THE ATOMIC NUCLEUS AND THE PERIODIC TABLE OF ELEMENTS

L. Meitner, Berlin-Dahlem *

The basis for the successful construction of the periodic system of elements by Mendeleev and Lothar Meyer was the idea that atomic weight could serve as a suitable constant for the systematic classification of the elements. Modern atomic theory, however, has arrived at an interpretation of the periodic system without at all touching upon atomic weight. The place number of any element in this system, and at the same time its chemical properties, are determined unambiguously by the positive charge of the atomic nucleus, or, what is the same thing, by the number of negative electrons arranged around it. The mass and structure of the atomic nucleus play no role in this; thus, at present we know that there exist elements or, more precisely, kinds of atoms which, with one and the same number and arrangement of outer electrons, possess significantly different atomic weights. Such elements are called isotopes. Thus, for example, in the family of zinc isotopes the atomic weight ranges from 112 to 124. Conversely, there are elements possessing substantially different chemical properties which exhibit the same atomic weight; they are called isobars. An example is the atomic weight 124, which has been found for zinc, tellurium, and xenon. However, if atomic weight, not determining unambiguously the nature of chemical elements, cannot be accepted as a characteristic constant for them, then for the atomic nucleus it represents one of the important characteristic constants. The fact that, notwithstanding this, on the basis of atomic weight Mendeleev succeeded in obtaining an error-free arrangement of the elements then known (about 70), and even in correctly predicting still unknown elements, may be attributed to his brilliant intuition, and also to the fortunate circumstance that atomic weight is, to a first approximation, proportional to the positive charge of the nucleus and, consequently, to the place number of the element in the periodic system.

For the determination of a chemical element, a single constant is sufficient, namely—the number of negative electrons arranged—

* A report delivered at the meeting devoted to the centenary of the birth of D. I. Mendeleev, in Leningrad, September 11, 1934. Published in German in Naturwissenschaften 22, 733, 1934; translated by A. A. Ilyina.

ones around the nucleus, since all chemical processes take place among these electrons. The mass and structure of the atomic nucleus play no role in this. On the contrary, in order to characterize the atomic nucleus, two constants are necessary: the atomic weight and the charge of the nucleus. Thus, the already mentioned atomic weight 124 can with equal success be assigned to zinc, tellurium, or xenon, but as soon as the nuclear charge, for example 54, becomes known, one can already indicate quite unambiguously a definite atomic nucleus, in the present case the nucleus of xenon 124. The existence of two constants necessary for this determination may be regarded as an indication that the atomic nucleus is built of two kinds of elementary particles. Otherwise the existence of isotopes would also be incomprehensible. According to the views now established, based on numerous experiments, these elementary particles must be recognized as protons and neutrons.

The number of protons \(n_2\) contained in the atomic nucleus determines its positive charge \(Z\), and thereby also the number of external electrons that determine the chemical properties of this element; a certain number of neutrons \(n_1\), enclosed in this same nucleus, together with \(n_2\) gives its atomic weight \(A = n_1 + n_2\). Conversely, the ordinal number \(Z\) gives the number of protons contained in the atomic nucleus, and from the difference between the atomic weight and the nuclear charge \(A - Z\) one obtains the number of nuclear neutrons. For example, the xenon nucleus mentioned more than once, with atomic weight 124 and charge 54, consists of 54 protons and \(124 - 54 = 70\) neutrons. According to these views, there exist in the nucleus neither positive nor negative electrons. An exact determination of the atomic weight makes it possible, however, not only to indicate how many elementary particles the atomic nucleus is composed of, but also to estimate the energy connected with the formation of the atomic nucleus. The mass of the atomic nucleus is usually less than the sum of the separate masses of the protons and neutrons composing it. It is known that mass is not an immutable quantity, but can be transformed into energy. The formation of a stable nucleus from separate particles is an exothermic process, and the energy released in this formation can be calculated from the mass defect of the nucleus formed, i.e., from the difference between its atomic weight and the sum of the weights of the protons and neutrons entering into it.

The circumstance that the rounded atomic weight correctly gives the number of protons and neutrons contained in the nucleus is due only to the fortunate intuition of Berzelius, who proposed, in determining atomic weights, to take as a basis the atomic weight of oxygen, equal to 16. If the atomic weight of hydrogen had been taken as the unit, the consequence would have been entirely different values of atomic weights; for example, for Bi the atomic weight would have been 207.3 instead of 209.

It has been established by numerous experiments that protons and neutrons are indeed constituent parts of the atomic nucleus. By various methods, pro-

protons and neutrons, and at the same time the original atomic nucleus passes into a new one. The process of liberation of protons, discovered by Rutherford and his students when bombarding certain elements, for example nitrogen, with α-particles, has long been known:

\[ \mathrm{N}_{7}^{14}+\alpha_{2}^{4}\to \mathrm{O}_{8}^{17}+\mathrm{H}_{1}^{1}. \]

The process proceeds in such a way that the α-particle remains in the nucleus and one proton is ejected. This will be a process of formation of a nucleus in which the resulting atomic nucleus contains a larger number of elementary particles than the original one.

A second example of processes of the same type may be the transformation of aluminum into Si under bombardment by α-particles:

\[ \mathrm{Al}_{13}^{27}+\alpha_{2}^{4}\to \mathrm{Si}_{14}^{30}+\mathrm{H}_{1}^{1}. \]

In Fig. 1 is shown a Wilson photograph obtained by us, which illustrates this artificial transformation. In it one can see the tracks of protons ejected from Al under the action of α-particles from polonium, which is located in a cylinder placed inside the Wilson chamber. The front half of the cylinder is made of an aluminum sheet of such thickness that α-rays and H-rays cannot pass through it into the external space. Therefore all the tracks emerging from the aluminum can be attributed only to protons ejected from the nucleus.

Fig. 1. Decomposition of aluminum by α-particles.

The existence of neutrons was discovered by Chadwick first of all for Li, B, Be, in connection with the investigations of Curie and Joliot, who continued the observations of Bothe and Becker. The process taking place here is entirely analogous to the one analyzed above:

\[ \mathrm{Be}_{4}^{9}+\alpha_{2}^{4}\to \mathrm{C}_{6}^{12}+\mathrm{n}_{0}^{1}, \tag{3} \]

i.e. the α-particle is captured by the nucleus and one neutron is ejected. Thus there is no doubt that protons constitute the principal constituent parts of the atomic nucleus. Alongside them there also appear, though already as secondary formations, helium nuclei (α-particles) and, probably, nuclei of heavy hydrogen \(\mathrm{H}_{1}^{2}\). That α-particles are constituent parts of atomic nuclei has long been known from observations of radioactive processes, and at the present time has also been observed repeatedly in processes

L. MEITNER

artificial transformation of elements with the emission of α-particles from stable atomic nuclei, both under bombardment by neutrons and by protons.

An example of such a disintegration, produced with the aid of a neutron, may be the process:

\[ \mathrm{O}^{16}_{8}+\mathrm{n}^{1}_{0}\to \mathrm{C}^{13}_{6}+\alpha^{4}_{2}. \tag{4} \]

It is shown in the Wilson photograph obtained in our institute (Fig. 2), where Be-neutrons pass through oxygen. One such neutron, in accordance with the above equation, split an oxygen nucleus. One can see the long track of the emitted α-particle and the short path of the resulting \(\mathrm{C}^{13}_{6}\) nucleus.

Fig. 2. Disintegration of oxygen by neutrons.

In disintegration obtained with the aid of protons (Cockcroft and Walton), only those processes have been established with certainty in which only nuclei built of α-particles can arise. From energetic considerations one can say that these nuclei will not be stable and must decay into their constituent parts. Examples of this are the following nuclear reactions:

\[ \begin{aligned} \mathrm{Li}^{7}_{3}+\mathrm{H}^{1}_{1}&\to 2\alpha,\\ \mathrm{B}^{11}_{5}+\mathrm{H}^{1}_{1}&\to 3\alpha. \end{aligned} \tag{5} \]

The simultaneous appearance of two α-particles in the disintegration of Li and of three α-particles from the cited B-process was obtained, apparently, by E. Kirchner and by Dee and Walton, as can be seen from Figs. 3 and 4. The fact that precisely those elements which are capable of being disintegrated by protons can form, with \(\mathrm{H}^{1}_{1}\), a new α-particle—so that their mass becomes an integral multiple of the mass of the α-particle—becomes understandable if one takes into account that the α-particle is a formation with a very large mass defect, owing to which its construction is associated with a high exothermic effect. Gamow, referring precisely to this circumstance, explained why elements with an even atomic number and even atomic weight occur much more frequently than elements with an odd number of neutrons or protons. Disintegration with the aid of deuterons (\(\mathrm{H}^{2}_{1}\)) was investigated above all by American researchers (Lawrence, Lauritsen, Crane, Tuve, Hafstad, Livingston, Henderson), and recently

time also by Rutherford and his pupils. The following processes may be cited as examples:

\[ \begin{gathered} \mathrm{B}_{5}^{11}+\mathrm{H}_{1}^{2}=\mathrm{C}_{6}^{12}+\mathrm{n}_{0}^{1}\\ \text{and}\\ \mathrm{Li}_{3}^{6}+\mathrm{H}_{1}^{2}=\mathrm{Li}_{3}^{7}+\mathrm{H}_{1}^{1} \end{gathered} \tag{6} \]

Fig. 3. Disintegration of lithium by protons.

along with the process

\[ \mathrm{Li}_{3}^{6}+\mathrm{H}_{1}^{2}=2\alpha. \]

In all the processes of artificial transformation of elements considered here, the newly arising nuclei are stable and all belong

Fig. 4. Disintegration of boron by protons.

to types of atoms already known from isotope studies. All this can be represented in the form of exchange reactions:

\[ \begin{aligned} 1.\quad & \alpha \rightleftarrows \mathrm{n}_{0}^{1}\\ 2.\quad & \alpha \rightleftarrows \mathrm{H}_{1}^{1}\\ 3.\quad & \mathrm{H}_{1}^{2}\longrightarrow \alpha\\ 4.\quad & \mathrm{H}_{1}^{2}\longrightarrow \mathrm{H}_{1}^{1}\\ 5.\quad & \mathrm{H}_{1}^{2}\longrightarrow \mathrm{n}_{0}^{1} \end{aligned} \tag{7} \]

The reaction \(\mathrm{H}_1^1 \to \alpha\) has so far been known only in the form of the breakup of the nucleus into its constituent parts (see above). For reactions 3, 4, and 5 the reverse processes have not yet been observed. Likewise, for this type of transformation there are no processes of the form \(\mathrm{n}_0^1 \rightleftarrows \mathrm{H}_1^1\). From energetic considerations one can say something about the relative probability of the indicated exchange reactions. The capture of one proton will always be the most exothermic process, since the mass of a free proton is 1.0072, whereas the mass of a nuclear proton does not exceed 1.000. This is clear without further discussion from a comparison of the masses of those nuclei which, in their structure, differ by one proton. For example, the atomic weight of \(\mathrm{C}_6^{12}\) is 12.0036, the atomic weight of \(\mathrm{B}_5^{11}\) is 11.0110; the difference between the weights of the two nuclei is 0.9921, i.e., the new proton joining \(\mathrm{C}_{12}\) from \(\mathrm{B}_{11}\) has, in the nucleus, a mass smaller by approximately 0.015 mass units, which corresponds to a decrease in energy by \(14 \cdot 10^6\) V as compared with the energy in the free state. This energy is liberated in the transformation of the nucleus capturing the proton, and it is indeed very large. This also explains why even protons with the lowest energies, down to 20,000 V, can cause the transformation, because precisely in the proton mass defect there is a sufficient reserve of energy.

The situation is exactly the same with the neutron. Let us compare two neighboring isotopes which differ from one another by 1 neutron. The difference between their atomic weights will always be equal to or less than unity. The mass of a free neutron, of which I shall speak later, apparently differs only insignificantly from the mass of a free proton.

For \(\alpha\)-particles, however, the actual relations will be different. In the free state an \(\alpha\)-particle, with its relatively small mass of 4.0012 units, has a very large mass defect, corresponding to 30 million V. It is a stable formation. As a constituent part of heavy nuclei, on the contrary, it will be relatively lost. If one compares two nuclei which differ from one another by one \(\alpha\)-particle, for example \(\mathrm{O}_{16}\) and \(\mathrm{Ne}_{20}\), then the difference of the atomic weights will be 4.0004; the difference in the energy magnitude relative to a free \(\alpha\)-particle does not amount even to 15 V. Consequently, in order to carry out the decomposition of an element with the aid of an \(\alpha\)-particle, the latter must possess an energy much greater than that of a proton, namely not less than \(2.5 \cdot 10^6\) V, whereas for a proton the lower limit is 20,000 V.

From these considerations it follows that the exchange processes \(\mathrm{H}_1^1 \rightleftarrows \alpha\) will occur more readily than the processes \(\mathrm{H}_1^1 \rightleftarrows \mathrm{n}\). The latter may be expected first of all for higher kinetic energies of \(\mathrm{H}_1^1\) and, correspondingly, for neutrons, which is in fact what was observed for neutrons of higher energy, though not, of course, for the transformations considered above with the direct formation of stable atomic nuclei.

Alongside these processes of artificial transformation of elements, in which already known stable atomic nuclei arise, the Curies and Joliot quite recently discovered processes of artificial radioactivity, in which the initially arising unstable atoms then pass into a stable product by radioactive decay with the emission of a positron. For example:

\[ {}^{27}_{13}\mathrm{Al}+{}^{4}_{2}\alpha = {}^{30}_{15}\mathrm{P}+{}^{1}_{0}\mathrm{n} \quad \begin{matrix} \\[-0.5em] \searrow \end{matrix} \quad {}^{30}_{14}\mathrm{Si}+e^{+} \tag{8} \]

The atomic nucleus \({}^{30}_{15}\mathrm{P}\) is transformed into \({}^{30}_{14}\mathrm{Si}\) in exactly the same way as ordinary radioactive elements, according to the exponential law. The half-life in this case is \(3'15''\).

Fermi and his collaborators showed that neutrons can also be used for the formation of a radioactive nucleus. Owing to the fact that no Coulomb field exists for the neutron, it can penetrate especially easily even into heavy nuclei. Indeed, the Italian investigators succeeded in bringing almost all elements into a radioactive state. The exceptions were the light elements H, Li, C, N, O and the heavy ones Os, Ru, Tl, Pb, Bi.

Processes of this type may be represented by the following examples:

\[ {}^{27}_{13}\mathrm{Al}+{}^{1}_{0}\mathrm{n} = {}^{24}_{11}\mathrm{Na}+{}^{4}_{2}\alpha \quad \begin{matrix} \\[-0.5em] \searrow \end{matrix} \quad {}^{24}_{12}\mathrm{Mg}+e^{-} \]

or

\[ {}^{27}_{13}\mathrm{Al}+{}^{1}_{0}\mathrm{n} = {}^{27}_{12}\mathrm{Mg}+{}^{1}_{1}\mathrm{H} \quad \begin{matrix} \\[-0.5em] \searrow \end{matrix} \quad {}^{27}_{13}\mathrm{Al}+e^{-} \tag{9} \]

Corresponding to these two types of transformation, two half-lives are observed, which, from Fermi’s determinations, proved to be 12 hours for the first process and 12 minutes for the second. In full agreement with this, we also found 12–15 hours for the first process and \(10 \pm 1\) minutes for the second.

The second process is especially interesting, since it leads back to the original atomic nucleus. Processes of a similar type have been quite reliably established by the Italian investigators for a considerable number of elements, for example for P, S, Fe, Cr, etc. The radioactive atomic nuclei arising in this way then pass into stable nuclei with the emission of \(\beta\)-rays. Similar transformations were also obtained by American investigators under bombardment with deuterons, for example:

\[ {}^{12}_{6}\mathrm{C}+{}^{2}_{1}\mathrm{H} = {}^{13}_{7}\mathrm{N}+{}^{1}_{0}\mathrm{n} \]

\[ {}^{13}_{6}\mathrm{C}+e^{+} \]

This process shows that in this way heavier isotopic nuclei can be obtained from one type of atom.

All the processes of artificial radioactivity observed up to now proceed either with the emission of a positive electron or with the emission of a negative one. The artificially obtained radioactive types of atoms that arise when nuclei are bombarded by heavy particles, such as a proton, neutron, or \(\alpha\)-particle, however, cannot be predicted in advance. The investigation of these nuclei likewise cannot be carried out by the usual methods that detect isotopes of known elements.

To the 200 stable types of atoms of the 92 elements of the periodic system known up to now, a whole series of radioactive nuclei is now being added. In Fig. 5 one can see part of the chart of the periodic system compiled by Delbrück at our institute. This chart contains all types of atoms known up to now, stable and unstable. In the figure reproduced here only part of this chart is shown, comprising atoms up to calcium. The abscissas here are the atomic numbers of the elements; the ordinates are the quantities \(n_1 - n_2\), i.e., the excess of neutrons over the number of protons. Stable atomic nuclei are indicated by black circles, radioactive nuclei by unfilled ones; the squares depict types of atoms that have not yet been established with complete certainty. The arrows show possible processes of transformation of some atoms into others according to the available experimental data.

Fig. 5.

This is, so to speak, the beginning of the chemistry of the atomic nucleus. Of extraordinary interest are the following facts: one and the same atomic nucleus can be constructed in different ways. For example, at present we know three reactions leading to the formation of one and the same radioactive \(\mathrm{Al}^{28}\):

\[ \begin{aligned} 1.\quad & \mathrm{Mg}^{25}_{12} + \alpha^{4}_{2} \longrightarrow \mathrm{Al}^{28}_{13} + \mathrm{H}^{1}_{1} \\ 2.\quad & \mathrm{Si}^{28}_{14} + \mathrm{n}^{1}_{0} \longrightarrow \mathrm{Al}^{28}_{13} + \mathrm{H}^{1}_{1} \\ 3.\quad & \mathrm{P}^{31}_{15} + \mathrm{n}^{1}_{0} \longrightarrow \mathrm{Al}^{28}_{13} + \alpha^{4}_{2}. \end{aligned} \]

The Al nuclei arising as the result of all these three reactions have identical half-life periods and transform into \(\mathrm{Si}^{28}_{14}\) with the emission of a negative electron.

Conversely, one and the same artificial nucleus, by means of various-

different transformations can yield entirely different nuclei, for example:

\[ \mathrm{Al}^{27}_{13} + \alpha^{4}_{2} \longrightarrow \mathrm{Si}^{30}_{14} + \mathrm{H}^{1}_{1} \]

or

\[ \longrightarrow \mathrm{P}^{30}_{15} + \mathrm{n}^{1}_{0} \]

or

\[ \mathrm{Al}^{27}_{13} + \mathrm{n}^{1}_{0} \longrightarrow \mathrm{Na}^{24}_{11} + \alpha^{4}_{2} \]

or

\[ \longrightarrow \mathrm{Mg}^{27} + \mathrm{H}^{1}_{1}. \]

It is highly probable that the ordinary stable nuclei of the known elements could also have arisen by the most diverse paths, just as one and the same chemical compound can be obtained by the most diverse methods.

The variation of the quantity \(n_1 - n_2\) (Fig. 5), i.e. the excess of neutrons over protons, gives, for a constant abscissa \(Z\), a region of atomic weights encompassing a band of isotopes of some particular element. In general this difference is a measure of the extent to which the atomic weight increases with increasing ordinal number. For \(n_1 = n_2\), i.e. for atomic nuclei consisting of equal numbers of neutrons and protons, the atomic weight is twice the ordinal number, for example \(\mathrm{O}^{16}_{8}\). Atoms of this type are known only up to \(\mathrm{Ca}^{40}_{20}\); in the series of all elements without exception following calcium, the atomic weight begins to increase faster than the ordinal number; \(n_1\) becomes greater than \(n_2\), i.e. atomic nuclei have far more neutrons than protons, and the neutron content, as the ordinal number increases, likewise increases faster than the proton content.

The existence of isotopes also shows that, for a given number of protons, there must be certain most stable configurations for different numbers of neutrons, just as in ordinary chemistry there are compounds of the type \(\mathrm{FeCl}_2\) and \(\mathrm{FeCl}_3\).

As has already been mentioned, the elementary particles of the nucleus can be only protons and neutrons. This does not contradict the fact that there are such transformations in which an atomic nucleus passes into some new nucleus with the emission of a positive or negative electron. At the present time, however, it is accepted that electrons cannot be located inside the nucleus. This is substantiated by very weighty experimental and theoretical data, on which there is no need to dwell here. The emission of a positive or negative electron in a certain nuclear process can be explained by the fact that a proton, forming part of an excited atomic nucleus, can in some way pass into a neutron, whereby the nucleus must lose one positive charge, which can indeed be observed through the emission of one positive electron from the nucleus. Conversely, a neutron in an excited nucleus can pass into a proton, as a result of which the nucleus acquires one positive charge and a negative electron will be ejected outward.

Thus the transition \(H_1^1 \rightleftarrows n\) inside the atomic nucleus is accompanied by the emission of a positive or negative electron. To create a clear picture of the details of this transition is as yet hardly possible. One can say only the following: if in the atomic nucleus such a transition of a neutron into a proton, or the reverse, takes place, then a more stable state of such a kind is obtained that the energy of the new nucleus will be less than the energy of the original nucleus by an amount corresponding to the mass of the newly arisen electron plus its kinetic energy. Accepting this proposition, so contradictory to our views, one must imagine both particles—the proton and the neutron—as elementary particles constituting the nucleus, completely equal in rights, capable of changing into one another with a certain expenditure of energy, and this transition, as we already know, will be accompanied by the appearance of one electron. Both particles, however, must be stable formations, so that a spontaneous transition cannot take place, and their masses must differ from one another by an insignificant amount, much smaller than the mass of one electron. Otherwise the particle with the greater mass would have to pass spontaneously into the particle with the lesser mass with the simultaneous appearance of one electron (\(+\) or \(-\)). The mass of the proton is well known, and we see that an exact determination of the mass of the neutron becomes absolutely necessary.

Various investigations were carried out with the aim of determining the mass of the neutron as accurately as possible. The only possible method for this at present is the determination of the exact energy balance of some nuclear transformation. Let us consider, for example, the process of the transformation of boron under the action of \(\alpha\)-particles, used by Chadwick for this determination. If one takes into account the energies of the particles entering into the reaction and those produced, and also converts their masses into equivalent quantities of energy, then one may write the following equality:

\[ \mathrm{B}_5^{11} + \alpha_2^4 + E_\alpha = \mathrm{N}_7^{14} + n_0^1 + E_n + E_N. \]

The masses of \(\mathrm{B}_5^{11}\), \(\mathrm{N}_7^{14}\), and \(\mathrm{He}_2^4\) (\(\alpha\)) are well known from Aston’s measurements; the kinetic energy of the \(\alpha\)-particles used for the bombardment of B is also known. The kinetic energy of the neutron \(E_n\) was determined by Chadwick by an indirect method, as was also the kinetic energy of the newly formed nitrogen nucleus \(E_N\). If the equality given above holds, then the mass of the neutron can indeed be determined. By this method Chadwick obtained for the mass of the neutron the value \(1.0068\), i.e. a mass which is less than the mass of the proton by an amount somewhat different from the mass of the electron. According to these data, the proton–neutron difference amounts to only \(0.0004\) mass units, while the mass of the electron is equal to \(0.00055\) of the same units. A spontaneous transition \(H_1^1 \to n_0^1\) at such a value of the neutron mass cannot take place, and the proton, as well as ...

neutron, will be stable. Curie and Joliot, from consideration of the processes of artificial radioactivity obtained by them, arrived at an entirely different value for the mass of the neutron. From calculations of the energy balance in this process they obtained \(m_n = 1.0010\), i.e., a mass greater than the mass of the proton; moreover, in this case the difference of the two masses is greater than the mass of the electron, so that for this value of \(m_n\) a spontaneous transition of the neutron into a proton would be possible.

It is difficult to arrive at any definite decision as to which of these two values (1.0068 and 1.0010) is more probable. Both in these and in other measurements there is a whole series of quantities whose limiting accuracy of determination is not sufficiently high. Against Chadwick’s data one could, as an objection, point out that perhaps the process of transformation of \(\mathrm{B}^{11}\), which underlies all the calculations, in fact leads not to nitrogen, as is assumed, but to \(\mathrm{B}^{10}\), whereby all his calculations would be reduced to zero.

On the other hand, the determination, made by Philipp and me, of the maximum kinetic energy of Be-neutrons speaks against the value of the neutron mass given by Curie and Joliot, and agrees well with Chadwick’s data. The decisive circumstance in this case will be the condition of stability, i.e., that the proton—neutron difference must be less than the mass of the electron, and thus the value \(m_n\) obtained by Curie and Joliot is eliminated.

In conclusion one may say a few more words concerning the general principles of constructing heavy nuclei from neutrons and protons. Heisenberg showed that, by means of comparatively simple assumptions, one can obtain a law of nuclear structure that conveys well certain characteristic facts concerning the atomic nucleus. Heisenberg proceeds from the assumption that the attractive force acting at short distances between a proton and a neutron will be greater than for a neutron and a neutron or for two protons, so that the interaction of a proton and a neutron will determine the process of construction of atomic nuclei. The form of this interaction is determined precisely by the above-mentioned possibility of the transition of a neutron into a proton, or conversely. From these conditions it immediately follows that the most stable formation (with maximum binding energy) will be obtained when the number of protons is equal to the number of neutrons, i.e., the ratio that is in fact observed in a number of elements up to \(\mathrm{Ca}^{40}\). In the region of heavy nuclei, where Coulomb repulsion for protons will be very significant, an excess of neutrons over protons is necessary in order for the nucleus to be stable. This corresponds to the fact already cited, namely the more rapid increase of atomic weight with increasing atomic number in the region of the heavy elements.

Heisenberg also succeeded in calculating the total energy required for the construction of various atomic nuclei, and, on this basis, in constructing a curve of the mass defect, in good agreement

experimental data. From these calculations one then obtains the limits of α- and β-decay. In Fig. 6, taken from Gamow’s work, precisely these regions of stable and unstable nuclei are shown. These results, while qualitatively agreeing with observations, nevertheless give a regular quantitative deviation, which Gamow interpreted as an indication of the possible existence within the nucleus, in addition to positively charged protons, also of negative protons. It is not yet possible to say anything about this, to some extent speculative, possibility.

Fig. 6.

With the discovery of the neutron, the periodic system received a certain addition in the region of small atomic numbers, since the neutron may be regarded as an element with atomic number equal to zero. In the region of high atomic numbers, namely from \(Z = 84\) to \(Z = 92\), all atomic nuclei are unstable, spontaneously radioactive; therefore one may suppose that an atom with a nuclear charge still higher than that of uranium, if it can only be obtained, must likewise be unstable. Fermi and his collaborators have recently reported their experiments in which, upon bombarding uranium with neutrons, the appearance of a radioactive element with atomic number 93 or 94 was observed. It is quite possible that in this region too the periodic system has a continuation. It remains only to add that, by Mendeleev’s brilliant foresight, the framework of the periodic system is so broadly conceived that every new discovery, while remaining within its scope, strengthens it still further.