NUCLEAR PHYSICS IN PHOTOGRAPHS*)

Tracks of Charged Particles in Photographic Emulsions

C. F. Powell and G. P. S. Occhialini

The method of thick photographic plates, first developed by L. V. Mysovskii and subsequently and with great success applied by A. P. Zhdanov and other Soviet physicists to the study of nuclear processes and cosmic rays, has proved very fruitful. In terms of the number of results obtained by means of this method it cannot yet compete with the Wilson chamber; nevertheless, recently it has begun to be used more and more often. This success was aided by the commercial production of photographic plates with special emulsions for nuclear research. The authors—C. F. Powell and G. P. S. Occhialini—are enthusiasts of this method and, in order to promote it, have written a small book, Nuclear Physics in Photographs, in which they illustrate various nuclear processes by means of interesting photographs obtained by them.

A complete translation of this book will be published in the present and following issues of our journal. In view of the aim set by the authors, the book is of an entirely popular character, especially in the first paragraphs. Nevertheless, taking into account the authors’ interesting aim—to illustrate nuclear physics exclusively with photographs obtained by the method of photographic plates—we are printing its translation in full.

The Editors

PREFACE

During the past eighteen months, in the course of our investigations in the field of nuclear physics, we have obtained a large number of microphotographs of the tracks of charged particles in photographic emulsions. We have found that this material makes it possible, very simply and directly, to show the main features of nuclear physics at the present stage of its development. In view of the interest in this subject on the part of a wide circle of readers, it was considered expedient to collect part of the photographs and supply them with a minimum of tex—

*) C. F. Powell and G. P. S. Occhialini, Nuclear Physics in Photographs, Oxford 1947. Translation by L. N. Belya.

... We have tried to make the text simple, so that it will be understandable to a large number of people; therefore the reader is assumed to have only a knowledge of elementary mechanics and electrostatics at the level of a secondary-school course.

However, in those cases where some subject was of special interest, a more detailed exposition of it was added in an appendix. In particular, a simple analysis is given of elastic collisions between various light nuclei, since such collisions illustrate the application of elementary dynamical principles better than problems about billiard balls, so familiar to many generations of schoolchildren. These latter problems are unrealistic and have no practical interest, whereas in nuclear physics analogous problems are very important, and all conclusions are fulfilled with great accuracy.

One of the most attractive features of the photographic method is its simplicity; many experiments on natural radioactivity, including experiments with photographic plates, can be performed with very simple apparatus available in many school laboratories. We have therefore added instructions concerning the development and fixing of plates, in the hope that some readers will be able to study nuclear physics independently. Amateur astronomers, who have made contributions to their science, have overcome considerably greater technical difficulties than those encountered in obtaining good microphotographs. It therefore seems to us that enthusiasts of nuclear physics may play a similar role.

The simplest field is radioactivity, but if a sufficient number of people become interested, it will probably be possible to obtain more extensive experimental material as well. Thus, for example, a rapidly moving film coated with new types of emulsion, after bombardment by a primary beam of particles from a cyclotron, would yield experimental material sufficient for several investigators working over many months. Examination of such a film under a microscope could not fail to reveal a number of interesting results concerning the disintegration of the light elements of the emulsion by fast deuterons.

Up to the present time the contribution of the photographic method to nuclear physics has been very small in comparison with the achievements obtained by means of the Wilson chamber or electrical counters. However, with the appearance of new emulsions and the associated improvement in the quality of the tracks, one may think that the significance of this method will increase in the near future. We therefore hope that, despite the elementary character of this book, it will also be of some interest to physicists, since the photographs presented illustrate the wide field of application of the method for studying the tracks of heavy charged particles.

ATOMS

The investigations of chemists in the last century showed that the diversity of the various objects of the world around us can be understood if they are regarded as consisting of an innumerable number of small particles—the so-called atoms of matter. Only a few substances, which received the names of chemical elements, proved to be simple in the sense that they consist of atoms of one kind; all other substances consist of two or more elements. Thus, for example, the smallest conceivable quantity of water, its molecule, which upon further division ceases to be water, contains two atoms of the element hydrogen and one atom of oxygen. In contrast to this simple case, the structure of biological organisms from the atomistic point of view is very complex, since they are built from a large number of different molecules, each of which contains many atoms. Chemists have learned well how to build, or, as they say, synthesize, complex molecules from simpler substances, and also to analyze various substances in order to determine their atomic composition.

Before the discovery of radioactivity it was customary to consider atoms immutable and indestructible units of matter, and, apparently, Clerk Maxwell expressed the general opinion of the scientific world of his time when, in his address before the British Association in 1873, he said: “Though catastrophes may have occurred from time immemorial and may continue to occur in the heavens, though ancient systems may have fallen apart and new ones arisen from their ruins, the molecules of which these systems are composed—these fundamental bricks of the material universe—will remain indestructible and unchangeable.”

At that time there was no possibility of studying deeply the question of the structure of the chemical atoms themselves and of determining whether they consist of simpler elementary units, although the first steps in this direction had already been taken. Chemists had already devised methods for determining the relative weights of different kinds of atoms.

In 1815 Prout pointed out that the atomic weights of many of the light elements are expressed almost exactly by whole numbers if the weight of the hydrogen atom is taken as unity. From this he concluded that all atoms are built from this light element; however, because of a number of quite noticeable deviations from this rule—for example, chlorine has an atomic weight equal to 35.5—this hypothesis was for many years regarded only as a scientific curiosity. Only with the discovery of radium and polonium by the Curies in 1898 did it become clear that at least some of the chemical elements do not constitute unchanging structures but, like biological species, are in a process of development, and this circumstance soon led to the realization that Prout’s old hypothesis contained the germ of an idea of decisive importance.

NUCLEI

The elucidation of the structure of atoms was to a considerable extent the result of the work of Rutherford and Bohr. It was found that in the various chemical elements one may observe an astonishing degree of order; that each atom may be regarded as a miniature solar system, at the center of which is a nucleus, corresponding to the sun, surrounded by a certain number of “planetary” electrons. As in the solar system, the nucleus is the heaviest part of the atom, but the chemical and other properties of the latter are determined by the surrounding electrons. This is true both when atoms are separated from one another, as in a gas, and when they are in various combinations, forming the great variety of materials familiar to us in everyday life. The atomic nucleus and the electrons accompanying it are themselves very small in comparison with the atom as a whole, and therefore the latter, like the solar system, should be regarded as a largely empty structure, with relatively large distances between its constituent particles.

Although the nucleus and the electrons accompanying it possess electric charge, an ordinary atom is electrically neutral, since the positive charge of the nucleus is balanced by the negative charge of all the electrons. If by \(e\) we denote the charge of one electron, then the charge of the nucleus will be \(+Ze\), where \(Z\) denotes the number of electrons in the neutral atom. When an atom loses one or more electrons, it acquires a positive charge and becomes a “positive ion.” \(Z\) is called the atomic number of the element. The ninety-six different chemical elements that are at present known can be arranged in the form of a numbered sequence, beginning with hydrogen, for which \(Z = 1\) (and consequently its neutral atom has one single electron), and proceeding further to helium (\(Z = 2\)), lithium—3, beryllium—4, boron—5, etc. Thus one may depict the first six members of this sequence, which is known to chemists as the periodic system of Mendeleev, in the form of the following simple schemes (Fig. 1).

The great difference between the masses of electrons and nuclei is evident from the fact that even in the case of the lightest element, hydrogen, the mass of the atomic nucleus is 1870 times greater than the mass of the electron. In heavy elements this ratio is a hundred times greater than this value.

The force compelling the electrons to move in their orbits in the atom, which we regard as a small solar system, is the force of electrostatic attraction between the oppositely charged nucleus and electrons. It is important to understand that the properties of all those objects with which we are familiar depend on the electronic structure of atoms, whereas the nuclei are responsible only for a large ...

part of the mass, and the magnitude of their charge determines the number of surrounding electrons. None of the ordinarily available means of action, such as, for example, high pressures, high temperatures, or deep cold, have any noticeable effect on the nuclei, since they are protected against such intrusions by the surrounding shell of electrons. Therefore only after the creation

Fig. 1. Diagram illustrating the electronic structure of the first six elements of the periodic table. The drawing gives only a rough idea of the distribution of electrons in atoms.

of special technical means, which arose after the discovery of radioactivity, did it become possible to raise the question of the behavior and structure of nuclei.

RADIATION

Up to now we have been speaking about the structure of matter, using such terms as atoms, nuclei, and electrons; but our knowledge of the world is obtained not only with the aid of hearing, smell, or direct touch, which can perhaps be explained by the behavior of atoms, but also on the basis of our sense of light. What “substance” is responsible for the visible image of objects that we perceive with our eyes? At the present time we speak of this “substance” as radiation, and we may regard it, like matter itself, as consisting of separate particles, which, in contrast to atoms, we shall call “quanta” or “photons.”

We now know that there is a close connection between atoms and quanta. For example, when a gas is strongly heated, say in a flame, the atoms composing it move with increased velocity. When atoms collide with one another, their electrons may pass to orbits of higher energy. Such atoms are said to

they are “excited.” Generally speaking, an excited atom rapidly returns to its normal energy state, and in such a transition the excess energy is released in the form of a quantum of radiation. If \(E_1\) and \(E_0\) denote, respectively, the energy of the atom in the excited and in the normal or lower states, then the energy of the emitted quantum of radiation is given by equation (1) \(h\nu = E_1 - E_0\). In this equation \(h\) is a constant, the so-called Planck constant, and \(\nu\) is the frequency of the emitted radiation.

It has been found that for an atom of a given type there is only a limited number of excited states of different energy in which the atom can exist. Accordingly, for the various possible transitions of the atom between different pairs of such states, there exists only a limited number of different photons, each possessing a definite quantum of energy, whose magnitude is given by equation (1). For this reason the visible light from each element can always be resolved in a spectroscope into a series of lines, each of which corresponds to light of a definite frequency and, consequently, to a definite quantum energy.

Our eyes are sensitive to radiation of frequency \(\nu\) lying within a rather narrow range. We now know, however, that in nature there exist radiations which, beginning with radio waves, extend to the region of infrared waves and farther, through the visible spectrum, to X-rays and \(\gamma\)-rays, all these radiations being essentially of one nature. In passing from radio waves to the most penetrating \(\gamma\)-rays, the value of \(\nu\) changes by more than forty octaves, but all the corresponding quanta move in a vacuum with one and the same velocity \(c\), equal to the speed of light, \(3 \times 10^{10}\ \mathrm{cm/sec}\).

According to the picture sketched above, a photon is not found in ready-made form in the atom that emits it, but is born when the atom passes from one state to another. The photon produced then flies from the radiating substance until it encounters another substance. Then, if the layer of the latter is sufficiently thick, the photon disappears, or, as they say, is absorbed. The process of absorption is rather varied in its details and depends on the frequency of the radiation, but in the case of visible light and X-rays it is to a considerable extent due to excitation or ionization of the atoms of the substance upon which the photon falls. “Ionization” means that, instead of an electron being transferred to an orbit of higher energy, it is knocked completely out of the atom, as a result of which the total charge of the latter becomes equal to \(+e\), and, consequently, a positive ion is produced. The photons that reached your eye from this page had a very brief existence, if you are reading by artificial light. The distance they traveled was probably of the order of \(300\ \mathrm{cm}\), and their flight time is equal to \(300/3 \cdot 10^{10} = 10^{-8}\ \mathrm{sec}\); on the other hand, in interstellar space quanta from the most distant nebulae travel the path to the Earth in the course of \(5 \cdot 10^8\) years.

WAVES AND PARTICLES

Two points in the material set forth in the preceding section may present certain difficulties for readers unfamiliar with the concepts of atomic physics. First, we assert that electrons in an atom can be found only in definite energy states. The analogy of the atom with a miniature solar system, therefore, has only limited applicability. The kinetic energy of the Earth, as it moves around the Sun, has at the present moment some value, but it gradually decreases as a result of the action of the tides. Therefore the energy and the radius of the orbit become smaller and smaller with each year. Our knowledge of the behavior of atoms, on the other hand, does not allow us to admit similar changes in the energy of their electrons. Experiment shows that an atom can exist only in certain states with definite energy, and transitions between these states are accompanied by the absorption or emission of photons.

Second, we began by asserting that radiation consists of particles of a definite type, photons, and then spoke of “radio waves.” This seems paradoxical, since according to our usual conceptions something can be either a wave or a particle, but not both at the same time; these two categories are mutually exclusive. Thus in both cases we find that, in order to describe phenomena in the world of atoms, it is necessary to introduce concepts that are foreign to our everyday notions.

Problems of this kind, at the time of their discovery—around the beginning of our century—created great difficulties for physicists. For two hundred years classical physics had developed on the basis of Newtonian mechanics. This system is founded on such concepts as mass and force, which are largely derived from ordinary everyday experience and, with time, have become part of our common scientific heritage. They can therefore be used uncritically, and we often regard them as something self-evident. For example, Newton’s law of universal gravitation is known to everyone acquainted with the elements of science, and it is usually perceived without any difficulty; it is precisely the unfamiliarity of the more modern laws that makes them difficult to understand.

The discovery of the quantum nature of radiation was one of the first discoveries to require a break with the classical traditions in physics. Some aspects of the behavior of radiation can be described by analogy with waves on the surface of a pond, whereas others only if we imagine radiation as concentrated in small packets, or quanta; however, neither of these analogies is complete. We can preserve the conception of atoms and photons as particles only if we accept that the motion of particles is described not by means of classical mechanics

Newton, and according to the new system—wave mechanics—which has close analogies with wave motion. Both systems give the same result when applied to heavy bodies consisting of many atoms.

Such crises of ideas are organically connected with the growth of human knowledge and the development of ways of controlling the forces of nature, and they occur from time to time in every field of science and human cognition. It is hardly to be expected that further research will resolve this difficulty in the sense that it will become possible to say whether radiation is “in reality” a wave or a particle. We now know that the “duality” of wave-particle is inherent in all realities encountered in the world of atoms and nuclei, and it remains for us to make it a familiar part of our conceptions. In this way we enrich the content of our thought and shall have enlarged reserves from which analogies can be drawn when, in the future, we penetrate still more deeply into the mysteries of nature. Let us recall that before the time of Copernicus it would have been impossible to describe the atom as a kind of miniature solar system.

The task of mastering these facts is made even more difficult for the student, in our opinion, by the fact that courses in optics in our schools follow the historical development of this subject only up to the end of the last century. Much attention is paid to the wave properties of light—interference, diffraction, polarization—while the quantum properties of radiation are often passed over. Thus a one-sided conception is created, whereas for understanding the nature of radiation, and also for the technical application of this knowledge, both sides must receive equal illumination.

MASS AND ENERGY

In ordinary calculations we use familiar units, for example, the gram for measuring mass and the erg or kilogram-meter for measuring work or energy. If one deals with individual atoms or electrons, it turns out that these units are too large. It is convenient to take \(1/16\) of the mass of an atom of ordinary oxygen as the unit of mass, and the energy of an electron that has passed through a potential difference of one volt as the unit of energy. The latter unit, called the electron-volt, is denoted by the symbol eV. The average kinetic energy of a gas molecule at ordinary temperatures is approximately \(0.03\) eV, whereas at the center of the Sun, where the temperature is of the order of \(2 \cdot 10^7\) degrees Celsius, the average energy of individual atoms is of the order of \(2\,000\) eV.

The convenience of the electron-volt as a unit of energy consists in the fact that it is often necessary to impart high velocities to atomic or nuclear particles by accelerating them in a vacuum between two points having a definite potential difference. If, as is usual

it happens that the charge of the particles is known, then their energy is determined at once if the potential difference traversed is given. The similarity of this unit to the well-known kilogram-meter is therefore very close, since the latter unit is defined as the kinetic energy acquired by a load weighing one kilogram when falling vertically from a height of one meter.

One of the principal features of classical physics, based on Newtonian mechanics, is that the mass of a body is a constant quantity, independent of the physical state of the body: of its velocity, temperature, etc. Furthermore, the mass and energy of a closed system are regarded as two separate and distinct quantities, each of which remains constant under any changes taking place within the system*). These two features find their expression in two famous axioms—the law of conservation of mass and the law of conservation of energy.

These foundations of physics were undermined by the development of Einstein’s theory of relativity. In contrast to Newtonian mechanics, in relativistic mechanics the mass of a body increases when it is set in motion, owing to the increase in its kinetic energy. For the velocities with which we are familiar in our ordinary life, these changes in mass are so insignificant that they cannot be detected even by the most precise instruments available. On the other hand, in nuclear physics particles with velocities approaching the speed of light are a common phenomenon, and changes in mass are of substantial importance. Under these circumstances it becomes necessary to designate the mass of a body at rest by a special term, and one therefore speaks of the body’s “rest mass.”

The preceding example is a special case of a more general law, following from the theory of relativity, according to which there exists a general equivalence between mass and energy. A given amount of mass in \(m\) grams is equivalent to an amount of energy in \(E\) ergs, namely, \(m = \dfrac{E}{c^2}\), or \(E = mc^2\), where \(c\) is the speed of light. Further, mass can be transformed into energy, or energy into mass, and therefore the separate principles of conservation of mass and conservation of energy must be replaced by one general principle of conservation of mass-energy. Energy must be measured in units of \(\mathrm{erg}/c^2\), which express in grams the mass to which it is equivalent.

This general law is again correct for the phenomena usually observed by us, but if the domain of nuclear physics is excluded, changes in energy, and consequently in mass, are too small for

*) The term “closed system” means that the system of particles under consideration is completely isolated from the action of surrounding bodies. Such isolation is, of course, practically impossible, but in some cases it is possible to create such a degree of isolation that the influence of the external world is negligible in relation to the particular processes under consideration.

they could be detected. If we burn a certain quantity of coal in a vessel, using, for example, a certain quantity of oxygen for this purpose, then the mass of all the products of combustion will be equal to the mass of the initial products, provided that the heat and light which appear during combustion are completely retained by the vessel. If, however, we collect these products and allow them to cool, then their mass in the cold state will be less than the mass of the initial products by an amount corresponding to the mass equivalent of the energy lost by the system. Modern balances do not permit measurements of such changes of mass, since the latter are a thousand times smaller than those which could be detected. The energy released in nuclear reactions, however, exceeds by more than a million times the amount of energy released in chemical reactions for one and the same quantity of participating materials, and changes of mass therefore become appreciable.

The equivalence between mass and energy, expressed by Einstein’s relation, makes it possible to determine the energy, in electron-volts, corresponding to the mass of the electron. The value obtained is 510,000 eV, or 0.51 MeV, where the symbol 1 MeV denotes one million electron-volts. If, therefore, we impart to an electron a kinetic energy of a million electron-volts, its mass will be approximately three times greater than that of an electron at rest. At still higher energies, such as occur in cosmic rays, charged particles will have masses many times greater than their rest masses, and now depending mainly on their energy.

From Einstein’s relation it also follows that with a photon there is associated a mass equal to \(\dfrac{E}{c^2} = \dfrac{h\nu}{c^2}\). In this case the mass depends on the frequency of the radiation, and for ordinary visible light it is very small in comparison with the mass of the electron. For very penetrating photons forming part of cosmic rays, the energy of the quanta may be so considerable that the corresponding masses even exceed the rest masses of atomic nuclei.

CONSERVATION OF MOMENTUM

While in modern physics the separate principles of conservation of mass and conservation of energy are replaced by Einstein’s more general law, the third fundamental principle of classical mechanics, namely the law of conservation of momentum, remains valid and finds very broad application. This law states that the momentum of a system does not change as a result of the interaction of its constituent parts. A simple example from classical mechanics is the firing of a gun. We may neglect the amount of motion of the gases produced as a result of the explosion of the charge. Suppose that \(m\) is the mass of the bullet and \(M\) the mass of the gun, \(V\) is the velocity of flight of the bullet and

$v$ is the recoil velocity of the rifle, and it is assumed that initially the rifle was at rest and, consequently, the initial momentum of the bullet and the rifle was zero. Then the principle of conservation of momentum asserts that the initial and final momenta are equal, i.e. $mV = Mv$, or the momentum of the forward-moving bullet is equal to the recoil momentum of the rifle.

We find many examples of the application of this equation in nuclear physics. It should be noted that it means that, as a result of the explosion of the charge, the bullet receives the greater part of the energy released. Thus, if the rifle has a mass of 100 units and the bullet a mass of 1 unit, then the velocities are in the ratio 1 to 100. The kinetic energy of a body of mass $m$ and velocity $v$ is equal to $\frac{1}{2}mv^2$. Thus the energy of the bullet, $\frac{1}{2}\cdot 1\cdot 100^2 = 5000$ units, is one hundred times greater than the energy of the rifle, equal to $\frac{1}{2}\cdot 100\cdot 1^2 = 50$ units. The greater the difference between the masses of both particles, the greater the share of the released energy received by the lighter particle.

In the more general case of the appearance of several fragments as a result of an explosion, it is necessary to determine the total momentum of the system from the resultant momenta of the individual fragments, taking their directions into account, or, as one says, by summing them vectorially.

RADIOACTIVITY OF NUCLEI: α-DECAY

The stage in the development of our knowledge of the structure of matter that was described in the preceding paragraphs had been reached by about 1912. It had been established that the phenomenon of radioactivity is due to the fact that the nuclei of the heaviest elements, such as uranium (92), radium (88), and polonium (84), are unstable and can spontaneously “explode.” In one type of this process, “radioactive decay,” the atomic nucleus emits a small fragment possessing its own structure—an $\alpha$-particle—which, as Rutherford showed, is identical with the nucleus of the second element of the periodic table, i.e. helium ($Z=2$). The loss of an $\alpha$-particle leads to a decrease in the nuclear charge by $+2e$. Thus, for polonium the nuclear charge changes from $+84e$ to $+82e$, and consequently the nucleus of the 82nd element of the periodic system is obtained, i.e. lead.

The $\alpha$-particles emitted by radioactive substances leave the parent nuclei with velocities approaching the speed of light and with energies of the order of several million electron-volts. They therefore move approximately 10,000 times faster than ordinary atoms at room temperature, which, as we have seen, possess thermal-motion energy of the order of 0.03 eV. If the radioactive substance is in air, then the emitted $\alpha$-particles pass through the atoms of the air, i.e. of oxygen and nitrogen, like a fast star passing through a multitude of solar systems, and

knock planetary electrons out of atoms, gradually losing their speed in the process.

Except in a few very rare cases, when passing through an atom an α-particle loses only an insignificant fraction of its energy, and only after passing through hundreds of thousands of atoms does it come to rest.

Fig. 2a. Range–energy curve for α-particles in Ilford emulsions of the “Nuclear Research” type.

However, even in a gas the number of atoms in a small volume is so great that the distance traversed by a radium α-particle is only 3.2 cm.

An important feature of the process of radioactive decay is the circumstance that almost all α-particles from a parent nucleus of a given type have the same velocities of emission and, consequently, traverse paths of almost the same length, i.e. they have approximately equal “ranges”*) in air under normal conditions of pressure and temperature. For different radioactive elements, however, the energy of emission is different and, consequently, the ranges of the corresponding α-particles also differ. Thus, knowledge of the range of an α-particle can greatly facilitate determining the nature of the parent atom that emitted it.

Fig. 2b. Range–energy curve for α-particles in Ilford emulsions of the “Nuclear Research” type.

An exact determination of the energy of α-particles emitted by various radioactive nuclei was carried out by Rosenblum by the method of magnetic deflection, but it would be inappropriate to go into the details of these experiments here. However, if the relation between the energy of the parti—

*) It is necessary to dwell on the term “spread” of α-particles for two reasons. First, many radioactive substances undergoing α-decay emit several different homogeneous groups of particles. In general, there is one principal group for a given type of nuclei, corresponding to the usual mode of decay, and one or more weaker groups with different ranges—

...emulsions and its range, one can estimate the particle’s initial energy from its range. Although this method is less accurate than the method of magnetic deflection, it is considerably simpler and to this day is used almost everywhere in experiments with nuclear particles. The “range–energy” curve for α-particles in an Ilford emulsion of the “Nuclear Research” type is shown in Figs. 2a and b.

FAMILIES OF RADIOACTIVE ELEMENTS

Another quantity characterizing a radioactive nucleus of a given type is its “half-life.” A gram of radium contains \(2.6 \cdot 10^{21}\) atoms. In radioactive decay, some of the radium atoms emit α-particles and are transformed into atoms of a new element—radon \((Z=86)\). Thus a gradual disappearance of radium takes place, and experiments show that in approximately 1500 years half of the nuclei of the original radium atoms undergo change. During the next 1500 years the original number is reduced by a factor of four, and so on. This “exponential” decay of radium, in which over a definite interval of time a definite fraction of the atoms originally present disappears as a result of radioactive decay, is characteristic of all radioactive substances. The interval of time during which half of the initial number of nuclei decays spontaneously is called the “half-life”*).

The half-life \(\tau\) depends strongly on the type of radioactive substance. Thus, for one kind of uranium \(\tau\) is equal to \(10^{10}\) years, whereas for \(\mathrm{RaC'}\) it is of the order of \(10^{-6}\) sec. (i.e., one millionth of a second)! There is a general relation between the range of the α-particles from a given element and its half-life, which in its mathematical form has received the name of the Geiger–Nuttall law. According to this law, the shorter the half-life of an element, the greater the ranges of the α-particles emitted by it.

...corresponding to special modes of decay. An example of such an α-particle with an exceptional range, emitted by thorium \(\mathrm{C'}\), is shown in photograph VI.

Secondly, although all the α-particles of a given group are emitted with velocities almost identical within a very narrow interval, the ranges of individual particles are subject to a certain variation. Each particle loses its energy as a result of a large but finite number of collisions experienced while passing through hundreds of thousands of atoms. Consequently, the distance traveled for a given energy loss is subject to statistical fluctuations. In this case one speaks of a “straggling” of α-particles; the consequence of this phenomenon is that, when determining the energy of an α-particle from its range, an error of the order of 1 percent may be made.

*) According to modern views, the decay of radioactive nuclei obeys the laws of chance. Thus, the number of α-particles emitted in a definite interval of time by an α-particle source of given strength is subject to statistical fluctuations. If, however, the number of α-particles is large, then the statistical fluctuations are relatively small.

We have seen that the radioactive decay of radium leads to the formation of a new element—radon, Rn \((Z=86)\). This element is also radioactive and decays rather rapidly \((\tau=3.8\) days), with the formation of radium A \((Z=84)\). There follows a whole series of transformations (see Fig. 3), until a stable nucleus of a special type of lead \((Z=82)\) is formed. It may be noted that in this sequence of transformations not every nucleus decays with the emission of an \(\alpha\)-particle. Some nuclei emit a fast electron, or \(\beta\)-particle, as a result of which the charge of the nucleus is not decreased by two units, as in the case of \(\alpha\)-decay, but is increased by one unit, which corresponds to the loss of one charge \((-e)\) by the nucleus.

The number of examples of \(\beta\)-decay that we shall meet in this book is very small, since at present it is impossible to detect traces of electrons in photographic plates; this question, however, is of very great importance.

Labels in Fig. 3

Radium series

• Radium; Ra — \(^{88}\), 1550 years, \(\alpha\)—4.79 MeV
• Radon; Rn — \(^{86}\), 3.82 days, \(\alpha\)—5.49 MeV
• Radium A; RaA — \(^{84}\), 3.05 min, \(\alpha\)—6.00 MeV
• Radium B; RaB — \(^{82}\), 26.8 min, \(\beta\)
• Radium C; RaC — \(^{83}\), 19 min
• branch: 5.50 MeV—\(\alpha\) to Radium C′; RaC′ — \(^{81}\), 1.32 min, \(\beta\)
• branch: \(\beta\) to Radium C″ — \(^{84}\), \(10^{-7}\) sec, \(\alpha\)—7.68 MeV
• Radium D; RaD — \(^{82}\), 22 years, \(\beta\)
• Radium E; RaE — \(^{83}\), 5.0 days, \(\beta\)
• Radium F; RaF — \(^{84}\), 140 days, \(\alpha\)—5.30 MeV
• Radium G; RaG — \(^{82}\), stable (lead)

Thorium series

• Thorium; Th — \(^{90}\), \(1.8 \cdot 10^{10}\) years, \(\alpha\)—4.27 MeV
• Mesothorium I; MsTh I — \(^{88}\), 6.7 years, \(\beta\)
• Mesothorium II; MsTh II — \(^{89}\), 6.1 hours, \(\beta\)
• Radiothorium; RdTh — \(^{90}\), 1.9 years, \(\alpha\)—5.42 MeV
• Thorium X; ThX — \(^{88}\), 3.6 days
• Thoron; Tn — \(^{86}\), 54.5 sec, \(\alpha\)—6.28 MeV
• Thorium A; ThA — \(^{84}\), 0.1 sec, \(\alpha\)—6.78 MeV
• Thorium B; ThB — \(^{82}\), 10.6 hours, \(\beta\)
• Thorium C; ThC — \(^{83}\), 60 min
• branch: 6.04 MeV to Thorium C″; ThC″ — \(^{81}\), 3.1 min, \(\beta\)
• branch: \(\beta\) to Thorium C′; ThC′ — \(^{84}\), \(10^{-7}\) sec, \(\alpha\)—8.78 MeV
• Thorium D — \(^{82}\), stable

Fig. 3. Family of radioactive substances of radium and thorium. The charge numbers \(Z\) of the nuclei are indicated by the figures in the small circles. Beside each circle are given the name of the nucleus, its symbol, and also its half-life \(\tau\). The type of radioactive decay \((\alpha\) or \(\beta)\) is indicated beside the corresponding arrows. For \(\alpha\)-active substances the mean energies are expressed in MeV (million electron-volts).

All atoms of the periodic table can now be obtained in radioactive form, and workers in the most diverse fields of science are now equipped with a new and powerful method of investigation. In almost all cases these radioactive nuclei decay with the emission of electrons, which can be detected by methods of electrical counting.

Consideration of Fig. 3 shows that, after the decay of the radium nucleus, the subsequent transformations proceed rather rapidly, since the half-lives of the corresponding nuclei are much shorter than the half-life of radium. This effect is still more noticeable in the family of radioactive nuclei for which thorium is the initial substance.

In this case, which is also shown in Fig. 3, all transformations following the decay of the radiothorium nucleus occur in practice within the course of several days. It may also be noted that when “C” substances are formed, a “branching” occurs in the radioactive series: both radium C and thorium C can decay with the emission of either an $\alpha$- or a $\beta$-particle.

TRACKS OF $\alpha$-PARTICLES IN PHOTOGRAPHIC EMULSIONS

The photographs (see at the end of the issue) show tracks produced by fast charged particles as they pass through a photographic emulsion. An ordinary photographic plate is a flat glass plate about two millimeters thick, on which a layer of emulsion is deposited, containing gelatin and a large number of the finest grains of silver halide compounds—most often bromide or iodide. These small crystals are formed in the emulsion by precipitation under definite temperature conditions and are usually called “grains” or “granules” of silver halide. After the emulsion has dried on the glass, a firm, stable layer is obtained.

In normal photography, the image of the object being photographed is formed on the surface of the emulsion when it is illuminated by light. As a result, in some of the grains there are formed small specks of silver, consisting of only a few atoms and too small to be detected with an ordinary microscope. Such a speck of silver is called a “latent image.” The greater the intensity of the light falling on a given area, the greater the number of grains that undergo alteration.

If, after exposure, the plate is placed in a solution called a “developer,” which contains suitable reducing agents, then those silver halide grains in which latent images exist are converted into black grains of metallic silver. On the other hand, grains without a latent image, or with latent images of insufficient size, are not sensitive to the developer. Next, the plate is placed in another solution, a “fixer,” which dissolves the undestroyed silver halide grains but leaves the developed grains untouched. The various degrees of blackening in the finally processed photographic plate correspond to the relative amount of light that has fallen on the different areas of its surface. The more intense the light, the greater the number of developed grains and the greater the corresponding blackening of the plate.

For work in nuclear physics, special photographic emulsions are prepared which contain approximately ten times more silver halide, relative to the given amount of gelatin, than ordinary emulsions. In addition, they are often made much more

thicker layers of emulsion than in ordinary photography, the thickness usually employed being approximately \(1/10\) millimeter*).

If \(\alpha\)-particles enter the emulsion of one of these special plates, they pass through grains of silver halide embedded in gelatin; but, owing to the greater density of the atoms of a solid as compared with a gas, their range in the emulsion is almost two thousand times smaller than the corresponding value for air. If, after exposure, the emulsion is developed and fixed, only the grains struck by \(\alpha\)-particles will be developed and will remain in the form of silver grains. As a result, when the plate is examined under a microscope, the particle tracks appear as lines of black silver grains, like black beads strung irregularly on an invisible thread. Because of the small range of the particles, one thousandth of a millimeter—the micron—is usually taken as the unit of length, denoted by the symbol \(1\mu\).

All the photographs presented were obtained with the aid of special photographic emulsions manufactured by the Ilford company and called “Nuclear Research” emulsions. Since the density of the silver halide in these emulsions is considerably greater than in ordinary photographic emulsions, the distance between neighboring grains is much smaller, and the tracks of \(\alpha\)-particles have the appearance of almost continuous chains of silver grains, so that they can easily be examined under a microscope. Various types of plates are manufactured—“A,” “B,” “C,” “D,” and “E”; moreover, the average grain size varies for the different types from \(0.5\mu\) to \(0.1\mu\). For the method of developing and fixing the emulsions, see Appendix A.

This method of obtaining visible tracks of particles that have passed through an emulsion is similar to the Wilson chamber method, which has played such an outstanding role in nuclear physics. The advantage of the photographic plate, however, is that it permanently retains its sensitivity and is extremely simple to handle. On the other hand, we have already seen that, at the present stage of its improvement, the photographic plate does not register fast electrons, which leave along their path an incomparably thinner trail of ions than heavier particles do, and which therefore have a much weaker photographic action on the grains of silver halide through which they pass.

The photographs in the following paragraphs illustrate simple experiments on radioactivity. Some of them can be obtained with very modest apparatus. For example, the tracks obtained can be made clearly visible with a microscope having a \(\times 40\) dry objective (4 mm) and a \(\times 6\) ocular, with sufficiently well-adjusted illumination. In order to obtain photographs of higher qual—

*) The use of thick-layer photographic plates was first proposed by L. V. Mysovskii, who developed the technique for their manufacture and methods of application. Subsequently this method was developed and applied with great success by A. P. Zhdanov and other Soviet physicists. —Ed.

to be used, objectives with a high aperture, immersed in oil, are usually employed in order to resolve the fine structure of the tracks. But then the difficulty arises that the focal length of such objectives is small, as a result of which only objects situated in a very thin layer are in focus. Under these circumstances a track can be photographed in its entirety only if it proves to lie in a plane parallel to the plane of the emulsion. If it is inclined to this plane, one has to focus on different portions of the track and take a whole series of photographs. The latter can then be used to make an overlapping mosaic, much as is done in aerial photography. A similar method is also used in cases, as often happens, when the object is too large to be photographed under the microscope in a single exposure.

Some of the photographs reproduced below were obtained in one exposure and show tracks that go out of focus. In those cases where several photographs were joined together into a single mosaic, this is specially indicated in the text.

ISOTOPES

Up to now we have distinguished nuclei by their charge \(Z\), which determines the chemical properties of atoms. A detailed study of radioactive families has shown, however, that the nuclei of heavy elements do not all have the same mass. It is convenient to measure the mass of a nucleus relative to the mass of the proton, which is the nucleus of the lightest element, hydrogen. In all cases this ratio is, though not quite exactly, equal to an integer, which is called the mass number of the nucleus. Thus a given nucleus is described by its charge and mass numbers.

Atoms having nuclei with the same charge but different mass numbers are called “isotopes,” and their chemical properties are so close that they cannot be separated by chemical means. For example, thorium and radiothorium both have nuclei with charge number 90, so that chemically they are practically indistinguishable, but their mass numbers are respectively 232 and 228. The charge and mass number of helium are respectively 2 and 4. It follows that when a nucleus decays with the emission of an \(\alpha\)-particle, its mass number decreases by 4. On the other hand, \(\beta\)-decay, which is associated only with the emission of an electron, does not change the mass number of the nucleus.

These facts can be illustrated with the aid of the radioactive families already considered above, if one plots the mass number of the nucleus as a function of the charge number. The successive changes in the radioactive families beginning with radium and thorium are shown by such a graph in Fig. 4. It may be noted that some of the elements represented in the figure have two or even more isotopes. Thus, for example, radium B, thorium B, radium D, thorium D

and radium G are all isotopes of lead with charge number \(Z=82\) and mass numbers, respectively, 214, 212, 210, 208, and 206. The first three nuclei are radioactive and decay with emission of a \(\beta\)-particle, while the last two are stable isotopes. Similarly, mesothorium I and thorium X are both isotopes of radium, the former emitting \(\beta\)-particles and the latter \(\alpha\)-particles.

Fig. 4. Another method of representing families of radioactive elements, in which the mass number of the nucleus is plotted as a function of the charge number.

Very many of the ordinarily existing chemical elements also consist of two or more isotopes. A particularly important case is hydrogen, which has three different types of nuclei, of which ordinary hydrogen has mass number 1, and the other two types have mass numbers 2 and 3. These three nuclei are so important that they have received special names, namely the proton, deuton, and triton, and are denoted respectively by

\[ {}_{1}\mathrm{H}^{1},\quad {}_{1}\mathrm{H}^{2}\ \text{and}\ {}_{1}\mathrm{H}^{3}, \]

where the symbol H denotes the chemical element hydrogen, and the upper and lower numbers are, respectively, the mass and charge numbers. Hydrogen consisting of atoms having deutons or tritons as their nuclei is called, respectively, deuterium and tritium. Small amounts of deuterium (0.015%) are found in ordinary natural hydrogen,

but tritium has to be obtained artificially, and so far only small quantities have been prepared.

It should be noted that in any nuclear transformation the total charge and mass number do not change. Thus, the emission of an $\alpha$-particle by polonium can be represented by the equation

\[ {}_{84}\mathrm{Po}^{208} \longrightarrow {}_{82}\mathrm{Pb}^{204} + {}_{2}\mathrm{He}^{4}, \]

where for both sides of the equation the total charge and mass number are the same and are equal, respectively, to 84 and 208. Strictly speaking, it is not necessary to give both the atomic number of an element and its symbol, since one follows from the other. It is, however, more convenient to do so, because such a notation saves us the need to determine charge numbers from tables.

THE BRAGG CURVE

Photographs VIII–XVI show the tracks of fast protons and deuterons in the emulsion. These particles are not emitted by radioactive nuclei, but can be produced in a number of ways, for example in the artificial transformation of nuclei or with the aid of some large machine such as a cyclotron. Being hydrogen nuclei, these particles carry a charge of only $+e$ as compared with $+2e$ for an $\alpha$-particle. As a result, at the same velocity they ionize the atoms through which they pass less effectively than do $\alpha$-particles, and therefore the number—and consequently the density—of the developed grains they produce in the emulsion is much smaller. Furthermore, because of their smaller ionizing power, they lose their energy more slowly than an $\alpha$-particle and, consequently, with the same initial energy traverse a longer path in the emulsion before coming to rest. The relation between range and energy for protons in Ilford “Nuclear Research” emulsions is shown in Fig. 5.

From Fig. 5 one can see that the range of a proton is not proportional to its energy. Thus, a proton with an energy of 5 MeV has a range more than ten times greater than that of a proton of 1 MeV; their corresponding ranges are 173 $\mu$ and 14.5 $\mu$. This is due to the fact that the ionization produced by a charged particle per unit path decreases as the velocity increases. For example, the range of a proton with an energy of 6 MeV is 234 $\mu$, while that of a proton with an energy of 5 MeV is only 173 $\mu$. Consequently, a proton with an initial energy of 6 MeV travels a distance of 61 $\mu$, losing 1 MeV of energy, whereas a proton with an energy of 1 MeV comes to rest after traversing a path only 14.5 $\mu$ long. A similar result is also true for $\alpha$-particles (see Fig. 2).

At first glance this result may seem paradoxical, because we are inclined to imagine the process of ionization as a process of purely mechanical collisions of a fast particle with the atoms encountered on its path, and in that case the number of “disruptions” would be

the greater, the greater the velocity of the impacting particle. We have, however, seen that the process of penetration of a fast particle into an atom can be represented by analogy with a fast star moving through the solar system. In that case one should expect that the planet will be knocked out not as a result of a direct impact—which, owing to the smallness of the dimensions of the corresponding bodies, will occur only very rarely—but as a result of the gravitational attraction between the planet and the star. But the magnitude of the gravitational attraction does not depend on the velocity of the interacting bodies, but only on the distance between them. Consequently, if the star is moving very fast, then the time during which this force acts will be relatively small. The motion of the planet will therefore change little, and it will acquire a small amount of motion. Similar considerations are also applicable to the interaction of an α-particle or a proton with an atom: the greater the velocity of the particle, the smaller the number of atoms along its path that undergo ionization.

Fig. 5. Range-energy curve for protons in Ilford emulsions of the “Nuclear Research” type. It should be noted that the scale is different in the two graphs.

The change in ionization along the tracks of α-particles was first studied by W. G. Bragg. The results obtained may be represented by a graph similar to the graph shown in Fig. 6 and referring to experiments on the ionization of air by α-particles. A similar result is also found for other substances. Thus, we should expect that near the end of the track, where the velocity of the particles is smaller, the grain density in the emulsion will be greater. For α-particles from radioactive substances with energies less than 10 MeV this effect is weakly expressed, since at all points of the track the ionization is so great that an almost “continuous” track is obtained, without gaps.

between grains. For protons with the same energy, however, the ionization is much smaller because of the greater velocity of the proton and the smaller charge, and as a result the initial portion of the track is thinner than in the case of $\alpha$-particles, and sometimes one can observe an increased grain density near the end of the range. For $\alpha$-particles, protons, and deuterons of much higher energies—from 100 to 400 MeV—which at the present time can be obtained with the aid of a synchrocyclotron, the ionization at the beginning of the particle tracks proves to be greatly reduced. The result of this is that the number of grains on the section of the particle path where the velocity of the latter was greatest proves so small that, in the case of protons and deuterons, it is impossible to detect the trajectory of these particles. (See, for example, photographs XXXII and XXXIII*.)

Fig. 6. Curve of the dependence of ionization for a parallel homogeneous beam of $\alpha$-particles on the distance traveled by them to the end of their range. Such curves are called “Bragg curves.”

For particles of still smaller mass—mesons, which we shall consider below in another paragraph—the change in grain density in the track proves to be more sharply expressed than for protons. Further, the limiting case is represented by electrons, which have a small mass and move so much faster than protons of the same energy that they do not create noticeable tracks in any of the emulsions available at the present time. It is possible that they create one or two grains at the end of their range, but it is difficult to identify them with any degree of reliability.

These conclusions may be summarized as follows: a particle with charge $Ze$ and velocity $v$ creates ionization per unit path length during its range which, very approximately, is given by the equation

$$ I \sim (Ze)^2/v^2 . $$

It is important to note that the ionization, and consequently also the energy losses per unit path length, depend only on the charge and velocity of the particle and do not depend on its mass.

* These photographs will be placed in the next issue. —Ed.

K. F. Powell and G. P. S. Occhialini

SCATTERING OF FAST PARTICLES AS A RESULT OF COLLISIONS WITH NUCLEI

The photographs placed below also acquaint us with another important feature of particle tracks. They reproduce tracks that reveal the effects of elastic scattering of particles by the nuclei of some of the atoms through which they pass. We have seen that, like an $\alpha$-particle, a fast proton or deuteron passes through hundreds of thousands of atoms before coming to rest in the emulsion. However, only in rare cases do they pass so close to a nucleus that the forces of electrostatic repulsion begin to act on them. When such a case occurs, the particle is repelled, and the direction of its motion changes, sometimes through large angles. In this case one says that the particle has undergone elastic scattering. The term “elastic scattering” means that in the collision the particle does not lose kinetic energy *).

The investigation of the scattering of $\alpha$-particles through large angles, carried out by Rutherford’s pupils Geiger and Marsden by the scintillation method, was of decisive importance for the development of the nuclear theory of the structure of atoms. For example, if the atom were a sphere uniformly filled with positive electricity, in which electrons were embedded like raisins in a pudding (and precisely this view was held by a number of physicists at the beginning of our century), then it would be impossible to explain the scattering of fast particles through large angles. The results of the experiments can be explained only on the assumption that both the principal mass and the positive charge of the atom are concentrated in a region of small dimensions—in the nucleus.

Geiger and Marsden studied the relative frequency of scattering through various angles of $\alpha$-particles passing through a given thickness of matter, for example gold foil **).

*) The term “elastic” scattering means that, in the interaction of two particles, kinetic energy is not lost, and it is precisely this circumstance that distinguishes this event from “inelastic” scattering. In the latter process the struck nucleus may be excited to a state with higher energy and then emit $\gamma$-rays and return to the normal state. According to the principle of conservation of energy, this energy of the excited state must correspond to an equivalent amount of kinetic energy, which disappears in such collisions.

**) The problem of scattering of $\alpha$-particles through large angles was originally solved by the methods of classical mechanics and is similar in its form to the problem of the motion of a planet around the Sun under the action of gravitational attraction. Such a treatment shows that the number of $\alpha$-particles $N(\theta)\,d\theta$, scattered through angles lying between $\theta$ and $\theta + d\theta$, is given by the equation

\[ N(\theta)d\theta = \frac{k}{E^2}\operatorname{ctg}\frac{\theta}{2}\operatorname{cosec}^2\frac{\theta}{2}\,d\theta, \]

where $E$ is the energy of the incident particles.

From the graph of this function one can see that the number of scattered particles falls sharply as the angle of scattering increases.

Deflections through large angles occur much less often than scattering through small angles. It was found that the results of the experiments could be precisely explained on the assumption that the force between the \(\alpha\)-particle and the nucleus is given by Coulomb’s law:

\[ \text{force}=\frac{e_1e_2}{r^2}, \]

where \(e_1\) and \(e_2\) are the charges of the two particles and \(r\) is the distance between their centers. Knowing the velocity and mass of the \(\alpha\)-particle, one can calculate the distance to which the particle must have approached the nucleus in order to be scattered through a given angle; in the case of scattering by gold nuclei through large angles, a value of the order of \(3\cdot 10^{-12}\ \text{cm}\) is obtained. It follows from this that the sum of the radii of the gold nucleus and the \(\alpha\)-particle must in any case be smaller than this value; otherwise one would have to expect that the \(\alpha\)-particle would penetrate the nucleus with which it collided, and then the scattering experiments would not yield results agreeing with those that should be expected on the assumption of the applicability of Coulomb’s law. From such experiments one can conclude that the radii of many types of nuclei are less than \(10^{-12}\ \text{cm}\), i.e., ten thousand times smaller than the size of the atom.

When passing through a photographic emulsion, protons more often undergo changes in the direction of their motion than \(\alpha\)-particles of the same velocity, because of their smaller mass. We shall see in another paragraph that the still more frequent scattering to which mesons are subjected makes it possible to distinguish their tracks from those of protons. It should be noted that for particles of any mass the probability of scattering is greater when their energy is small, and therefore we find that bends in tracks are encountered more often near the ends of the particles’ ranges.

The photographs VII–X given below were obtained under conditions in which the particles entered the emulsion in the form of an almost parallel beam at a small angle of inclination to the surface, and in each case the arrows indicate the corresponding directions of entry.

SCATTERING OF PARTICLES BY LIGHT NUCLEI

Photographs VII–X show the scattering of protons by heavy nuclei, in which the recoil nuclei leave no noticeable track. If, however, a fast proton collides with the nucleus of a light element, then an appreciable fraction of its energy may be transferred to the latter, and it becomes possible to detect the tracks of both particles. The first three of the following photographs give an example of such an extreme case, when the masses of the striking and struck nuclei are equal. Each of the branched tracks resulted from the collision of a fast proton with another proton, which was at rest in the gelatin of the emulsion. It is not quite correct to say that the proton was at rest

“at rest” in the emulsion, since the hydrogen atom, of which it is a part, participates in the general thermal motion. However, the velocities of this motion at ordinary temperatures are so small in comparison with the velocities of nuclear particles that, for our purposes, they may be neglected.

Simple mechanical considerations show that in such cases, after the collision, both protons must move in mutually perpendicular directions. This problem is similar to the problem of the elastic collision of a billiard ball with an identical ball initially at rest. In practice, a collision between billiard balls is not fully elastic, since the balls are on a table, which exerts some effect on their motion; but this treatment is applicable with high accuracy to collisions between nuclei. For readers familiar with elementary dynamics, the corresponding derivation is given in Appendix C. The results of such an analysis are of great importance in measuring the energy of another type of particle—neutrons, which will be discussed later. Photographs XI–XVI show cases of elastic collisions of deuterons and $\alpha$-particles with various light nuclei.

(To be continued in the next issue.)

NUCLEAR PHYSICS IN PHOTOGRAPHS

“Explosive” disintegration of a nucleus

A mosaic of microphotographs of the “explosive” disintegration of a silver atom nucleus, caused by a high-energy particle in cosmic rays. The tracks of twenty-five fragments can be seen under the microscope, including the tracks of protons, $\alpha$-particles, and heavier nuclei. Many of the tracks are strongly inclined to the plane of the plate and end in one of the emulsion planes.

PHOTOGRAPH 1

Tracks of α-particles from a grain of radium

This photograph was obtained after shaking a photographic plate over which a certain small amount of radium had been deposited. Grains of radioactive material, which in many cases were too small to be seen under a microscope, were thereby separated from the needle and settled on the plate. Several days later the plate was developed and examined under a microscope, where it was found that it was covered with a large number of “stars,” one of which is shown here. In the photograph one can see the tracks of α-particles emerging from a small region at the center of the star. The photograph illustrates the large number of particles emitted by the amount of radium that is too small to be detected under a microscope. Since, over the exposure time, only about one-hundredth of all the nuclei of radium decayed, the photograph gives a clear idea of the enormous number of atoms contained even in negligible amounts of matter.

PHOTOGRAPH II

“Stars” from radiothorium

In this case the α-particles penetrated into the emulsion not from a point on its surface, but the radioactive substance itself was incorporated into the emulsion by means of a special technique for treating the latter. The plate was impregnated with a solution of thorium acetate in water (1 percent by weight) for 10 minutes, washed in running water for 1 minute, and after drying was left in the dark for 3 days. Then it was washed again and developed. Under the microscope, in such a sample of treated plates one can observe a large number of “stars” from radiothorium. Each star is produced by the successive decay of the original nucleus of radiothorium (see Fig. 3). In some cases it may be observed that the tracks do not emerge strictly from a single point. This is a consequence of the fact that, when emitting an α-particle, the residual nucleus experiences recoil, like a gun when fired. Sometimes these recoil nuclei are called α-particles. Their energy and path are so small that it is difficult to observe the difference in the position of the points from which α-particles are emitted. The sharp star in the photograph was specially selected for photographing, since all four tracks accidentally proved to lie almost in one plane, parallel to the surface of the emulsion. By measuring the length of the individual tracks of the star, one can determine which nucleus emitted the given α-particle, and consequently also the order in which they were emitted. The photograph also shows images of other tracks that were not in focus.

PHOTOGRAPH III

“Stars” from a radiothorium

The stars in this photograph were photographed by C. R. Burch with the aid of a reflecting microscope constructed by him. With the same grain sizes of silver bromide as are used in modern emulsions, normal microscope objectives with a high aperture make it possible to examine most of the details of charged-particle tracks; the limit of accuracy of the method is determined by the size of the grains, and not by the “resolving power” of the microscope. However, the preparation of emulsions with smaller grains requires optical instruments of greater resolving power. The advantage of the reflecting microscope consists in the fact that it makes it possible to photograph in ultraviolet light, which gives higher resolution. In addition, its “working distance” is much greater than in ordinary instruments and, consequently, it can be used for examining emulsions of considerably greater thickness, greater than 100 μ. The long track in the star slightly below the middle of the photograph was produced by a ThC′ particle with a range of 8.6 cm of normal air.

PHOTOGRAPH IV

“Stars” from radium

This photograph was obtained after treating a plate in a radium bromide solution with a concentration of one hundredth of a milligram per liter. The focal distance of the objective from the high-aperture limit is bounded, so that only a very few of the tracks are in focus along their entire length. The long, thin tail of the track is produced by a proton. The latter appeared as a result of the penetration of one of the α-particles into the nucleus of an atom of the emulsion and the subsequent transformation of one nucleus into another. Splitting of this type was first observed in 1919 by Rutherford, who used the scintillation method for detecting particles; these were the first successful cases of the artificial transmutation of elements.

PHOTOGRAPH V

Radium “stars” after intensification

In ordinary photography it sometimes happens that the exposure is too short and the negative is weak and insufficiently dark in those places where the light was most intense. In such cases the darkening can be increased by immersing the negative in a suitable solution, in which another metal is deposited around the developed silver grains in the emulsion, so that the degree of darkening is increased. A similar method can also be used for “intensifying” the tracks of charged particles, in order to make them darker. The above microphotograph shows the effect obtained in this way. For intensification in this case, uranium salts were used. This process may prove useful in cases where it is necessary to count the number of tracks. On the other hand, although the tracks are now more clearly visible, they are thicker than in the untreated plate, and consequently a number of details may be lost.

PHOTOGRAPH VI

Long-range α-particles from thorium C′

In Photograph I an example was shown of an α-particle from thorium C′ (range in normal air, 8.6 cm). In one case out of 10,000, an α-particle arising from the decay of this nucleus has an abnormally large range—11.6 cm*). The horizontal track shown in this photograph is an example of such a long-range α-particle. There is an even rarer group with a range of 9.7 cm. Photographs of two ordinary stars of radiothorium, taken at the same magnification, are given for comparison.

*) This event is the first indication that nuclei, like atoms, possess a limited number of energy states. From Fig. 3 it can be seen that thorium C decays with the emission of a β-particle and the formation of thorium C′ (ThC′). The nucleus thus formed usually decays in the state of lowest energy (the lowest state) and emits an α-particle with a range of 8.6 cm in air. However, the ThC′ nucleus may also be formed in an excited state with an energy of 1.8 MeV. An α-particle emitted by such an excited nucleus has increased energy and, consequently, a greater range. An even rarer group of particles with a range of 9.6 cm in air corresponds to the decay of ThC′ in another excited state with an energy of 0.7 MeV.

PHOTOGRAPH VII

Elastic scattering of a proton by heavy nuclei

Traces of protons in the Ilford emulsion “Nuclear Research,” type B 1. One can examine proton tracks, one of which was scattered three times in collisions with the nuclei of atoms of the emulsion. This and the following photograph show very rare events of this kind, but the tracks of all protons exhibit deflections through small angles as they pass through the emulsion. The nuclei with which the particles collide experience a certain recoil, but because of their large mass they receive only a small fraction of the proton’s kinetic energy. Therefore their track is too small to be observable.

PHOTOGRAPH VIII

Tracks of protons and α-particles

A mixed beam of protons and α-particles was directed onto the emulsion. One of the protons was deflected through a large angle as a result of collision with an atom of the emulsion. The short tracks in the upper part of the photograph are due to α-particles. It may be noted that in these tracks the grain density is greater than in the proton tracks. Some of the α-particle tracks also reveal curvatures caused by collisions with nuclei.

PHOTOGRAPH IX

Double scattering of a proton

A rare case in which a proton was scattered twice during its passage through the emulsion.

PHOTOGRAPH XIV

Scattering of a deuteron by a proton

Tracks of deuterons in a photographic emulsion. One of the deuterons collided with a proton and communicated to it part of its momentum. Analysis of this case, carried out in the appendix, shows that in such a collision a deuteron cannot be deflected through an angle greater than \(30^\circ\). We are therefore entitled to assume that the deuteron track is to the right, where its deflection is \(23.5^\circ\), while the proton, whose track is on the left, is ejected at an angle of \(52.5^\circ\). In order for the tracks to be in focus over their entire length, two photographs had to be taken.

PHOTOGRAPH XI

Collision of a proton with a proton

Scattering of a proton that was near the end of its range by another proton. In this case, after the collision, each of the tracks forms an angle of almost \(45^\circ\) with the initial direction of motion of the primary proton, and the energy is approximately divided equally between the two particles. It may be noted that at the end of their ranges the proton tracks are almost continuous. The shorter tracks are due to \(\alpha\)-particles.

PHOTOGRAPHS XII and XIII

Other examples of the scattering of protons by protons

In the upper photograph it can be seen that the proton scattered through a large angle has a shorter range than the second proton (see Appendix C).

PHOTOGRAPH X

Scattering of a proton at a large angle

An extremely rare case of scattering of a proton through an angle of \(160^\circ\), probably as a result of collision with the nucleus of an atom of silver or bromine. The photograph shows that the probability of scattering increases near the end of the range. This fact, as well as the increased density of grains in the track near the end of the range, makes it possible to determine the direction of motion of the particle.

Photograph XV

$100\mu$

Scattering of a fast deuteron by a carbon or oxygen nucleus

Elastic collision of a deuteron with a light nucleus in the emulsion. It is impossible to determine whether this nucleus belonged to carbon, oxygen, or nitrogen. In the case considered, the ratio of the masses of the two interacting particles was such that the recoil nucleus received a noticeable fraction of the energy of the incident deuteron, and the recoil track, although short, is clearly visible in the photograph.

PHOTOGRAPH XVI

Collision of an $\alpha$-particle with a proton

The $\alpha$-particle from a radioactive-star event, produced in the left upper corner of the photograph, collided with a proton, knocking the latter out. It can be seen that the track of the proton in the immediate vicinity of the collision point is thinner than the track of the $\alpha$-particle, and becomes denser near the end of its range. The path of the other $\alpha$-particle ends close to the proton track, but these two events should be regarded as independent of one another. An analysis of this case is given in Appendix E.