The Structure of Atoms and the Physico-Chemical Properties of the Elements1

Niels Bohr.

The first postulate of Bohr’s theory of the atom consists in the assumption of the existence of “stationary states” of the atom, in which the latter does not emit energy. According to the second postulate, radiation occurs only during transitions of the atom from one stationary state to another, and the radiation then proceeds in the form of a discontinuous series of purely harmonic waves; the frequency of the light oscillations is determined in this case by the following condition:

\[ h\nu = E' - E'' \tag{1} \]

where \(\nu\) is the frequency, \(h\) is Planck’s constant, and \(E'\) and \(E''\) are the energies of the initial and final stationary states. Relation (1) gives a direct interpretation of Balmer’s empirical law, which determines the frequency of the oscillations of the line spectrum of hydrogen:

\[ \nu = K\left(\frac{1}{(n'')^{2}}-\frac{1}{(n')^{2}}\right), \tag{2} \]

where \(K\) is a constant, and \(n'\) and \(n''\) are integers. Comparing postulate (1) with the empirical law (2), we see that the energy of a certain \(n\)-th stationary state (up to a constant) is determined as follows:

\[ E_n=-\frac{K\cdot h}{n^{2}}. \tag{3} \]

If one neglects the proper motion of the heavy nucleus of the hydrogen atom, then the hydrogen electron must move along an ellipse, at one focus of which the nucleus is situated. The major axis \(2a\) of the elliptical orbit is determined as follows:

\[ 2a_n=\frac{n^2 e^2}{K\cdot h}. \tag{4} \]

The simple periodic motion with which we are dealing in the hydrogen atom, neglecting the proper motion of the nucleus, is completely characterized by a single quantum number \(n\). It determines the energy of the atom and, at the same time, the major axis of the elliptical orbit, but leaves undetermined the second axis, or the eccentricity. The energy of the \(n\)-th stationary state is as follows:

\[ E_n=-\frac{2\pi^2 N^2 e^4\cdot m}{n^2 h^2}, \tag{5} \]

where \(e\) and \(m\) are the charge and mass of the electron, and \(N\) is the number of charges of the nucleus. For hydrogen \(N=1\). Comparing equations (3) and (5), we have:

\[ K=\frac{2\pi^2 e^4 m}{h^3}. \tag{6} \]

For a nucleus with two charges, \(K\) has a value four times larger. This is the case of the ionized helium atom, which emits a line spectrum whose frequencies are determined by the following law:

\[ \nu=4K\left(\frac{1}{(n'')^2}-\frac{1}{(n')^2}\right). \tag{7} \]

We encounter the same hydrogen-like spectra also in the X-ray spectra of the elements. Moseley showed that various chemical elements, when emitting the hardest rays of the so-called \(K\)-group, give a spectrum whose most intense line has a frequency determined as follows:

\[ \nu=N^2K\left(\frac{1}{1^2}-\frac{1}{2^2}\right), \tag{8} \]

where \(N\) is the number of charges of the nucleus, or the so-called atomic number of the element. The most intense line of the “softer” \(L\)-group is determined for various elements by the relation:

\[ \nu=N^2K\left(\frac{1}{2^2}-\frac{1}{3^2}\right). \tag{9} \]

All the preceding relations were derived for the case in which the proper motion of the atomic nucleus is neglected. If this factor is taken into account, then the motion of the electron ceases to be purely periodic. The electron performs a complex central motion, in which the orbit, differing little from an ellipse, possesses a uniform additional rotation. In this case, for the determination of a stationary state, one principal quantum number \(n\), characterizing the energy and the magnitude of the major axis of the ellipse, is no longer sufficient. A second quantum number \(k\) is required, determining the eccentricity, or the parameter of the ellipse \(2p\) (the parameter is the chord passing through the focus of the ellipse perpendicular to the major axis \(2a\)). For \(2a\) and \(2p\) the following expressions are obtained:

\[ 2a=n^2\frac{h^2}{2\pi^2Ne^2m};\qquad 2p=k^2\frac{h^2}{2\pi^2Ne^2m}. \tag{10} \]

Taking into account the dependence of the electron mass on the velocity of motion, Sommerfeld found the following expression for the energy of a stationary state characterized by the quantum numbers \(n\) and \(k\):

\[ E_{n,k}=-\frac{2\pi^2 N^2 e^4 m}{n^2 h^2}\left[1+\frac{4\pi^2 N^2 e^4}{h^2 c^2}\left(-\frac{3}{4n^2}+\frac{1}{nk}\right)\right] \tag{11} \]

where terms of higher orders have been omitted.

The spectrum of hydrogen gives definite data on the process of attachment of an electron to the hydrogen nucleus. The study of the spectra of other elements must serve as the key to understanding the processes of attachment of \(N\) electrons, which determine the atomic number of a given element. We must imagine that the formation of an atom with serial number \(N\) proceeds in \(N\) successive stages, corresponding to the capture of \(N\) electrons in the field of the nucleus, and one may expect a special spectrum for each process of binding an electron. Such spectra are known only for hydrogen and helium. For the remaining elements we in no case know more than two types of spectra, usually designated as “arc” and “spark” spectra. These spectra are considerably more complicated than the spectra of hydrogen and helium (2) and (7). In many cases, however, it is possible to find simple laws, similar to (2) and (7), which determine part of the lines of these spectra. Disregarding the complex structure of individual lines (doublets, triplets, etc.), in many cases the frequencies of the lines of arc spectra can be determined with considerable accuracy by the so-called Rydberg formula:

\[ \nu=\frac{K}{(n''+\alpha'')^2}-\frac{K}{(n'+\alpha_k)^2}, \tag{12} \]

where \(K\) is the same constant as in formulas (2) and (7), \(n'\) and \(n''\) are integers, and \(\alpha_k\) and \(\alpha_{k'}\) are constant terms of a series characteristic of the given element. Bohr’s theory gives a direct interpretation of formula (12). The lines of the series (12) are emitted in transitions between stationary states of the atom, while, in contrast to the hydrogen spectra, we are dealing here with a whole group of series of stationary states. The energy of the \(n\)-th stationary state of the \(k\)-th series is determined from formula (12) as follows:

\[ E_k(n)=-\frac{Kh}{(n+\alpha_k)^2}. \tag{13} \]

The structure of “spark” spectra, as Fowler’s investigations show, is determined approximately by a formula of the same type as formula (12), with the only difference that instead of \(K\) the quantity \(4K\) appears, quite analogously to what we have in the spectrum (7) of ionized helium. From this point of view the arc spectrum corresponds to the last stage of the formation of the atom—the capture of the last, \(N\)-th electron. The spark spectrum (the spectrum of the ionized atom) is emitted in the penultimate stage, the capture of the \((N-1)\)-st electron by the nucleus.

In studying the formation of the atom by means of the capture of electrons in the field of the nucleus, we have no need to dwell long on the capture of the first electron. The final result of this process of capture is that state of the atom whose energy is determined by formula (5), if we substitute in it \(n=1\), or, more precisely, by formula (10), where one must put \(n=k=1\). We shall call such an orbit of the electron a one-quantum orbit; if the principal quantum number has the value \(n\), we shall speak of an \(n\)-quantum orbit. In applications where it proves essential to distinguish orbits characterized by different values of the quantum number \(k\), we shall denote the orbit determined by the quantum numbers \(n\) and \(k\) as the “\(n_k\)-th orbit.”

Turning to the capture of the second electron, we at once encounter a considerably more complicated problem. We can obtain information about this process on the basis of the arc spectrum of helium. In contrast to the other simple spectra, this spectrum consists of two systems of lines, each of which is determined by formulae of type (12). On this basis it was formerly thought that helium is a mixture of two gases: “orthohelium” and “parahelium.” At present, however, we know that the two spectra mean only that the binding of the second electron can occur in two different ways. Landé (Landé), in an interesting paper, attempted to clarify theoretically the basic features of the helium spectrum. He imagines that the spectrum of orthohelium is emitted in transitions between stationary states in which both electrons revolve in the same plane and in the same direction around the nucleus; the electron captured second moves in an orbit enclosing the orbit of the first electron. In the states corresponding to the spectrum of parahelium, according to Landé’s conception, the orbits of the two electrons form a certain angle with one another. A closer investigation of the interaction of the two orbits of the stationary states of the helium atom was carried out by the speaker in joint work with Dr. Kramers (Kramers). The results of our investigation, begun long before the appearance of Landé’s work, have not yet been published. Without going into details, I shall mention, however, that although our conclusions differ substantially in many points from Landé’s results, they nevertheless agree with Landé’s general conclusions concerning the origin of the ortho- and parahelium spectra.

Closely connected with considerations on the origin of the helium spectrum is the question of the final result of the binding of the second electron in the atom. This point has been elucidated by the important experiments of Franck (Franck) and his collaborators. The experiments showed that helium atoms subjected to bombardment by electrons can be brought into a state which Franck called “metastable” (superstable). The atom cannot pass from this state into the normal one by a simple process accompanied by radiation; the transition is possible only by way of a chemical reaction, since its occurrence requires the presence of atoms of other elements. This result is closely connected with the circumstance that the capture of the second electron in the helium atom can occur in two ways, as we know on the basis of the spectrum. From Franck’s experiments it follows that the normal state of the atom corresponds to the process of binding the electron accompanied by emission of the parahelium spectrum. In this case the second electron, just like the first, is bound in a \(1_1\) orbit. The above-mentioned metastable state, on the contrary, corresponds to the process accompanied by emission of the orthohelium spectrum; in this case the second captured electron, unlike the first, will move in a \(2_1\)-orbit, in which the strength of the binding is approximately 7 times less than that of the electron in the normal state of the atom.

A closer consideration of this fact, astonishing at first glance, shows that it finds a natural explanation and, in any case, can be understood on the basis of the principle of correspondence. It is easy to see that between the two processes of electron capture there is a great difference, clearly manifested in the study of the last stages of the process. Considering the orbits of orthohelium, in which both electrons are in one plane, we see that the orbit of the outer electron has the same character as the orbit of an electron moving in a simple force field possessing central symmetry: the existence of transitions of the above-mentioned type must therefore be directly connected with the properties of the motion of the outer electron. But all this is so only as long as we restrict ourselves to orbits with principal quantum number \(n\) greater than 1; closer investigation shows that the connected class of motions to which the orbits of orthohelium belong does not contain the \(1_1\) orbit. If, nevertheless, we insist on the existence of a state in which both electrons move in a \(1_1\)-orbit in the same plane, then there is no other possibility (provided that the motion retains the periodic properties necessary for defining a stationary state) than to assume that both electrons move in one and the same circular orbit around the nucleus, being at each given moment at the ends of a diameter. This simplest “circular configuration” should correspond, as the formal application of the quantum theory shows, to the strongest binding in the atom, and therefore it was proposed by me in my first paper on the structure of the atom as a model of helium. If, however, we ask about the possibility of a transition from any of the states of orthohelium to the circular configuration, we encounter relations quite different from those which occur in transitions from one state of orthohelium to another. We cannot imagine such a series of simple intermediate forms of orbits for both electrons in which the motion of the last captured electron would be sufficiently similar to central motion that one could speak of a correspondence of the required type. Therefore one must assume that the last captured electron in the case where both electrons move in one plane is bound no more strongly than in the \(2_1\)-orbit. Considering, on the other hand, the process of binding accompanied by the emission of the parhelium spectrum, in which the electrons in the stationary states move in planes forming a certain angle with one another, we encounter essentially different relations. Here there is no need for a radical change in the interaction of the first and second electrons in order to preserve the equivalence of their motions; we may therefore imagine that the last stage of the binding process proceeds in the same way as the preceding stages, to which there correspond transitions between orbits characterized by large quantum numbers \(n\) and \(k\). It must be thought that in the normal state of the helium atom both electrons move-

move in equivalent \(1_1\)-orbits. In the first approximation these orbits may be regarded as circles, whose planes form an angle of \(120^\circ\), in accordance with the condition which, according to quantum theory, is imposed on the angular momentum of the atom. As a result of the interaction of the electrons, the orbits slowly rotate about the fixed axis of angular momentum.

Recently Kemble, proceeding from foundations substantially different from those developed above, proposed an analogous model of the helium atom. At the same time he pointed out (with respect to the fine interactions of the electrons) the possibility of a type of motion with a clearly expressed symmetry of such a kind that the electrons, throughout their motion, occupy positions symmetric with respect to a fixed axis. Kemble did not, however, investigate this motion more closely mathematically. Even before the appearance of this work, Dr. Kramers began to carry out an exact calculation of precisely this type of motion, intending in this way to take into account the strength of the binding of the electrons in the helium atom, which can be measured on the basis of the so-called ionization potential. Earlier measurements of this potential led to a value which may be expected for the above-described circular configuration of the electrons, 28.8 volts. New, more accurate measurements of the ionization potential gave a considerably smaller value—25 volts. This circumstance alone, independently of the considerations set forth above, makes the circular configuration of the electrons of helium in the normal state entirely unacceptable. An exact investigation of the spatial configuration of the electrons, in distinction from the relations for a circular plane configuration, requires extensive computational work, not yet completed by Kramers. With the approximation with which these calculations have been carried out up to the present, they give grounds for hoping for agreement with experimental results.

Hydrogen and helium constitute the first period of the system of elements. The great difference in the chemical properties of hydrogen and helium depends on the difference in the strength and type of electronic binding, of which we know from the investigation of spectra and ionization potentials and which, apparently, is fully accounted for by quantum theory. Helium has the highest ionization potential of all the elements; in the hydrogen atom, on the other hand, the electron is so weakly bound that we are able to understand the tendency of hydrogen in aqueous solutions and chemical compounds to become a positive ion. A detailed consideration of this question requires, however, a comparison of the type and strength of the electronic configurations of atoms of other elements.

Passing now to the consideration of the structure of atoms of substances containing, in the neutral state, more than two electrons, we shall assume, first, that everything said about the formation of the helium atom holds, in its main features, for the capture and binding of the first two electrons of any atom. We shall assume, therefore, that in the normal-

state of the atom these electrons move along equivalent orbits, denoted \(1_1\). In asking the question of the binding of the third electron, we obtain direct information about this by investigating the spectrum of lithium. This spectrum indicates the existence of a group of series of stationary states in which the strength of the binding of the last captured electron is almost the same as in the formation of the hydrogen atom. In addition to these series of stationary states, for which \(k \geqq 2\) and in which the third electron moves entirely outside the region in which the first two electrons move, the spectrum of lithium also indicates a series of states for which \(k = 1\) and the energy differs considerably from the energy of the corresponding states of the hydrogen atom. The normal state of the atom also belongs to the number of such states, as is evident from experiments on the absorption of lithium vapor. In these states the last captured electron approaches the nucleus once during its revolution to a distance of the same order of magnitude as the dimensions of the orbits of the first two electrons, although perhaps for the greater part of its path it is at large distances from the nucleus. On this basis, the electron in such states is bound considerably more strongly than in hydrogen for stationary states with the same value of \(n\). In the normal state, where, as is evident from the spectrum, the work required to remove an electron from the atom amounts to only \(0.396 W_n\) (\(W_n\) is the ionization potential of hydrogen), the electron moves in a \(2_1\)-orbit; in this case the binding is approximately one and a half times greater than in the case of a hydrogen electron situated on a \(2_1\)-orbit, where the work required to extract the electron is \(0.25 W_n\). The transition from the states indicated by the spectrum of lithium to a state characterized by the motion of the third electron on a \(1_1\)-orbit is excluded on grounds analogous to those we encountered in interpreting the metastable state of helium.

A closer investigation of the possible motions shows the following. The transition which would have to lead to a stationary state of the atom with the third electron as an equal participant in the mutual relations of all three electrons of lithium would be of an entirely different type than the transitions accompanied by radiation of the actual spectrum of lithium; in contrast to these latter transitions, in the assumed process there would be no correspondence to the harmonic components of the motion of the atom. We thus obtain a picture of the formation and structure of lithium which gives a natural explanation of the large differences between the chemical properties of lithium and those of helium and hydrogen. We have grounds for understanding the fact that the binding of the last captured electron in the lithium atom is approximately five times weaker than the binding of the electrons in helium, and more than twice weaker than in the hydrogen atom.

It must be assumed that all that has been said is valid not only for the formation of the lithium atom, but in general for the binding of the third

electron of each atom; the third electron will move, therefore, in the \(2_1\)-orbit, in contrast to the first two electrons, which move in the \(1_1\)-orbit. An analogous supposition may be made for the binding of the fourth, fifth, and sixth electron. I shall not dwell here in greater detail on the conceptions that may be formed concerning the successive capture and binding of these electrons. I shall only point out that the reason why the capture of the first of the named electrons does not hinder the inclusion of the following electrons in two-quantum orbits lies in the fact that these orbits are not circular, but highly eccentric. Therefore the third electron, for example, cannot keep further electrons away from the inner system, in contrast to the action of the first two captured electrons of lithium, which hinder the inclusion of the third electron in a one-quantum orbit. On this basis we must expect that the 4th, 5th, and 6th electrons, just like the 3rd, will at certain points of their path penetrate into the region where the first two electrons move. One must not, however, think that these visits to the inner system by four electrons occur simultaneously; it is very probable that the four electrons pass near the nucleus in turn, at equal intervals. In earlier works on the structure of the atom it was usually assumed that the electrons in the various groups of an atom move in regions separated from one another, and that within each group, at every given moment, the electrons are in a configuration possessing symmetry of the same kind as regular polygons or polyhedra; one consequence of this was the assumption that the electrons are simultaneously situated at those points of their orbits at which they are closest to the nucleus. It may be said that such a structure of the atom is characterized by the fact that the motions of the electrons in separate groups are connected independently of the interaction of the different groups. A characteristic feature of the atomic structure set forth here, on the contrary, is the assumption of a close connection between the electronic orbits of different groups, determined by different quantum numbers, and of a great independence of the type of binding of the electrons of one and the same group, determined by the same quantum numbers. In emphasizing the latter circumstance, I have in mind not only the relatively small influence exerted on the strength of the binding of a later electron by the previously captured electrons of the same group. It is also essential that the motions of the electrons within each group reflect the independence of those processes of capture of the individual electrons as a result of which the group was formed.

The considerations set forth make it possible to understand the fact that the elements following lithium, beryllium and boron, act in compounds with other substances as electropositive elements with two or three valencies. The last captured electrons in these elements, like the third electron of lithium, are bound much more weakly than the two

first electrons. At the same time it becomes clear to us why the electropositive character of these elements is less pronounced than in lithium. The electrons of the two-quantum orbits of these elements move in stronger fields, and therefore they are more strongly bound in beryllium and boron than in the lithium atom. In the next element—carbon—we encounter new relations; in its typical chemical compounds this substance appears as a neutral atom, and not as an ion. This circumstance is connected not only with the greater strength of the electronic bonds, but also depends essentially on the symmetrical properties of the electronic configuration.

One must suppose that, in the capture of the fourth, fifth, and sixth electron into \(2_1\)-orbits, the relative configuration of the orbits is accompanied by an increasing spatial symmetry. In the capture of the sixth electron the orbits of the four last electrons must form an extremely symmetrical configuration. The normals to the planes of the orbits then assume, relative to one another, almost the same position as the lines connecting the vertices of a regular tetrahedron with its center. Such a configuration of the group of two-quantum orbits in the carbon atom is, apparently, indeed suitable for understanding the structure of organic compounds. I shall not, however, dwell here more closely on this question; its solution requires a thorough study of the interactions of electronic motions in the atoms present in the molecule. In this connection it should only be pointed out that the types of molecular models to which the considerations set forth lead are essentially different from those models which the speaker proposed in his first works. In those works “valence bonds” were assumed to correspond to “electronic rings” of the same type as the electronic groups in individual atoms. If, without going into such questions, it is nevertheless possible to give an idea of the chemical properties of the elements on the basis of the study of their atoms, the reason for this is as follows. The consideration of molecular formations of such a type as a compound of several atoms of the same element, or many organic compounds, does not play for us the same role as the analysis of compounds in which the individual atoms manifest themselves as electrically charged ions. Compounds of the latter type, often called “heteropolar” (to them belongs the majority of simple inorganic compounds), are much more typical than “homopolar” compounds, and possess individual properties to a considerably greater extent. Therefore, in what follows, the chief task will consist in considering the suitability of electronic configurations for the formation of ions.

Before finishing with the question of the structure of the carbon atom, I must point out that a model of the carbon atom in which the configuration of the orbits of four weakly bound electrons possesses a clearly expressed “tetrahedral” symmetry had already been proposed by Landé. Taking into account

experimental data on the size of the atom, he also proposed that the corresponding electrons move in \(2_1\)-orbits. Between the above-mentioned grounds and the considerations of Lande there is, however, an essential difference. In Lande, the justification of the characteristic properties of the carbon atom is based on an investigation of the simplest spatially symmetric forms of motion which four electrons can perform. Our reasoning is reduced to the stable properties of the entire atom; the assumptions about the orbits of the electrons are based on an investigation of the interactions of newly captured electrons with those already captured.

Turning to the properties of the following elements, we encounter first of all the special stability of the configuration of 10 electrons in the neutral neon atom. Usually the solution of this problem is based on the assumption that the properties of such a configuration are due to the interaction of 8 electrons moving in equivalent orbits around the nucleus and of an inner group of two electrons, analogous to the corresponding group of the neutral helium atom. We shall see, however, that the solution must apparently be sought in another direction. In considering the question of the capture of the seventh electron, we cannot expect that this electron will also be bound in a \(2_1\)-orbit equivalent to the orbits of the preceding four electrons. The appearance of five such orbits would undoubtedly disturb the symmetry of the interaction of the electrons. It is impossible to imagine that such a process of attachment of the fifth electron would be analogous, according to the correspondence principle, to the process accompanied by the emission of a spectrum. We must suppose that the four electrons, with their unusually symmetric configuration of orbits, hold the new electrons at a distance, so that they are bound in orbits of another type.

The orbits which appear in the binding of the seventh electron in the nitrogen atom and of the 7th, 8th, 9th, and 10th electrons in the following elements are circular orbits of type \(2_2\). The diameter of these orbits is considerably greater than the diameter of the orbits of the two inner electrons, but nevertheless they lie within the region in which the next four electrons move. The elongated parts of the eccentric \(2_1\)-orbits must therefore protrude somewhat beyond the circular \(2_2\)-orbits. I do not propose to dwell more closely on the question of the successive capture and binding of new electrons; for this, an exact investigation is required of the interactions in the motion of electrons along two types of two-quantum orbits. I shall only indicate that in the neon atom, where it is necessary to assume the existence of four \(2_2\)-orbits, the planes of these orbits possess not only a high degree of spatial symmetry with respect to one another, but also form a harmonious configuration with respect to the four elliptical \(2_1\)-orbits. Interaction of this kind, without coincidence of the planes of the orbits, is possible only when the configuration of the orbits in both subgroups has a systematic deviation

from tetrahedral symmetry. The electronic group with two-quantum ($2_1$ and $2_2$) orbits in the neon atom will therefore possess only one simple axis of symmetry, coinciding—as must necessarily be assumed—with the axis of symmetry of the configuration of the inner group of two electrons on one-quantum orbits.

With regard to explaining the clearly expressed electronegative character of oxygen and fluorine, the elements preceding neon and having atomic numbers 8 and 9, the following must be emphasized. The tendency of the neutral atoms of these elements to form, by capturing new electrons, negative ions of structure similar to that of the neutral neon atom must be attributed not only to the greater symmetry and the consequently increasing stability of the electronic configuration. It is also essential that the newly captured electrons are located inside the region of the $2_1$-orbits. This circumstance accounts for the difference between the elements of the second and the first halves of the second group of the periodic system; in the first half of the named elements there exists only one type of two-quantum orbit.

We now turn to the question of the structure of the atoms of the elements of the third period of the system of elements and first of all encounter the problem of the manner in which the eleventh electron is bound in the atom. The relations here are similar to those we met in investigating the capture of the seventh electron. Just as in the carbon atom, the configuration of the neon atom would be essentially or even completely distorted by the capture of a new electron into a $2_2$ orbit. As in the case of the 3rd and 7th electron, one may expect that the 11th electron will be located in an orbit of a new type, $3_1$. An electron moving in such an orbit will for the most part lie outside the configuration of the first ten electrons; at certain moments of its path, however, it penetrates not only into the regions of the $2_1$- and $2_2$-orbits, but even into regions where its distance from the nucleus will be smaller than the radius of the one-quantum orbits of the first two captured electrons. This circumstance, extremely important for understanding the stability of the atom, leads to the following interesting result. In the sodium atom the electron in the outer parts of the orbit will move in a field little different from the field around the nucleus of the hydrogen atom; nevertheless the dimensions of the corresponding parts of the orbit of the 11th electron of sodium differ substantially from the dimensions of the $3_1$-orbit of the hydrogen atom. The reason for this is that although the 11th electron is in the region of the orbits of the first ten electrons for a very short time, nevertheless this part of the path is essential for determining the principal quantum number; the motion of the electron along the inner part of the path differs very little from the motion of the previously bound electrons in $2_1$-orbits.

The 11th electron of the sodium atom is bound still more weakly than the third electron of the lithium atom, which explains the electropositive properties of sodium.

Passing from sodium to the other substances of the third period of the system of elements, in the capture of the 12th, 13th, and 14th electron we have relations entirely analogous to those which we encountered in considering the capture of the 4th, 5th, and 6th electron. It may be assumed that in the neutral atom of silicon there is an electron configuration in which the last 4 captured electrons move in \(3_1\)-orbits; these orbits, like the \(2_1\)-orbits of carbon, form so symmetrical a configuration that the capture of a new electron (in other atoms) into a \(3_1\)-orbit is impossible. The 15th electron in elements with a higher atomic number will therefore be captured into an orbit of a new type. Unlike the 7th electron, however, this orbit will not be circular, but an eccentric, rotating orbit of type \(3_2\). This is closely connected with the fact that an eccentric orbit corresponds to a stronger binding of the electron than a circular one with the same principal quantum number; in the former case the electron will, at certain intervals of time, penetrate deep into the atom. The \(3_2\)-orbit will not, it is true, reach the regions of the \(1_1\)-orbits, but it can approach the nucleus to distances considerably smaller than the radii of the \(2_2\)-circular orbits. The relations for the 16th, 17th, and 18th electron are the same as for the 15th. We may therefore expect for the argon atom a configuration in which the 10 inner electrons move in orbits of the same type as in the neon atom, while the last eight electrons move in four \(3_1\)- and four \(3_2\)-orbits; moreover, it may be assumed that the symmetry relations correspond to the configuration of the two-quantum orbits of the neon atom. Such a representation makes comprehensible the qualitative similarity in the properties of neon and argon, as well as of the elements in the second and third periods; at the same time it opens the possibility of a natural explanation of the important quantitative differences in the properties of these homologous elements.

Passing to the fourth period of the system of elements, we first encounter substances chemically analogous to the elements at the beginning of the two preceding periods. This is in agreement with what could have been expected in advance. We imagine that the 19th electron is bound in an orbit of a new type, \(4_1\). The relations to which we pointed in considering the capture of the 11th electron in the sodium atom appear here still more sharply, owing to the larger values of the quantum numbers determining the orbits of the inner electrons. The inner loop of the \(4_1\)-orbit almost coincides with the \(3_1\)-orbit; therefore the dimensions of the outer parts of the orbit of the 19th electron of the potassium atom not only differ greatly from the dimensions of the \(4_1\)-orbit of the hydrogen atom, but, as should be expected, almost coincide with the dimensions of the hydrogen orbit of type \(2_1\), approximately four times smaller than the dimensions of the \(4_1\)-orbit. This result at once makes it possible to account for the main features of the spectral and chemical properties of potassium. Similar results

are obtained for calcium, whose neutral atom contains two valence electrons in \(4_1\)-orbits. The elements of higher atomic numbers of the fourth period, however, as is known, differ more and more from the corresponding elements in the third period. The family of the iron metals already differs substantially in its properties from the elements of the preceding period. Passing to still higher atomic numbers, we encounter a series of substances again approaching, in chemical respect, the elements of the last part of the preceding period; atomic number 36 again corresponds to the noble gas krypton.

These relations correspond to our expectations. In considering the formation and stability of the electronic configurations of atoms of the first three periods, we based ourselves on the fact that each of the first 18 electrons in the following element is bound in an orbit with the same principal quantum number. This is not true, as is easy to see, for the 19th electron. With the increase of the nuclear charge, and with the associated decrease in the difference between the force fields inside and outside the region of the orbits of the first 18 captured electrons, the dimensions of that part of the \(4_1\)-orbit which is situated outside the region of the inner configuration approach more and more the dimensions of the four-quantum orbit calculated without taking into account the interactions of the electrons of the atom. With increasing atomic number there finally comes a moment when the \(3_3\)-orbit corresponds to a stronger binding of the 19th electron than the \(4_1\)-orbit. This occurs at the very beginning of the fourth period. The study of the spectrum of potassium shows that the \(4_1\)-orbit corresponds to a binding twice as strong as the \(3_3\)-orbit. (In the spark spectrum of calcium the binding of the electron in the \(4_1\)-orbit is weakened.) For scandium one may already expect that the \(3_3\)-orbit will be firmer than the \(4_1\)-orbit, although the binding of the 19th electron in the atom in the \(3_3\)-orbit is weaker than the binding of the first 18 electrons, which is in agreement with the electropositivity of scandium in chemical compounds (where it is trivalent).

In the following elements, in the normal state of the atom, a larger number of electrons will appear in the \(3_3\)-orbit; the number of such orbits will depend on the strength of the electron’s binding in comparison with the strength in the \(4_1\)-orbit. With regard to the formation and stability of atoms, we encounter here relations essentially different from those which we considered in the preceding periods of the periodic system. In contrast to the former case, we are dealing, as the atomic number increases, with the formation of one of the inner electronic groups of the atom, in our case—with a group of electrons in three-quantum orbits. Only when the formation of such a group is completed can we expect changes in the properties of the elements with increasing atomic number similar to those with which we dealt in the preceding periods of the system. An analysis of the properties of the elements of the last part of the fourth period shows directly that the corresponding group

and in its completed form must contain 18 electrons; we must think, for example, that krypton, besides groups of one-, two-, and three-quantum orbits, has a symmetrical configuration of 8 electrons in four-quantum orbits (four \(4_1\)-orbits and four \(4_2\)-orbits).

The question arises: how are we to picture the formation of a group of electrons in three-quantum orbits? By analogy with the structure of the electron group in two-quantum orbits, one might at first sight expect that the completed group of three-quantum orbits consists of three subgroups of 4 electrons each, situated in orbits of the types \(3_1\), \(3_2\), and \(3_3\); the total number of electrons would then be 12 instead of 18, as it is necessary to assume in order to understand the properties of the elements. Closer examination shows the erroneousness of such an assumption. The stability of the configuration of 8 electrons in two-quantum orbits in neon is explained not only by the symmetry of the electronic subgroups consisting of electrons in \(2_1\)- and \(2_2\)-orbits, but also by the possibility of bringing the orbits of these subgroups into harmonic relations with respect to one another. In electron groups with three-quantum orbits the situation is different; three subgroups of four orbits cannot be brought into interaction so simply. On the contrary, the capture of electrons into \(3_3\)-orbits disturbs the harmony of the configuration of the orbits of the first two subgroups and their interactions; this will occur in any case when, with increasing atomic number, we reach the point at which the 19th electron is no longer bound so weakly in comparison with the electrons previously captured in three-quantum orbits, as in the scandium atom, but is drawn into the interior of the atom, moving chiefly in the region of the inner electrons. It must be supposed that this decrease in harmony “opens,” so to speak, the previously “closed” configuration of electrons in \(3_1\)- and \(3_2\)-orbits, as a result of which the capture of further electrons of this type becomes possible. As for the final result, the number 18 indicates the formation of groups of three subgroups of 6 electrons each. Although up to now it has been impossible to trace step by step the formation of these groups, nevertheless our conclusion is rather interestingly confirmed by the fact that three configurations of 6-electron orbits can be oriented extremely simply with respect to one another. This configuration of subgroups does not, however, possess tetrahedral symmetry, as do the groups of two-quantum orbits of carbon; here the symmetry may be called trigonal. Despite the great difference in the properties of the elements under consideration, it may be said, on closer examination, that the completion of the group of 18 electrons in three-quantum orbits is revealed in a manner similar to the completion of the group of two-quantum orbits. We see that this completedness determines not only the non-reactivity of neon, but also the electronegative properties of the preceding elements and the electropositive properties of the succeeding elements. The absence of a noble gas with an outer group of 18 elect—

...of electrons in three-quantum orbits is explained simply by the fact that the dimensions of the \(3_3\)-orbit are considerably greater than the dimensions of the \(2_2\)-orbit, which is established under the influence of the same force field. The consequence of this is that the three-quantum group cannot serve as the outer group of a neutral atom, but appears only in a positively charged ion. In the characteristic decrease of the valency of copper, expressed in the appearance of copper ions, we see a tendency toward the completion of a symmetrical electronic configuration, which is confirmed by the spectrum of copper. In contrast to the complexity of the spectra of the preceding elements, which is the result of asymmetry of the inner system, the arc spectrum of copper is, in its type, close to the spectrum of sodium. This similarity must undoubtedly be ascribed to the circumstance that the copper ion, like the sodium ion, possesses a simple symmetrical structure. On the other hand, copper compounds show that the group of three-quantum orbits of copper does not possess the strength of binding of the two-quantum group of sodium. Only in the following element—zinc, which is divalent, are the electrons of the three-quantum group so strongly bound that they are not split off in ordinary chemical processes.

The ideas developed above concerning the formation and structure of the elements of the fourth period make it possible not only to understand in general outline the chemical and spectral properties of these substances, but are also confirmed by the consideration of characteristic features of another type. As is known, the elements of the fourth period differ in various respects from the substances of the preceding periods, in particular partly in their magnetic properties, partly in the peculiar coloration of their compounds. Of course, paramagnetism and coloration also exist in substances of the preceding periods, but, however, not in compounds where the atoms are ions. Many elements of the fourth period possess, even in dissociated aqueous solutions, clearly expressed paramagnetic properties and a characteristic coloration.

The usual electrodynamic conceptions do not give us a basis for explaining atomic magnetism. This should not surprise us, if we recall that the same conceptions are not capable of explaining the phenomena of radiation, conditioned by the close interaction of electric and magnetic forces arising from the motion of electrons. Regardless of how this difficulty is resolved, one may make the probable assumption that the appearance of magnetism is connected with an absence of symmetry in the internal structure of the atom. Because of this, the magnetic forces arising from the motion of electrons cannot form, within the atom itself, a system of closed lines of force. In contrast to the elements of the preceding periods, whose positive or negative ions possess clearly expressed symmetry, in substances of the fourth period the atoms contain electrons in three-quantum orbits in a transitional stage between a symmetrical con...

configurations of 8 and 18 electrons, and therefore the ions possess an asymmetric electronic configuration. Kossel pointed out that the experimental data are extremely simple: ions of the corresponding elements with an equal number of electrons have one and the same magnetic moment. In excellent agreement with the assumptions on the structure of copper and zinc, experiment shows that magnetism disappears precisely for ions with 28 electrons, where, as we have already indicated, there exists a completed group of triquantum orbits. On the whole, the analysis of the magnetic properties of the elements of the fourth period leaves a vivid impression of the existence here of a certain “wound” in the structure of the atom, symmetrical in other cases; in the gradual transition from one element to another we become witnesses to the arising and healing of this wound. One may hope that the nearest investigation of magnetism will provide a guiding thread for a detailed understanding of the process of the gradual development of the electronic group of triquantum orbits.

The coloration of ions also confirms the view developed above concerning the structure of the atoms of the fourth period. According to the postulates of quantum theory, we must imagine that both absorption and emission of light occur in transitions between stationary states. The presence of coloration, i.e. absorption of light in the visible part of the spectrum, indicates the possibility of transitions in the atom accompanied by a change of energy of the order of magnitudes observed in the optical spectrum. In contrast to the ions of the preceding periods with strongly bound electrons, we may expect in advance the possibility of transitions of the indicated type in the elements of the fourth group; the formation and completion of the group of triquantum orbits proceeds all the time, so to speak, in a struggle with the possibility of binding electrons in orbits with a higher quantum number. It must therefore be thought that the number of triquantum orbits appearing is determined by the fact that the electrons in these orbits are more strongly bound than in the \(4_1\) orbits; the binding of electrons in triquantum orbits must continue until, so to speak, an equilibrium of the capture of electrons into orbits of both types is established. This circumstance is closely connected not only with the coloration of ions, but also with the tendency of the elements of the fourth period to form ions of different valencies, in contrast to the elements of the first periods, where the charge of the ions in aqueous solutions is always constant for a given element.

With respect to the following elements of the periodic system, our analysis may develop by natural analogy with what has been said above. Considering the first elements of the fifth period, we must suppose, as is apparent from the arc spectrum of rubidium and the spark spectrum of strontium, that the 37th and 38th electrons are bound in the \(5_1\)-orbit. The spark spectrum of strontium, however, indicates the existence of \(4_3\)-orbits; it must therefore be thought that in the fifth period,

content, like the fourth, of 18 elements, we are dealing with a further stage in the formation of the electronic group of four-quantum orbits. The first stage of this group may be regarded as krypton, with a symmetric configuration consisting of two subgroups of 4 electrons each in the \(4_1\)- and \(4_2\)-orbits. A further preliminary completion of this group occurs in silver, in the symmetric configuration of three subgroups of 6 electrons each in orbits of the types \(4_1\), \(4_2\), and \(4_3\). Everything said about the formation of the electronic group of three-quantum orbits remains valid also for the stage of development of the group of four-quantum orbits under consideration, since we did not make assumptions about the absolute values of the quantum numbers or about the form of the orbits, defining only the number of the types of orbits considered. It is interesting, however, at the same time to note that the elements of the fifth period differ somewhat from the elements of the preceding periods, which corresponds to the difference in the types of orbits. Deviations from the valence relations characteristic of the second and third periods are observed in the fifth period later than in the fourth; in the fourth period titanium already has a definite tendency toward variable valence, whereas the corresponding element of the fifth period, zirconium, is constantly tetravalent, just as carbon is in the second and silicon in the third period. A simple investigation of the kinematic properties of electronic orbits shows that the electron in the eccentric \(4_3\)-orbit of an element of the fifth period is bound more weakly than the electron in the circular \(3_3\)-orbit of the corresponding element of the fourth period; electrons bound in eccentric orbits of the types \(5_1\) and \(4_1\), however, possess almost the same strength of binding.

At the end of the period, in xenon with atomic number 54, we may expect, besides the already indicated configurations of 2 one-quantum, 8 two-quantum, 18 three-quantum, and 18 four-quantum orbits, also a symmetric configuration consisting of two subgroups of 4 electrons each in the \(5_1\)- and \(5_2\)-orbits.

For elements with a higher atomic number we must first of all assume, as the spectra of cesium and barium show, that the 55th and 56th electrons are bound in \(6_1\)-orbits; we must, however, be prepared to encounter entirely new relations. It may be supposed that, as the charge of the nucleus increases, there will come not only a moment when the electron in the \(5_3\)-orbit will be bound more strongly than in the \(6_1\)-orbit, but also when the 47th electron will not be captured into the \(5_1\)-orbit, but into the \(4_1\)-orbit, where the electron’s binding will be stronger; this corresponds to that moment in the elements of the third period when the 19th electron, for the first time, instead of the \(4_1\)-orbit, becomes bound in the \(3_3\)-orbit. Having reached this point, one may expect that, with increasing atomic number, we shall encounter a group of elements, following one after another, possessing, like the family of the iron metals, almost identical properties. In the present case this appears still more strongly, since we are dealing with the successive formation of electronic configurations situated deep within the atom. You have, of course, understood that I have in mind

a simple explanation of the presence of the family of rare earths at the beginning of the sixth period of the system of elements. From the length of the sixth period we can directly determine the number of electrons (namely 32) present after the final development of the group of electrons in four-quantum orbits. By analogy with the relations in the group with three-quantum orbits, one may conclude that the completed group contains eight electrons in each of the four subgroups. Although it is not yet possible to trace the development of the group step by step, we can nevertheless, in the present case as well, obtain from simple considerations a basis for a theoretical understanding of the appearance of a symmetrical configuration of precisely 32 electrons. I shall point out in this connection that a symmetrical arrangement of four subgroups of six electrons each is unattainable without coincidence of the planes of the orbits; such a relation is possible, however, among three subgroups with a configuration possessing simple trigonal symmetry. The difficulties that we encounter in this case make it probable that a symmetrical configuration is realizable with four subgroups of 8 electrons each; the configuration of the orbits must then possess axial symmetry.

Just as in the family of the iron metals of the fourth period, our explanation of the presence of the rare-earth family in the sixth period is confirmed by an investigation of the magnetic properties of these elements. Despite the great similarity in chemical respects, the members of the rare-earth family possess very different magnetic properties: some exhibit negligible magnetism, while others possess an atomic magnetic moment exceeding the moment of all other substances investigated. In exactly the same way, the coloration of rare-earth compounds receives a simple explanation by analogy with the elements of the fourth period. In addition to the completion of the formation of the group of four-quantum orbits, we observe in the substances of the sixth period a second stage in the formation of the group of five-quantum orbits, manifested in the family of platinum metals, as well as the first preliminary stage in the formation of the six-quantum electron group in the radioactive, chemically inert gas niton, which closes the period. In the atom of this element we must assume the existence of 2 one-quantum, 8 two-quantum, 18 three-quantum, 32 four-quantum, and 18 five-quantum orbits, and, in addition, an outer symmetrical configuration of 8 electrons in six-quantum orbits, consisting of two subgroups of four electrons each in \(6_1\)- and \(6_2\)-orbits.

Passing finally to the seventh and last period of the system of elements, we are entitled to expect the appearance of seven-quantum orbits in the normal state of the atom. In the neutral atom of radium, in addition to the electron configuration corresponding to niton, there appear two electrons in \(7_1\)-orbits. During their revolution these electrons will penetrate not only into the regions of orbits with smaller principal quantum number, but also to such distances from the nucleus as are smaller than the radi—

conditions of internal one-quantum orbits. The properties of the elements of the seventh period are very reminiscent of the properties of the substances of the fifth period. In contrast to the sixth period, at the beginning of the seventh there are no elements analogous to the rare earths. In full agreement with what we said about the relation of the properties of the elements of the fourth period to those of the fifth, the circumstance just cited is explained by the fact that the eccentric \(5_4\)-orbit corresponds to a weaker binding of the 79th electron in the atom of the seventh period than the binding of the 47th electron in the circular orbit of an element of the sixth period; the difference in the strength of the binding of these electrons in the \(7_1\)-orbit and in the \(6_1\)-orbit remains insignificant.

As is known, the seventh period still remains unclosed, since we know no element with an atomic number greater than 92; in all probability this is connected with the radioactivity of the last elements of the system; apparently, atomic nuclei with a charge greater than 92 are insufficiently stable and cannot be observed under those conditions in which we study the properties of the elements. It is a rather enticing problem to sketch a picture of the structure of atoms with ordinal number greater than 92, formed by the capture and binding of electrons in the field of the nucleus, and thence to determine the chemical properties of these hypothetical elements. I do not propose, however, to dwell on this question, since the interpretation I have developed of the properties of actually observed substances already makes sufficiently clear to you the method of approach to the solution of such a problem. The following table, containing a symbolic representation of the structure of the atoms of the noble gases, closing the first six periods of the system of elements, may serve as the best summary of the results of our considerations. To emphasize the general tendency more strongly, the table also gives the presumed configuration of the electrons of the next atom, with the same properties as the other noble gases.

It is possible, of course, to develop the considerations I have set forth further in many respects; nevertheless, I must point out that our initial point of view, resting on quantum theory and the correspondence principle, does not yet permit us to trace all stages of the formation of the atom in detail. We cannot yet say that the results of the table given above should be regarded in all details as the sole possible result of applying the correspondence principle. On the other hand, the considerations presented explain the empirical data to such an extent that a substantially different interpretation of the properties of the elements on the basis of the postulates of quantum theory is hardly possible.

Translated by S. Vavilov.

1. The article is an abridged translation and, in part, a summary of Bohr’s extensive report, read on October 18, 1921, at a joint meeting of the Physical and Chemical Society in Copenhagen. The report, with additions, was printed in the journal Zeitschrift für Physik (9, pp. 1–65, 1922) and, from the formal point of view, is a continuation and development of Bohr’s article “On the serial spectra of the elements,” a full translation of which was given in Uspekhi fizicheskikh nauk (vol. III, no. I, p. 28). The views developed by the author in the present report are being published for the first time and are of special interest not only for a broad circle of readers, but also for the specialist. In our translation there has been omitted chiefly: 1) the part of the report devoted to the theory of X-ray spectra, 2) polemical excursuses, and 3) the entire extensive introductory part of the report, in which principally the theory of line spectra and the correspondence principle are set forth. The reader will find their detailed exposition in the previously mentioned article by Bohr. In the introductory part, printed in small type, the fundamental relations of Bohr’s theory of spectra, to which the author refers in the subsequent exposition, are recalled. Bohr’s new theory of the structure of the elements has recently received splendid confirmation in the study of X-ray spectra (D. Coster, Phil. Mag. 43, p. 1070, 1922). —Trans. ↩