 70, 605 (1950).

17. S. G. Thompson, A. Ghiorso and G. T. Seaborg, Phys. Rev. 77, 838 (1950).

18. S. G. Thompson, K. Street, Jr. A. Ghiorso and G. T. Seaborg, Phys. Rev. 78, 298 (1950).

19. Glenn Seaborg, Transuranium elements. Chemistry of Isotopes. Collection No. 1, pp. 29, 36, IL, 1948; Seaborg, Advances in Chemistry 19, issue 4 (1950).

20. Ghiorso, Thompson, Street, Jr. and G. T. Seaborg, Phys. Rev. 81, 154 (1951).

21. B. Dzhelepov and S. Petrovich, Table of atomic nuclei, UFN 40, 497 (1950); G. T. Seaborg and I. Perlman, Table of Isotopes, Rev. Mod. Phys. 20, No. 4 (1948).

22. A. P. Znoiko, DAN 68, 837 (1949); A. P. Znoiko and V. I. Semishin, DAN 74, 917 (1950).