FROM THE HISTORY OF PHYSICS

D. I. MENDELEEV’S PERIODIC LAW AND THE INERT GASES

B. M. Kedrov

“Periodicity was the first to make it possible to see certain elements even at such a distance to which unaided chemical vision had not yet reached...”

(D. I. Mendeleev)

1. A TABLE INDICATING THREE ELEMENTS OF THE FUTURE ZERO GROUP

In D. I. Mendeleev’s study at the A. A. Zhdanov Leningrad State University, work is under way on the study of the vast manuscript heritage of the great Russian scientist. One after another, most interesting documents are coming to light, shedding light on various aspects of his scientific work. Materials relating to the discovery of the periodic law are being studied with particular care. Among them, special attention is attracted by one small table compiled by Mendeleev in February or at the beginning of March 1869, i.e., in the very days when the periodic law was discovered. Below is given its deciphering, made by us (see Table I). In order to understand it, we reproduce the upper part of another manuscript table of the elements (see Table II), which was written by Mendeleev on the reverse side of the very same sheet of paper on which Table I was written.*)

) A volume, The Scientific Heritage of D. I. Mendeleev*, is now being prepared for publication; it brings together 19 publications of various kinds of documents relating to Mendeleev’s discovery of the periodic law (publications by D. I. Mendeleeva-Kuzmina and T. S. Kudryavtseva, with commentaries by the author of the present article). Tables I and II are included in the first of these publications. In Table I, entries made after the compilation of both columns are indicated in light type.

Table I

[[unclear: at the bottom of Table I there is a hand-drawn branching numerical scheme with the sequence \(1, 2, 3, 4, 3, 2, 1\), a top \(3\), and a bottom \(4\), connected by lines.]]

Table II

Denoting any element in a generalized way by the letter R, one may write under each column of Table II the formula of the oxide or the formula of the hydrogen compound:

\[ \begin{array}{|c|c|c|c|c|c|c|} \hline \mathrm{R}^{2}\mathrm{O} & \mathrm{RO} & \mathrm{R}^{2}\mathrm{O}^{3} & \begin{array}{c} \mathrm{RO}^{2}\\ \mathrm{RH}^{4} \end{array} & \mathrm{RH}^{3} & \mathrm{RH}^{2} & \mathrm{RH} \\ \hline \end{array} \]

Denoting further by \(X\) the equivalent of \(O\) or \(H\), we shall rewrite these formulas as:

\[ \mathrm{RX}^1 \quad \mathrm{RX}^2 \quad \mathrm{RX}^3 \quad \mathrm{RX}^4 \quad \mathrm{RX}^3 \quad \mathrm{RX}^2 \quad \mathrm{RX}^1. \]

Indicating only the numerical value of the atomicity (valence) of the elements, we obtain the series:

\[ 1 \quad 2 \quad 3 \quad 4 \quad 3 \quad 2 \quad 1. \]

Even- and odd-atomic elements here alternate successively; moreover, in each row the number of groups with even-atomic elements is equal to three, and with odd-atomic elements to four. This is also expressed in the lower part of Table I.

In Table I Mendeleev reduces the odd-atomic elements to two columns (the left column) and the even-atomic, or, as he calls them, diatomic elements (the right column); in each column, the sequence of increasing atomic weights is maintained. This is achieved by removing from Table II all elements of the future even groups (II, IV, and VI) (shown in boldface):

\[ \begin{array}{ccccccc} & & & \mathrm{H} & & & \\ \mathrm{Li} & \mathbf{Be} & \mathrm{B} & \mathbf{C} & \mathrm{N} & \mathbf{O} & \mathrm{F} \\ \mathrm{Na} & \mathbf{Mg} & \mathrm{Al} & \mathbf{Si} & \mathrm{P} & \mathbf{S} & \mathrm{Cl} \\ \mathrm{K} & \mathbf{Ca} & & \mathbf{Ti} & & \mathbf{Cr} & \end{array} \]

From the remaining elements a separate column is formed in the same way as from those removed. At the same time Mendeleev examines the distinction between even and odd rows in the periodic system. (In Table II the former are marked with the sign \(//\), the latter with \(\backslash\).) Subsequently Mendeleev shifts his main attention to the distinction between even and odd rows, leaving entirely aside the question of the distinction between even and odd groups. Nevertheless, the fact is noteworthy that at the very first moment, as soon as the periodic law had been discovered, Mendeleev examined his newly created system of elements from the standpoint of comparing even and odd groups.

Having formed a column of odd-atomic elements following one another in order of increasing atomic weights, and then a column of even-atomic elements, Mendeleev proceeds to consider the differences between the atomic weights for each pair of neighboring elements, separately in each column. This means that he finds the differences between the atomic weights of elements standing one place apart in the periodic system, except for the extreme ones, standing at the beginning and at the end of each row, which, being in both cases odd-atomic, are directly adjacent to each other, since there is no even-atomic element between them.

In the left column of Table I, in all cases (except three) the difference in atomic weights is equal to 4; in two cases (two adjacent pairs: \(N - B = 3\) and \(F - N = 5\)) it is equal to 3 and 5, so that their sum is 8; on the average this again gives 4; and only in one case, for \(Li - H = 6\), does it strongly deviate from the mean value, equal to 4; but with respect to hydrogen, as the most typical element standing at the beginning of the whole system, Mendeleev allows a sharp deviation from the average norm in this case as well. He even attempts to determine the differences in atomic weights between the first member of the column (\(H = 1\)) and the subsequent members (\(Li - H = 6;\ B - H = 10\)), but then abandons this attempt, puts a question mark in both cases, and passes on to the right column.

Initially the right column began with beryllium (\(Be = 9\)), as the lightest of all known even-atomic elements. The difference in atomic weights of adjacent elements at the beginning of the column is close to 4 (\(C - B = 3\)) or equal to 4 (\(O - C = 4\)); then there occurs, as it were, a jump over an empty place, and the difference gives exactly the doubled value: \(4 \cdot 2 = 8\) (\(Mg - O = 8\)); then again come two fours (\(Si - Mg = 4\) and \(S - Si = 4\)), and once more a jump by 8 (\(Ca - S = 8\)). The same kind of jump is observed at the very beginning of this column—from zero straight to 9. Mendeleev assumes that in each of the three noted cases there is an unknown even-atomic element with an intermediate atomic weight; then in both rows there would be observed a general regular order in the change of atomic weights for each pair of adjacent odd-atomic elements, and for each pair of adjacent even-atomic elements. This order would be expressed in the fact that the indicated difference would everywhere be equal to 4, with a rare deviation by 1 in one direction or the other, except for the lightest (typical) elements standing at the beginning of each row, where it could deviate considerably from 4.

Guided by the indicated consideration, Mendeleev introduces the following hypothetical additions into the right column:

first, he enters above \(Be = 9\) molecular hydrogen \(H^2 = 2\), which in this case must play the role of the lightest even-atomic element, occupying in the system the place between \(H = 1\) and \(Li = 7\);

second, he notes that between \(O = 16\) and \(Mg = 24\), among the even-atomic elements, an element \(X\) with atomic weight 20 is missing; supposing for a moment that \(X\) is possibly fluorine, Mendeleev then crosses out the symbol \(F\), since fluorine is an odd-atomic element, whereas the matter concerns an unknown even-atomic element with an atomic weight 1 greater than that of fluorine; it is obvious that in the system of elements the missing element \(X = 20\) must occupy a place between the two odd-atomic elements: \(F = 19\) and \(Na = 23\);

Thirdly, he notes that between \(S = 32\) and \(Ca = 40\), among the same even-atomic elements, one more element \(X\) with atomic weight 36 is still lacking; assuming for the moment that it might be chlorine, Mendeleev then crosses out the symbol \(Cl\), for \(Cl\), like \(F\), is an odd-valent element; the missing element \(X = 36\) must take its place in the system of elements between \(Cl = 35\) and \(K = 39\). Thus, by the hypothetical introduction of three missing elements, Mendeleev split in half (into two quartets each) both anomalous octets in the differences of atomic weights; moreover, he reduced the jump to the first member of the column, since now, instead of a direct transition to 9, there was a transition from 0 to 2 \((H^2 = 2)\) and from 2 to 9, i.e. by 7 \((Be - H^2 = 7)\). As a result, the regular increase of atomic weights by 4 units for each pair of adjacent elements in both columns of Table I was maintained almost impeccably, with a correction only for the initial (typical) members of each column.

But what are these missing elements? What is their position in the general series of elements throughout the whole system? What other properties, besides the already calculated presumed values of their atomic weights, do they possess? The answer to these questions is of exceptional interest.

First of all, let us note that all three proposed elements have approximately the same atomic weights \((2; 20; 36)\) as helium, neon, and argon, discovered 25–30 years later \((4; 20.2; 39.9)\). The order of the magnitudes themselves and their sequence are the same in both cases; what is important is that the atomic weights \(H^2 = 2\) and \(He = 4\), despite their difference, lie in the interval between \(H = 1\) and \(Li = 7\).

Next, let us note that all three missing elements had to occupy a definite position in the system at the end (or at the beginning) of each of its first three rows, i.e. such a position that nowhere would two odd-atomic elements adjoin one another directly, but would adjoin only even-atomic elements; in that case, in the system of elements, even- and odd-atomic elements would alternate consecutively, without any interruptions.

In this connection, the unknown elements would have had to form one common, entirely special group (precisely a group), which would stand before the first group of alkali metals \((H^3\) before \(Li\); \(X = 20\) before \(Na\); \(X = 36\) before \(K)\) and after the seventh group of halogens \((X = 20\) after \(F\); \(X = 36\) after \(Cl)\), or after hydrogen, which is to a certain extent close to the halogens \((H^3\) after \(H)\). This is exactly the same place in the system that was later occupied by the zero group of inert gases.

The position of the expected group of missing elements in the periodic system indicates the possible properties of its members:

to the right of it stand the strongest metals, to the left—the strongest nonmetals; according to the periodic law, an element occupying in the system an intermediate place between two others must show an average value of properties between their properties. In accordance with this, Mendeleev adds together the numerical values of the properties of both extreme members and finds the mean. The same also applies to the qualitative characterization of the intermediate member; for example, the place between a strong and a weak metal is occupied by an element with moderately expressed metallic properties. If, however, this device is applied to the case of determining the average properties with respect to the strongest metals and the strongest nonmetals, for which purpose these two extreme opposites must mentally be added to one another, then, obviously, one must come to the conclusion that the two opposites will neutralize one another, will mutually compensate each other, just as negative and positive electricity are compensated. (Incidentally, Mendeleev himself spoke of nonmetals as electronegative elements and of metals as electropositive elements.)

In the large periods of the system the transition from one extreme (from the beginning of the period, for example from K) to the other (to its end, respectively, to Br) takes place gradually and successively, through 15 elements occupying intermediate places in the system, lying between sharply expressed (alkali) metals and equally sharply expressed nonmetals (haloids). In moving from left to right through the system, from the beginning of each period to its end, the metallic properties of the elements successively weaken, while the nonmetallic properties strengthen just as successively. At the same time, in Mendeleev the most typical example of elements of transitional character is furnished by the metals of Group VIII[^1]. (Let us note that in 1869 Group VIII had not yet been formed by Mendeleev.) Thus the transition from an alkali metal to a haloid is accomplished in the system.

The situation was different in the transition from the end of one period to the beginning of the next period after it, i.e. from a haloid to an alkali metal. Here the leap, being very sharp, in no way represented the same kind of successive change of properties as in the first case; in 1869 no intermediate forms whatever were discovered here, and there occurred at once and directly a transition from the strongest nonmetal (for example, Cl) to the strongest metal (K). The question arose: what properties should an element possess if it stood between Cl = 35 and K = 39? Obviously, it would have to represent a transition from a certain negative magnitude (characterizing the chemistry of the haloid) to an approximately equal positive magnitude in absolute value (characterizing the chemistry of the alkali metal). Such a transition could only be zero, complete neutrality, the absence of chemical activity; this is similar to the way in which—

MENDELEEV’S PERIODIC LAW AND THE INERT GASES

electroneutrality (absence of charge) is an intermediate state in passing from a negative charge to an equal positive charge in absolute magnitude, which may be expressed as follows: \(-z;\ 0;\ +z\). Similarly, one may represent the transition from a temperature equal, say, to \(+100^\circ\) C, through one intermediate mean value, directly to a temperature of \(-100^\circ\) C; obviously, such an intermediate, mean value can only be \(0^\circ\) C.

This is why, if one begins to develop further Mendeleev’s prediction of three elements that should occupy places in the system between the haloids (or hydrogen) on the one side and the alkali metals on the other, one would inevitably have had to arrive at the conclusion that they possess a complete absence of chemical activity. For, in qualitative chemical respect, only such an element \(X = 20\) could be intermediate in comparison with \(F = 19\) and \(Na = 23\), which would be entirely devoid of chemical activity, since the slightest predominance of a metallic (positive) or nonmetallic (negative) character would make this element not strictly intermediate with respect to its neighbors \(F\) and \(Na\). The same applies also to the element \(X = 36\), since it would have had to occupy the place between \(Cl = 35\) and \(K = 39\).

Unfortunately, Mendeleev apparently did not attempt to investigate in greater detail the properties of the three missing elements he had already groped toward from the qualitative side, in the sense of an assumed determination of their chemical peculiarity. He confined himself merely to deriving their presumed atomic weights and indicating their place in the system between the haloids and the alkali metals. But, we repeat, Table I in itself already contains all the data needed to draw from it the most important consequence, namely that the supposed elements must be characterized by complete chemical neutrality, by a complete absence of chemical activity.

It is extremely important to note that precisely the same conclusion ought to have been led to by considering the revealed dependence between elements of even and odd atomicity (as it is presented in Table I) also from the quantitative side. Indeed, let us place in a single row the numerical values of the atomicities of the first four rows of the periodic system, as they are shown in Table I (beginning with \(H\), whose atomicity is equal to unity); here let us denote by \(x\) the value of the atomicity of the missing elements, remembering that, according to Mendeleev, it must be even. Then the following series is obtained:

\[ \begin{array}{cccccccccccccccccccccc} & & & 3 & & & & & & & & 3 & & & & & & & & & & \\ & & \diagup & | & \diagdown & & & & & & \diagup & | & \diagdown & & & & & & & & & \\ 1 & x & 1 & 2 & 3 & 4 & 3 & 2 & 1 & x & 1 & 2 & 3 & 4 & 3 & 2 & 1 & x & 1 & 2 & 3 & 4\ldots \\ \diagdown & & & \diagdown & & \diagdown & \diagup & & \diagup & & & \diagdown & & \diagdown & \diagup & & \diagup & & & & & \\ & 1 & & & & 4 & & & & & & & & 4 & & & & & & & & \end{array} \]

Without allowing new, missing elements, the number of odd-atomic elements in each row of elements proves to be one greater than that of the even-atomic ones: 1 versus 0 in the first row; 4 versus 3 in the next two rows. Mendeleev notes this in Table I (below). The supposition of missing even-atomic elements eliminates the discrepancy between the number of even and odd groups in the small periods and creates, in this respect, complete symmetry: in each period their number becomes the same.

How great a significance Mendeleev attached to symmetry is shown by his notes in the scientific diary that he kept from the end of 1870 to the end of 1871.* Here he writes: “Two concepts lie everywhere: symmetry and sympathy.” And further: “Three concepts in the philosophy of science: sympathy, symmetry, and motion; they are everywhere.” The striving to reflect, in the rows of elements, the objectively existing symmetry of the relations among the elements was precisely what compelled Mendeleev to introduce additional even-atomic elements with atomic weights 2, 20, and 36.

But the essence of the matter consists not only, and not even so much, in recognizing and expressing a certain symmetry in the number of groups of even- and odd-atomic elements. The essence of the matter lies in the numerical value itself of the atomicity \(x\) of the proposed missing elements. The successive order of decrease of atomicity from 4 to 1 in the second half of one row and its equally successive increase from 1 to 4 in the first half of the following row required that \(x\) be equal to 0; only in that case would the general course of change in atomicity be observed both within each row and in the transition from one row to the next following it.

Although Mendeleev designated the right-hand column in Table I as the column of “diatomic elements,” this must be understood to mean that all even-valent elements are included here; for example: C, giving \(\mathrm{CO_2}\); Si, giving \(\mathrm{SiO_2}\); Ti, giving \(\mathrm{TiO_2}\). Therefore, the admission that \(x = 0\) would in no way contradict the general characterization of the right-hand column, but, on the contrary, would fully correspond to it.

Further, if for the sake of symmetry in the number of even and odd groups the number of the former had to be increased by one (by introducing missing elements between the future I and VII groups), then, for the same consideration, as it seems to us, it was impossible to assign to these missing elements any atomicity other than zero, for the sum of all the atomicity values of the four odd-atomic elements of each small period \((1 + 3 + 3 + 1 = 8)\) was already equal

* This diary is kept in the D. I. Mendeleev room at LSU and is listed as notebook No. 1. The entries cited below were made in it on pp. 42 and 48. In the above-mentioned volume The Scientific Heritage. D. I. Mendeleev, part of this diary constitutes the fifteenth publication.

to the sum of all values for its three even-atomic elements \((2 + 4 + 2 = 8)\). Consequently, in this respect symmetry had already been achieved; any other value for the atomicity \(x\) of the missing elements, except \(x = 0\), would have disturbed the symmetry already attained for both types of groups (even- and odd-valent). Therefore, approaching the solution of the question from this side as well, it was necessary to admit that the atomicity of the missing elements had to be equal to zero. Incidentally, this was also indicated by the inclusion of the molecule \(\mathrm{H}^2\) in the place between \(\mathrm{H} = 1\) and \(\mathrm{Li} = 7\), for in \(\mathrm{H}^2\) both free atomicities of hydrogen are mutually saturated; therefore the total atomicity of \(\mathrm{H}^2\) is equal to zero.

As a result, replacing \(x\) in the preceding series by zero, one could obtain the following series of atomicity values:

\[ \begin{array}{cccccccccccccccccccc} & 1 & & & & & 4 & & & & & & & & 4 & & & & & \\ & \backslash & & & / & / & & \backslash & \backslash & & & / & / & & & \backslash & \backslash & & & \\ 1 & 0 & 1 & 2 & 3 & 4 & 3 & 2 & 1 & 0 & 1 & 2 & 3 & 4 & 3 & 2 & 1 & 0 & 1 & 2\ 3\ 4\ldots \\ & \backslash & & & \backslash & \backslash & / & & & / & & \backslash & & \backslash & / & & & / & & \\ & 1 & & & & & 4 & & & & & & & & 4 & & & & & \end{array} \]

For both small periods here, complete symmetry is observed throughout.

Thus, apparently, matters would have stood with the elucidation of the quantitative side of the question (in the sense of determining the numerical value of atomicity), if one attempted, on the basis of Table I, to continue the investigation of the assumed properties of the missing elements. Although Mendeleev did not carry out such a more detailed investigation, nevertheless Table I already contains all the data needed to draw the conclusion that the atomicity of the missing elements should have been equal to zero.

Thus, consideration of the system of elements (Table II) both from the qualitative side (with regard to the chemistry of the elements) and from the quantitative side (with regard to the magnitude of their atomicity) leads to one and the same result: the properties of the three missing elements with atomic weights 2, 20, and 36 should express their complete chemical neutrality, inertness, absence of chemical activity, and, correspondingly, the equality of their atomicity to zero.

But the most remarkable thing, perhaps, was Mendeleev’s prediction not of individual missing elements in already existing groups, but precisely of an entire new group of elements, which was to stand before the group of alkali metals and after the group of halogens, i.e. between the future groups I and VII. As is known, the difficulty connected with singling out in the system of elements just such a group of elements was the reason that, in the period from 1894 to 1900, Mendeleev had doubts about the elementarity of argon and its analogues. Meanwhile, the resolution of this difficulty was already contained in Table I, compiled by

by Mendeleev 25 years before the discovery of argon and 30 years before the introduction into the periodic system of a new (zero) group.

Thus, Table I contains: 1) Mendeleev’s prediction of three unknown elements; 2) an indication of their atomic weights, 2, 20, and 36; 3) an indication of their place in the system of elements between H and Li, F and Na, Cl and K; 4) an indication that the missing elements must possess even atomicity; and 5) that they must form a special group, analogous to the groups of the alkali metals and the halogens.

In addition, from Table I one could have concluded that 6) the missing elements must be chemically neutral, inert (“intermediate” between the halogens and the alkali metals), and 7) that they must possess an atomicity equal to zero, i.e., the minimal one, which has its place in the transition from the descending line of atomicities at the end of one period (4, 3, 2, 1) to the ascending line of atomicities at the beginning of the next period (1, 2, 3, 4). Although Mendeleev himself did not draw the last two conclusions, they are contained implicitly in his arrangement.

2. MENDELEEV’S ANTICIPATION OF ONE OF THE DISCOVERIES OF NUCLEAR PHYSICS

Let us draw attention to one more feature inherent in the numbers contained in Table I. Comparing the differences in atomic weights between elements of even atomicity and between elements of odd atomicity, Mendeleev felt his way toward one of the regularities of nuclear physics². Let us note that in the first three rows of the periodic system the evenness and oddness of the ordinal numbers of the elements (established in 1913) coincide with the evenness and oddness of the atomicity of the corresponding elements, as Mendeleev defined it in Table I. This is explained by the fact that an increase in the number of valence electrons in the shell of the atom corresponds to an increase in the nuclear charge \(Z\), numerically equal to the ordinal number of the element. In other words, elements with odd atomicity (equal to 1 or 3) at the same time also have odd ordinal numbers, while elements with even atomicity (equal to 2 and 4, as well as zero) have even ordinal numbers. Thus, the left column in Table I actually represents elements with odd nuclear charges (\(Z^{\text{odd}}\)), and the right column—those with even charges (\(Z^{\text{even}}\)). It is known that among the light elements with \(Z^{\text{odd}}\), from F to P, there is one stable isotope each; moreover, the composition of the nucleus of \(P^{31}\) contains one helion (alpha particle) more than that of \(Al^{27}\), that of \(Al^{27}\) contains one helion more than that of \(Na^{23}\), and that of \(Na^{23}\) contains one helion more than that of \(F^{19}\). This means that the difference in atomic weights (more precisely, in mass numbers) in a pair of adjacent elements with \(Z^{\text{odd}}\) is equal to 4. The same is observed

PERIODIC LAW OF MENDELEEV AND THE INERT GASES

is also given for the predominant isotopes of the following two (in the system) elements \(Z^{\text{odd}}\) one after the other: for \(\mathrm{Cl}^{35}\), whose nucleus is greater by 1 helion than that of \(\mathrm{P}^{31}\), and for \(\mathrm{K}^{39}\), whose nucleus is greater by 1 helion than that of \(\mathrm{Cl}^{35}\). The same is also observed for the predominant isotopes of the two preceding (in the system) elements: for \(\mathrm{B}^{11}\), whose nucleus is greater by 1 helion than that of \(\mathrm{Li}^{7}\). A certain deviation is observed only in nitrogen, for which the predominant isotope is not \(\mathrm{N}^{15}\), but the isotope \(\mathrm{N}^{14}\); nevertheless the general regularity is maintained here as well, so that the difference in the composition of the nuclei of \(\mathrm{F}^{19}\) and \(\mathrm{B}^{11}\) (i.e., of two elements \(Z^{\text{odd}}\) separated by one) is equal to two helions. Thus, if one considers the sole or predominant isotopes of the elements \(Z^{\text{odd}}\) from Li to K, then the difference in the composition of their nuclei will, as a rule, be equal to one helion, and hence the difference in atomic weights (more precisely, in mass numbers) is equal to 4.

For the elements \(Z^{\text{even}}\) from He to Ca, as a rule, the same picture is observed, with the exception of argon and beryllium. But for elements \(Z^{\text{even}}\) separated by one, the general regularity is observed here as well: the predominant isotopes of the elements \(Z^{\text{even}}\) are isotopes whose nuclei contain an integral number of helions, and therefore their atomic weights (more precisely, mass numbers) differ from one another by 4 or by a multiple of four; moreover, beginning with C and up to Ca, for elements \(Z^{\text{even}}\) (except argon) the predominant isotope is the lightest isotope. But the difference between the nuclei of the isotope \(\mathrm{Ca}^{40}\) and the isotope \(\mathrm{S}^{32}\) (separated by one) is equal to two helions, just as between the nuclei of the isotope \(\mathrm{C}^{12}\) and the isotope \(\mathrm{He}^{4}\). In the remaining cases the increase in the number of helions in the nuclei of the most widespread isotopes of the elements \(Z^{\text{even}}\) proceeds very regularly, by one helion from \(\mathrm{C}^{12}\) to \(\mathrm{O}^{16}\) and further to \(\mathrm{Ne}^{20}\), \(\mathrm{Mg}^{24}\), \(\mathrm{Si}^{28}\), and \(\mathrm{S}^{32}\). It is characteristic that the argon isotope \(\mathrm{Ar}^{36}\) is predominant relative to the isotope \(\mathrm{Ar}^{38}\), but apparently because \(K\)-capture occurs in the isotope \(\mathrm{K}^{40}\), a predominant amount of the isotope \(\mathrm{Ar}^{40}\) was formed; if this additional process had not taken place, then the predominant isotope of argon would probably have been \(\mathrm{Ar}^{36}\).

All this leads to the conclusion that, as a rule, the difference in the composition of the nuclei of the predominant isotopes of adjacent elements \(Z^{\text{odd}}\) and of adjacent elements \(Z^{\text{even}}\) is equal to one helion (or two, if elements separated by one are considered); this means that the difference in atomic weights (more precisely, mass numbers) in both cases for adjacent elements is on average equal to four.

After calcium this simpler regularity no longer holds; the picture becomes greatly complicated, since the difference in the composition of the corresponding nuclei of adjacent elements \(Z^{\text{odd}}\) (and, correspondingly, \(Z^{\text{even}}\)) reaches that of a more complex helion, consisting of two protons and four neutrons, and hence the difference in atomic weights (more precisely, in mass numbers) reaches six.

It was precisely this general regularity for the elements occupying the first 20 places in the periodic system that Mendeleev discerned in Table I. Rounding the values of the atomic weights to whole numbers, he in fact, though of course without suspecting it himself, entered in both columns of the little table the mass numbers of the most widespread, predominant isotopes of the corresponding elements, for example \(Cl = 35\) instead of the usual 35.5; \(Al = 27\) instead of the usual 27.4; \(Be = 9\) instead of the usual 9.4. The prediction that between \(O = 16\) and \(Mg = 24\) there should exist an element \(X = 20\), i.e. one whose atomic weight is greater than that of \(O\) by 4 and less than that of \(Mg\) also by 4, was brilliantly confirmed: this element proved to be neon, whose predominant isotope is \(Ne^{20}\). Guided by this regularity, which he had in fact discovered, Mendeleev predicted not only argon (\(X = 36\)), but also its most probable atomic weight, in the event that the indicated regularity were not complicated by the process of \(K\)-capture in \(K^{40}\) superimposed upon it; but, of course, Mendeleev could not in any way foresee this “anomaly,” even in the most tentative form; therefore he proceeded from the regularity he had discovered in its pure form, and in such a case for argon it is important to take into account the most widespread isotope after the isotope \(Ar^{40}\), formed, apparently, from \(K^{40}\); precisely such a predominant isotope of argon (after \(Ar^{40}\)) is \(Ar^{36}\).

Finally, noteworthy is also the fact that Mendeleev succeeded in sensing the boundary at which the manifestation of the regularity under consideration, in its simpler form, comes to an end, when the differences between adjacent elements \(Z^{\text{odd}}\) (and, correspondingly, \(Z^{\text{even}}\)) are equal to one helium, i.e. four units of atomic weight. In reality, such a boundary for the elements \(Z^{\text{odd}}\) is potassium, and for the elements \(Z^{\text{even}}\) it is calcium. It is precisely with these elements that Mendeleev ends the derivation of the differences (equal to four) in the left and right columns of Table I; at potassium he altogether breaks off the left column of odd-atomic elements (i.e. elements \(Z^{\text{odd}}\)); in the right column he tries to continue the list of elements: under \(Ca = 40\) he writes \(Ti = 50\) and, still lower, \(Fe = 56\); but here the difference in atomic weights immediately reaches the value 10, whereas it is already quite impossible to open places in the system here for the missing elements. Therefore Mendeleev in fact breaks off the right column at calcium, which fully corresponds to the way modern nuclear physics treats the regularity, sensed by Mendeleev, in the change of mass numbers and isotopes for the first 20 elements of the periodic system.

3. THE SUBSEQUENT FATE OF MENDELEEV’S PREDICTIONS

Thus, more than 80 years ago Mendeleev predicted individual elements of the future zero group, some of their properties and their entire group, as well as the general regularity in the change of atomic weights (more precisely, mass numbers) among elements of even

and odd atomicity for the first 20 elements of the periodic system.

Questions arise: (1) why did Mendeleev not bring these predictions of his to the same comprehensive substantiation as he did with respect to ekaaluminium, ekaboron, and ekasilicon? What prevented him from following to the end the path already begun, which was unquestionably correct? (2) Why later did he not return to his initial assumptions about elements with atomic weights 2, 20, and 36, forming a special group between the alkali metals and the halogens, when the discovery of helium and, especially, argon seemed to have shaken the whole edifice of the periodic law? (3) Finally, why did he never, anywhere, mention his predictions after argon and its analogues had taken in the periodic system precisely those places which he had indicated as early as 1869 for missing elements with just such atomic weights?

Let us try to answer these questions.

First of all, let us recall that Table I was compiled by Mendeleev at the moment of the discovery of the periodic law, when neither the number of groups in the system, nor the distinction between even and odd series in it, nor even the positions in it of many chemical elements had been firmly established. Mendeleev was then seeking ways of further refining the first, still far from perfect, version (attempt) of his system. One such path is indicated in Table I; this path placed the groups of elements in the foreground, with their subdivision into even and odd ones and with the additional creation of a zero group between the halogens and the alkali metals. But not a single representative of this zero group was yet known at that time; it was entirely empty. Meanwhile, all nine elements of the future VIII group (also an even one) were present and required a clear resolution of the question of their place in the periodic system. The creation of an empty zero group after the halogens could hinder the formation, between groups VII and I, of a new, VIII group, which was still absent in the various variants of the system of elements compiled by Mendeleev in 1869.

It is also beyond doubt that at that time the assumption of the idea of zero valency must have seemed paradoxical to Mendeleev; indeed, the law he had discovered indicated a periodic dependence of the ability of elements to form chemical compounds on atomic weights, whereas here one would have had to admit elements with a complete absence of such ability. Of course, such a doubt would not have arisen if at least one chemically inert element had been known at that time and studied experimentally; but helium had been discovered only on the Sun, and its properties (apart from the spectral ones) were not known; the other inert gases were discovered only 25–30 years later. It is clear that Mendeleev had grounds to doubt the correctness of the assumption that followed

about zero atomicity, and therefore also about the probability of the existence of elements with atomic weights 2, 20, and 36.

Another path in the development of the periodic system, which at that time opened up much broader prospects, consisted in placing the series of elements in the short table of the elements at the forefront. Already in February—March 1869 Mendeleev for the first time began to subdivide the series in the system into even and odd ones, alternating the displacement of elements to one side or alternating various kinds of symbols (see Table II). Later, in 1870, Mendeleev introduced numbering of the series and already clearly divided the series into even and odd. Thus Mendeleev transferred the criterion of evenness and oddness from the groups to the series of elements.

The separation of even series allowed Mendeleev to indicate their distinctive features, in particular the presence in them of transition elements (the families of iron, palladium, and platinum); from the latter, in 1870, there arose in Mendeleev a new, VIII group, the emergence of which no longer made it possible to raise the question of a zero group, since the transition from group VII to group I turned out to be occupied by the elements of group VIII. As a result, this last group displaced the suppositions concerning a zero group of elements that had been arising in Mendeleev.

Mendeleev’s view also changed concerning the characterization of the atomicity of elements and its dependence on atomic weights. In March 1869, when Table I had been compiled, Mendeleev wrote: “The fluorine group represents elements that combine chiefly with one bond of hydrogen, the oxygen group—with two, nitrogen—with three, and carbon—with four bonds of hydrogen or chlorine, so that in this respect the naturalness of the distribution of the groups in a definite order is not violated by the numbers expressing their atomic weight, but, on the contrary, is as if anticipated. In the very first comparison we have 7 columns ..., of which Li and F are monatomic and represent the greatest separation in the electrochemical order, Be and O, following them, are diatomic; they are followed by B and N—triatomic, while in the middle is placed the tetratomic C. Looking at the separation of Na and Cl, Ag and I, etc., we see that the numerical conjunction of the elements corresponds, to a certain degree, also to atomicity and to the notions of affinity.”³

Hence there arose the seven-membered series of values of atomicity considered above:

$$ 1\ 2\ 3\ 4\ 3\ 2\ 1 $$

In accordance with this, at that time it would have been possible to suppose that the series might be eight-membered and end with zero. But here Mendeleev still had two kinds of atomicity (valence) mixed together—according to hydrogen and according to oxygen. Half a year later, in the autumn of 1869, he separated both kinds of atomicity and showed that in the higher

MENDELEEV’S PERIODIC LAW AND THE INERT GASES

oxygen compounds that give salts (i.e., in the higher salt-forming oxides), the atomicity of the element increases from 1 for elements of group I to 7 for elements of group VII, so that the value of the atomicity proves equal to the number of the group. On the contrary, the composition of hydrogen compounds among elements of groups IV—VII proves to be such that the number of hydrogen atoms does not increase, but decreases with increasing group number. As a result, the originally single series of atomicities of the elements \((1\ 2\ 3\ 4\ 3\ 2\ 1)\) split into two series:

\[ \begin{array}{llllllll} \text{for the higher salt-forming oxides:} & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \text{for the hydrogen compounds:} & \text{—} & \text{—} & \text{—} & 4 & 3 & 2 & 1 \end{array} \]

It was precisely this more refined view of atomicity that ruled out the possibility of admitting that after group VII there could stand an element with zero atomicity. On the contrary, it was necessary to admit that the atomicity of such an element in the higher salt-forming oxide would be equal to 8 (in the order of increase of the figures in the upper row), while its atomicity with respect to hydrogen would be equal to 0, i.e., that it would not give hydrogen compounds. At the same time Mendeleev had already drawn attention to the fact that the sum of both values of atomicity (with respect to O and to H) proves equal to 8; therefore, for an oxide of composition \(\mathrm{RO}^{4}\), the hydrogen compound should be taken as \(\mathrm{RH}^{4}\).

Thus, by the autumn of 1870 Mendeleev had formed the following two series, showing the maximum atomicity of the elements with respect to O and to H:

\[ \begin{array}{cccccccc} 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \text{—} & \text{—} & \text{—} & 4 & 3 & 2 & 1 & 0 \\ \hline \multicolumn{3}{l}{\text{sum:}} & 8 & 8 & 8 & 8 & 8 \end{array} \]

Under such circumstances, zero atomicity proved to be the inability of elements of group VIII to give hydrogen compounds. The concept of zero atomicity could contain nothing else, and there remained no possibility of developing further those predictions that had been made by Mendeleev in February—March 1869 and that were reflected in Table I. The very path that had been outlined in that table probably must, by the end of 1870, have seemed false to Mendeleev himself, for that path proceeded from taking into account such characteristics as, a year and a half later, either disappeared altogether or were refined, revised, and split apart.

In connection with this, let us cite one passage from Mendeleev’s article, written in November 1870: “In exactly the same way there may be impossible elements with lower atomic weight—from 1 to 7, i.e., lying between hydrogen and lithium, and elements of group VIII with atomic weight about 20, i.e., lying between fluorine and sodium, just as the elements of the iron group are placed between manganese and copper.”⁴ Here Mendeleev doubts in

of the existence of elements which in Table I are denoted by \(H^3 = 2\) and \(X = 20\), and this time he speaks of them as hypothetical members of Group VIII.

Just at this same time Mendeleev began to keep the diary mentioned above, on p. 9 of which he entered a peculiar table of elements, compiled as follows: from the atomic weight of each element the atomic weight of a typical element of the same group is subtracted, and the difference is divided by the number of the period. For example, for potassium one obtains

\[ \frac{K - Li}{1} = 32. \]

But the hydrogen row and the first two small periods in the system have no representatives of their own in Group VIII, the first members of which appear only in the first large period (in the potassium row). Therefore, under the number of Group VIII Mendeleev wrote: “unknown what to subtract.” However, below he makes the following calculation for platinum:

\[ \frac{Pt - 21}{4} = 35. \]

Here, as the typical element of Group VIII, an unknown element is introduced, standing between \(F = 19\) and \(Na = 23\), and therefore possessing an average atomic weight \(X = 21\). This is still the same future neon, but included now not in a special, zero group, but in the just-formed Group VIII.

It is very interesting to note the following: earlier Mendeleev arrived at the idea of the existence of the element \(X = 20\) (between F and Na) by considering the differences of atomic weights between even-atomic and between odd-atomic elements arranged in horizontal rows; from the atomic weight of the heavier element there was subtracted the atomic weight of the lighter element situated first to the left along the row (through one). Now Mendeleev studies the differences of atomic weights between members of one and the same group, i.e. elements arranged vertically in the system, one beneath another. In this case he comes to the same conclusion as in Table I, that in the lithium row there must exist an element precisely in the same place (between F and Na) and with approximately the same atomic weight (\(X = 21\)). Thus, the number 20 or 21 arose for Mendeleev at the point of intersection of both directions—horizontal and vertical—in which he investigated the differences of atomic weights among elements arranged in the system by rows and groups. The conclusions that an element with atomic weight 20–21 must exist between F and Na followed for Mendeleev quite independently from consideration of the periodic system in two different cross-sections (horizontal and vertical), and this should have spoken with particular persuasiveness in favor of the supposition of an element \(X = 20\). However, judging by the data so far available, Mendeleev apparently did not return again to his prediction of elements of the future zero group. The sheet with Table I evidently fell, in Mendeleev’s papers, among rough drafts or already used-

called entries and was lost among them. The same applies to the diary in which Mendeleev, beginning on December 14, 1871, began to record his studies of the elasticity of rarefied gases. As is known, Mendeleev himself regarded the discovery of the inert gases as unexpected. This could be explained as follows: by the time argon was discovered Mendeleev was already 60 years old; by then he had probably completely forgotten his initial predictions of elements with atomic weights 2, 20, and 36, which were to occupy places between the halogens and the alkali metals and form a special group of elements.

4. THE METHODOLOGICAL BASIS OF MENDELEEV’S PREDICTIONS

In 1887, seven years before the discovery of argon, Mendeleev said: “Before the periodic law, simple substances appeared to be only fragmentary, accidental phenomena of nature; there were no grounds to expect any new ones, and those newly found were, in their properties, a complete and unexpected novelty. Periodicity was the first to make it possible to see still undiscovered elements at such a distance that chemical vision, unaided by this law, had not reached before; and at the same time the new elements, before their discovery, were outlined with a whole mass of properties.”⁵

The underlined words, taken as the epigraph to our article, may be applied in full measure to Mendeleev’s prediction of the future elements of the zero group and of some of their very substantial properties.

What, then, was the methodological basis of this remarkable prediction? From the statement just cited it follows that the immediate guiding principle for Mendeleev was the periodic law he had discovered. But in its turn this law itself rested on a broader methodological foundation, which was in fact served above all by the law of the transformation of quantitative changes into qualitative ones, as applied to chemical elements. I. V. Stalin writes: “Mendeleev’s ‘periodic system of elements’ clearly shows what great significance in the history of nature the emergence of qualitative changes from quantitative changes has.”⁶ Engels wrote of the same thing.⁷

The transformation of quantitative changes (of atomic weight) into qualitative ones (the chemical individuality of an element) occurs in such a way that there is a definite course in the increase of atomic weights, expressed in definite differences between them in passing from one element to another, and these differences themselves, in their magnitude, change with the increase of the atomic weight of the elements. Let us consider the series from which Mendeleev proceeded

in the compilation of Table I:

The course of the differences in atomic weights here is quite clear: from O to Co the magnitude of these differences is equal to 1, 3, or 4, but no more than 4, and the alternation of 1 and 3 predominates. Each time the atomic weight first changes by 1, and then by 3, then again by 1, and so on, which determines the transition to a qualitatively new element in a definite (periodically recurring) sequence. Only in one of 16 cases is there a sharp deviation: the difference between Ca = 40 and Ti = 48 at once reaches 8; moreover, the leap is made from the divalent element (Ca) straight to the tetravalent (Ti), bypassing the odd-atomic (trivalent) element. Obviously, here the general course of the increase of atomic weights and of their transformation into qualitative differences of elements, characteristic of this section of the periodic system, is disrupted. In order to remove this disruption, it was necessary consistently to apply the proposition concerning the transition of quantitative changes into qualitative ones, allowing that between Ca and Ti there should stand some still unknown triatomic element with an atomic weight of about 44; in that case the anomalous jump to 8 in the differences between atomic weights would be eliminated, and their general course would not be disturbed. Consequently, the very idea of the possibility of predicting new, still unknown elements and describing their properties in Mendeleev actually rested on the law of the transition of quantitative changes into qualitative ones. But Mendeleev did not give himself a clear account of precisely what method he was using in practice, what precise law he was in fact applying in his predictions.

Mendeleev in fact also applied the named law of dialectics in predicting the elements of the future zero group and their properties. This is clearly seen in the columns of even- and odd-atomic elements of Table I. Indeed, Mendeleev establishes as a regularity for this section of the periodic system such a course in quantitative changes (i.e., in the differences of atomic weights) whereby the emergence of a new quality, for example a new odd-atomic element, occurs as the result of adding four units to the atomic weight of the preceding likewise odd-atomic element. The same is true for even-atomic elements. This means that the proposition concerning the transition of quantitative changes into qualitative ones is specified here as follows: for the transition to a new quality, a quantitative change of 4 units of atomic weight in the nearest element of the same evenness or the same oddness of atomicity is necessary.

When a difference exactly twice as large is found, then, unconsciously applying the law of the transition of quantitative changes into qualitative ones, Mendeleev comes to the conclusion that this doubled difference \((4 \cdot 2 = 8)\) testifies to the existence of elements missing at this point, with intermediate values of atomic weights: \(X = 20\) and \(X = 36\); such values make it possible to eliminate the apparent violations of the general course of quantitative changes, i.e. of the course of differences in atomic weights. The same also applies to the hypothesis of the missing element \(H^2 = 2\). Here the supposition suggested itself of an unknown element with atomic weight 4, which would have made it possible to extend the observed regularity also to the first members of the column of even-atomic elements. However, believing that in the region of the lightest (typical) elements there must be specific deviations from the average norms, Mendeleev introduced here not \(X = 4\), but \(H^2 = 2\).

Further, Mendeleev considered the series of values of atomicity, changing within one row from 1 to 4 and then from 4 to 1, as a periodic function of the atomic weights, with a maximum in the middle of the row at C, Si, Ti and with a minimum at the end and beginning of each row. Consequently, here too the fact is expressed that quantitative changes in atomic weight pass into qualitative changes in the chemistry of the element, while these latter in turn are expressed in new quantitative indicators of the element’s atomicity: each time it changes by 1 (increasing or decreasing), thereby changing its character, i.e. passing from even to odd and from odd to even. Mendeleev’s establishment of the successive decrease of atomicity by one in the second half of the row inevitably had to lead to the conclusion that after H, F, and Cl, whose atomicity is equal to one, a further decrease by 1 must give zero. Consideration of the process of increase of atomicities by 1 in the first half of the row should have led to the same conclusion; the question arose: what value of atomicity should the missing element have, so that adding one to it would give the atomicity value of Li, Na, and K, equal to one? Obviously, it would have had to be equal to zero. Thus, the consistent application of the law of the transition of quantitative changes into qualitative ones led to the conclusion that the missing elements must possess zero atomicity and, consequently, constitute a zero group of elements in the system; each of them would have to represent the minimum value of atomicity with which the branch of decreasing atomicities of the preceding row ends and the branch of increasing atomicities of the following row begins.

The predictions considered show what a truly powerful cognitive instrument is his periodic law, in which the law of the transition of quantitative changes into qualitative ones is concretized.

References Cited

1. See D. I. Mendeleev, Selected Works, vol. II, p. 146.
2. See I. P. Selinov, “D. I. Mendeleev’s Periodic System of the Elements and Certain Questions of Atomic Physics,” Uspekhi fizicheskikh nauk, vol. 44, no. 4, 1951, pp. 518–520.
3. D. I. Mendeleev, Selected Works, vol. II, pp. 9–10.
4. Ibid., p. 161.
5. D. I. Mendeleev, Two London Lectures, 2nd ed., 1895, p. 54. (Emphasis ours. — B. K.)
6. I. V. Stalin, Works, vol. 1, p. 301.
7. F. Engels, Dialectics of Nature, 1950, pp. 42–43.