MATTER, Constitution of. - The problem of the constitution of matter is undoubtedly one of the fundamental scientific problems: indeed, research concerning this question has been informed by the idea of accounting for the more or less complex and numerous laws of the most diverse phenomena that fall under the senses (macroscopic phenomena), by means of the essentially simpler laws, limited in number, of microscopic complexes (molecules and atoms) conceived as constituting macroscopic bodies.
The investigation of the constitution of bodies thus comprises a twofold process: 1) analysis of bodies into their microscopic constituents, thus involving the problem of determining the nature and the laws of such constituents; 2) synthesis, by means of which the macroscopic laws are derived in their variety and with their limitations.
Hence the importance of the question, which, seen in this way, includes within itself the problem of reducing to a higher unity the diverse appearances of macroscopic natural phenomena and of determining the field of validity and the true meaning of the laws that govern them.
I. THE KINETIC THEORY OF HEAT
As is well known, even the ancients (Leucippus, Democritus) had some intuition regarding the atomic structure of matter and molecular agitation. These hypotheses were taken up again in the 17th century by Gassendi and then by Daniel Bernoulli, who made the first quantitative applications of them to the deduction of Boyle's law on the pressure of gases. A further impulse to the atomic conception came from the discovery of the fundamental laws governing chemical phenomena, which were very naturally interpreted by means of atomic and molecular hypotheses. Thus the notion of "atom" and of "molecule" was made precise (v. CHIMICA). The laws of reactions between substances in the gaseous state then suggested to Avogadro his famous hypothesis: equal volumes of gas at the same pressure and temperature contain the same number of molecules. This hypothesis made it possible to determine the notion of molecular weight (v. CHIMICA) and, in this way, the ratios between the masses of the molecules of the various substances.
The first way of tackling the question of the absolute dimensions of atoms, and therefore of the true value of the atomic hypothesis, was provided by the study of gases, by means of the so-called kinetic theory of heat. This theory was suggested by the following observations: in the mechanical phenomena that fall under direct observation, it generally appears to a rough investigation that part of the mechanical energy brought into play is lost; in reality this energy is not lost, but is transformed into internal energy of the bodies in which mechanical work has been dissipated. One can in fact observe in such bodies a rise in temperature, as if a quantity of heat proportional to the quantity of work dissipated had been supplied (first principle of thermodynamics, or principle of the equivalence between work and heat: v. TERMOLOGIA).
The first principle of thermodynamics suggests very clearly the idea that heat is a particular form of mechanical energy (an idea that, in a more or less clear form, had been glimpsed by the atomists before the discovery of the first principle). In fact, if one tries to examine closely the manner in which macroscopic mechanical energy disappears as such in order to give rise, for example, to rises in temperature in certain bodies, it is possible to observe that this phenomenon occurs through a fragmentation of the energy of collective motions into energy of disordered motions (for example, vibrations) of ever smaller and more numerous portions of the bodies involved in the phenomenon.
This fact can be observed with great clarity, for example, in the case of a stone striking a stretch of water that is initially calm: at first relatively long and broad waves are observed; among them, waves of ever smaller wavelength tend progressively to predominate, until every apparent motion disappears.
The direct analytical examination of this phenomenon of energy transformation shows that if matter had a continuous structure, the process of fragmentation of energy into ever more numerous and ever finer motions would never end.
The atomic structure of matter, on the other hand, gives rise to a limit to the successive fragmentation and disorganization of the internal energy of bodies: in fact, if matter is made up of simple elementary particles, not divisible into further parts, since no internal motion of these simple particles can occur, one must admit that the finest motions that can take place in matter are precisely the motions of translation of the individual elementary corpuscles.
In the primitive atomic theories, it was supposed that the atoms themselves were the elementary particles; today it is known that this hypothesis is not exact, but for the purposes of the considerations on the kinetic nature of heat, for the reasons that will be seen, atoms can be regarded precisely as simple particles, and therefore the way of seeing things of the founders of the kinetic theory itself can be considered fundamentally correct. The great importance of this observation will be seen later.
The point of view of the kinetic theory of heat can therefore be stated in this way: 1) the molecules and atoms that make up a body are endowed with disordered motions, and by this it is meant precisely that the motion of each corpuscle is, to a very notable degree, independent of the motions of the other particles making up the body. The energy relating to such motions is "disorganized internal energy"; 2) the temperature of bodies depends on the disorganized internal energy: to give up (or absorb) heat means to give up or absorb energy in disorganized form; 3) as a consequence of this, temperature and the quantities depending on it (for example, the pressure in a gas) can be defined only for large assemblages of atoms or molecules: in fact, the notion of the disorganization of the motion of one molecule is relative only to the motion of the other molecules. In other words: temperature, pressure, etc. are statistical quantities, which can be defined only for sets of very many atoms, that is, for macroscopic bodies, just as, for example, the average mortality rate is a statistical quantity, definable only for a set of many living individuals (v. PROBABILITÀ).
The bodies to which the concepts of the kinetic theory are most easily applicable, and which were historically the first to be studied from this point of view, are gases. In fact, in gases the motion of each molecule can be considered almost entirely independent of the motion of the others, or, as it is said, the interaction between molecules is practically negligible (in the limit, for so-called perfect gases, it is nil).
Since the molecules of the gas are consequently not bound to one another by forces (with the exception of gravity, which is generally negligible), they will tend, as a result of the disordered motions by which they are animated, to move away in all directions: it follows, as is well known, that the gas occupies all the space placed at its disposal; it follows furthermore that the molecules, striking against the walls of the vessel containing the gas, exert on these a pressure that is the resultant effect of all the impacts occurring per unit time on unit surface area.
As the temperature increases, the liveliness of the molecular motion increases, and consequently so does the pressure.
On the basis of the preceding concepts it becomes possible to recover the experimental laws of gases (Boyle's law, Gay-Lussac's law, etc.) in their quantitative expression; the mean velocity of the molecules was determined in relation to temperature (a velocity that was later recovered by means of very precise direct quantitative measurements in the present century by Stern, and which at the usual temperatures has turned out to be on the order of a few hundred meters per second); the quantitative theory was given of the phenomena of diffusion, of the viscosity of gases, of the conduction of heat (v. TERMOLOGIA), introducing the important concept of mean free path, that is, of the average of the distances traveled in a straight line by the molecules of the gas between two consecutive collisions; it was demonstrated (a quite remarkable result) that Avogadro's hypothesis is a consequence of the fundamental hypotheses of the kinetic theory; finally, the very important result was reached (Maxwell) according to which the kinetic energy of translation of the molecules, due to thermal agitation, is distributed on average among the different molecules in a manner independent of their size (the kinetic energy of rotation too is linked in a simple way to the energy of translation). This principle (the principle of the equipartition of energy) made it possible to construct the theory of the specific heats of gases, with wholly satisfactory results and in agreement with experience. Finally (and together with the principle of the equipartition of energy, this may be regarded as the most important result of the kinetic theory) it proved possible to determine Avogadro's number N (that is, the number of atoms contained in a gram-atom) by means of measurements on the viscosity of the gas and on the deviations of the behavior of real gases from that of perfect gases (v. TERMOLOGIA). With the data relating to Argon it was found:
N = 6.22 · 10²³
It also turned out, as a measure of the diameter of the atom (again for Argon)
D = 2.8 · 10^{-8} cm.
II. BROWNIAN MOTION AND THE DETERMINATION OF AVOGADRO'S NUMBER
The determination of Avogadro's number N is of very great importance, not only insofar as it provides the key to atomic dimensions, but also insofar as such a determination provides the foundation for the experimental evidence of atomic theories.
The path that has been indicated for the measurement of N, and which, as has been said, was the first to be followed, because of the arbitrary and difficult-to-evaluate hypotheses it contains (such as the hypothesis of the spherical shape of the molecules), could not be considered sufficient to provide the required experimental demonstration; and indeed even the devotees of kinetic theories themselves, despite the brilliant successes obtained, were not disposed to grant their theories much more credit than to working hypotheses. But a far more direct evidence, and one founded moreover on the fundamental concepts of the kinetic theory, was reached by another path.
It has already been observed that the existence of atoms implies that the successive fractionation of mechanical energy (or in any case organized energy) that is dissipated into disorganized energy must have a limit; conversely, the existence of this limit implies an atomic structure of matter (and, as will be seen, of energy).
Consequently, the observation of a permanent agitation in matter, independent of external circumstances and a function only of temperature, can be considered in a certain sense an indirect but sure confirmation of the atomic structure. Now such an agitation, which escapes direct examination by the senses, can really be brought to light with sufficiently refined means of experimental investigation, and it is known under the name of "Brownian movements" (after their discoverer, the botanist Brown).
If one examines under a microscope with strong magnification a suspension of very minute particles in a fluid (for example, a so-called colloidal solution), one can notice that the particles observed there are in a state of irregular and often very lively motion: the characteristics of this sort of motion are quite different from those of ordinary macroscopic motions. In fact, these are not organized motions of the whole, provoked by external perturbations (motions that are moreover quite recognizable, and that can also occur, but that disappear after some time if appropriate precautions are taken). Brownian motion persists unaltered for any length of time one experiments and independently of all the precautions that can be taken to protect the system from external disturbing influences; it is in any case clearly distinguishable from motions due to external causes by the following two facts: particles however close to one another have velocities independent of one another, both in magnitude and in direction; the direction and magnitude of the velocity of each particle changes continuously in a wholly irregular manner; Brownian motion appears, in a word, dominated by the law of chance.
"Brownian motion appears in contrast with the ordinary behavior of macroscopic bodies; analyzed thermodynamically, it presents itself as a phenomenon analogous to the spontaneous passage of heat from a colder body to a hotter body. Brownian motion is therefore the direct experimental confirmation of the conception that has been said to constitute the profound foundation of studies on the constitution of matter, according to which the laws of the macroscopic world are but approximate and deducible as limiting cases, often by means of the calculus of probabilities, from the laws of the microscopic world."
How is the mechanism of Brownian motion interpreted in the light of kinetic theories? It has already been said that pressure is generated in a fluid by the very numerous impacts of molecules: the forces due to pressures and to pressure differences are therefore due to such impacts. If therefore one immerses in a fluid a body so minute that the number of impacts it receives from the molecules of the fluid in an appreciable time is not very large, it may very well happen that in that certain small interval of time it receives relatively many more impacts from one side than from the opposite side: it will therefore be urged to move by an appreciable force for an appreciable time. Since the phenomenon of impacts is moreover wholly random, this force will continually change direction and the motion will be wholly irregular.
If conversely one immerses in the fluid a relatively large body, this, given its considerable inertia, will practically not feel the effects of forces that continually change direction, and no appreciable motion will be observed, whence it appears macroscopically that in a fluid in equilibrium the pressure is uniform.
The confirmation of this way of interpreting Brownian phenomena and at the same time of the exactness of the kinetic theory of gases is given by the following fact of very great importance: by means of the study of Brownian phenomena it is possible by various paths to arrive at the determination of Avogadro's number, and results are found that agree with one another and in agreement that can be considered excellent with the determination founded on the measurement of the viscosity of gases, which was recalled earlier.
The average of the determinations of Perrin, who in the first decade of this century carried out the first fundamental measurements in question, is
N = 6.8 · 10²³
After such a result it is very difficult to misconstrue the exactness of the atomic theory of matter. Let one consider in fact, as Perrin himself points out, that a priori in the study of Brownian phenomena any value of N between zero and infinity could have resulted.
It is not possible to describe all the methods employed for the determination of N by means of measurements on Brownian phenomena; to give an idea of them, one of these is mentioned, particularly simple and significant: if one attaches a small mirror to a very fine quartz thread, the little mirror, by effect of Brownian motion, performs very small oscillations which can be observed by making light reflect on the little mirror itself. It can be demonstrated that under such conditions the average kinetic energy of the motion of the little mirror must be one third of the average kinetic energy of a molecule at the same temperature, and this energy turns out to be inversely proportional to Avogadro's number N.
On the other hand the average energy of the little mirror can be directly measured, by measuring the average amplitude of the oscillation, and thus one can arrive at the determination of the number N. The experiment was performed by Gerlach and Kappler, and gave a result in good agreement with the other measurements.
It should be noted that Brownian motion can be observed in all measuring instruments comprising movable assemblies of very great sensitivity, and being absolutely ineliminable, it constitutes a limit to the sensitivity of measuring apparatus.
It has thus been seen that the kinetic theory of heat allows one to define the fundamental concepts of the atomic theory of the structure of matter and to provide a first, although not entirely sufficient, experimental evidence of it.
Such evidence is completely attained with the study of Brownian motion, which can be interpreted quantitatively on the basis of the concepts formulated in the kinetic theory and constitutes its direct experimental verification.
In all the considerations made in the kinetic theory, atoms are considered as indivisible particles: now instead the discoveries concerning the atomicity of electricity, radioactivity, etc., have shown that atoms are composite particles: despite this the kinetic theory is not invalidated, and the reason for this fact will be clarified when the atomicity of energy is discussed.
III. THE ATOMICITY OF ELECTRICITY AND THE EXISTENCE OF THE ELECTRON
Faraday's laws of electrolysis (v. ELETTROLOGIA) had made it clear that every gram-atom of a monovalent electrolyte carries a constant quantity of electricity through the solution, equal to 96,500 Coulombs. Since, on the other hand, again by Faraday's laws, the quantity of electrolyte decomposed is rigorously proportional to the quantity of electricity carried, independently of any other circumstance (and therefore in particular for any however small quantities of electrolyte), extrapolating this law down to the atoms, one must conclude (Helmholtz and Stoney) that each monovalent atom carries with it through the electrolyte a constant charge, equal precisely to 96,500 Coulombs divided by the number of atoms contained in a gram-atom, that is, divided by Avogadro's number.
In the phenomenon of electrolysis, therefore, the electric charges all prove to be multiples of an elementary charge "e" equal to 96,500 Coulombs : N. Assuming for N the value 6.04 · 10²³, the result is e = 4.80 · 10⁻¹⁰ e.s.u. C.G.S.
The atomicity of electricity manifests itself not only in the phenomenon of electrolysis, but as a general property of electric charges, that is, all the electric charges that manifest themselves in any phenomenon whatsoever must be considered integer multiples of the quantity of electricity "e". This fact, directly verifiable when one works with sufficiently sensitive devices, permits a direct measurement of the elementary charge "e", and at the same time an equally direct demonstration of the atomicity of electricity.
Measurements of this kind were made by Millikan. One cannot enter into the details of these experiments; suffice it to say that Millikan succeeded in measuring the electric charge carried by a small droplet of a non-volatile substance and in demonstrating that this charge is always an integer multiple of a constant quantity.
The elementary quantity of electricity thus determined turned out to be 4.8 · 10⁻¹⁰ e.s.u. As can be seen, the agreement with the value determined by the previous method and on the basis of knowledge of Avogadro's number is truly excellent. Further experiments made with Millikan's method and with particular care led to an even better agreement.
On the other hand, by studying the discharge in extremely rarefied gases, Thomson succeeded in demonstrating the existence of negatively charged particles having a mass much smaller than that of the lightest atom (the hydrogen atom). The demonstration of the existence of such particles came about through the determination of the ratio between their charge and their mass, something that can be done by studying the combined action of a suitable electric field and a suitable magnetic field on their trajectory. Assuming that these particles all had a charge equal in absolute value to the elementary charge of electricity (a hypothesis that further experiments showed to be true), one could in this way derive the mass of such a particle, which turned out to be about 1860 times smaller than that of the hydrogen atom.
The particles in question were called "electrons". Electrons were then found in numerous other phenomena, as, for example, in the thermionic effect, consisting in the emission of electrons by hot bodies, in the photoelectric effect (emission of electrons from matter under the action of radiation), etc.
Now, since electrons are found in the discharge in highly rarefied gases, whatever the nature of the electrodes and of the interposed gas, and since, for example, the photoelectric effect occurs for any substance (it suffices to use light of sufficiently high frequency), it becomes natural to conclude that electrons form a general constituent of matter. The proof that electrons are among the constituents of atoms was soon able to be gathered. It is indeed well known that luminous radiations have an electromagnetic nature. They must therefore be emitted by electric charges in motion. Since the motion of electric charges is perturbed by a magnetic field, one could foresee that the characteristic spectra emitted by substances in the gaseous state (V. OTTICA) would be modified by placing the light source in a magnetic field: the phenomenon already foreseen by Faraday, and not found by him for lack of experimental means, was later actually discovered by Zeeman. Now, as theory can show, the change in frequency of the emitted spectral lines depends on the ratio between the charge and the mass of the emitting electric charges. It is thus possible to determine this ratio by purely optical measurements. This fundamental result has been obtained: the ratio in question turns out to be equal to that between the charge and the mass of the electron. One must therefore conclude that the electric charges that emit the characteristic spectral lines of bodies in the aeriform state are electrons.
On the other hand, among the characteristic spectra are those of the elements (it is even possible to base on this fact a highly sensitive method of chemical analysis that has permitted, among other things, the determination of the elements present in the stars). Consequently one must admit that such spectra are characteristic of the atoms, and therefore that electrons are constituents of the atoms. Thus the hypothesis that atoms were simple particles fell. We shall return shortly to this most important result.
It should here also be recalled that electrons are responsible for the high electrical conductivity of metals: within metals, in fact, one must think that there exist electrons that, at least to a first approximation, can be considered as free, that is, not stably bound to any atom. These electrons, under the action of the electric field that is established within the metal when a certain potential difference is maintained between two points of it, will then be able to set themselves in motion, giving rise to the electric current. Now the existence of free electrons within metals can be demonstrated by experiments of a direct character: if, in fact, a piece of metal is subjected to a strong acceleration, the free electrons, by effect of their inertia, will shift within the metal, as if they were subjected to an electric field, thus giving rise to an electric current. The phenomenon can be observed with very delicate experiments, and the ratio between the charge and the mass of the particles involved can be measured. Now, the same ratio derived for electrons by the other methods has been obtained (Nichols, Tolman, Stewart).
IV. RADIOACTIVE PHENOMENA AND THE CONSTITUTION OF THE ATOM
At the end of the last century, it was discovered that certain substances have the property of spontaneously emitting radiations capable of ionizing gases (that is, of making them electrically conductive by tearing electrons from their molecules). Such substances were called radioactive. Studies on radioactive substances received a great impulse following the discovery made by the Curies of a particularly radioactive element that was called radium.
Following the work of numerous researchers, it was demonstrated that the radiations emitted by radioactive substances can be of three different types, which were called α radiations, β radiations and γ radiations.
α radiation consists of particles endowed with extremely high velocity, positively charged (as can be demonstrated by deflecting them in a magnetic field), whose electric charge is equal to twice the elementary one, and whose mass is equal to about four times the mass of the hydrogen atom.
These particles can be revealed by various means that allow one to distinguish and count them one by one (e.g., Wilson cloud chamber, Geiger counters: the Wilson cloud chamber allows one to photograph the "tracks" of these particles).
From the photographs taken with the Wilson cloud chamber one can observe, for example, that these are particles all having identical properties: their mass is determined by measuring the ratio between their charge and their mass with methods analogous to those used for electrons. The charge of these particles can also be measured directly, by collecting them within a Faraday cup and counting their number (note that this measurement can be considered a new determination of Avogadro's number, and it is in agreement with the previous ones). An α particle can be considered a doubly ionized helium atom: if it captures two electrons it is transformed into a neutral helium atom, as was demonstrated experimentally in a direct way. β radiation, on the other hand, consists of electrons of great energy, and is studied with means analogous to those used for the particles. γ rays are electrically neutral, and, as was demonstrated, of the same nature as light, but of extremely high frequency.
Moreover, it was demonstrated that the emission of these radiations is accompanied by a disintegration of the atoms, and by a consequent transformation of radioactive elements into other elements. It was thus proved in a direct way that atoms are composite particles, and the problem arose of knowing what their structure was. This problem was fundamentally solved by Rutherford using precisely α particles as a means of investigation.
As has been said, it was known that electrons had to be part of the atom; since electrons are negatively charged and atoms are neutral, positively charged particles certainly exist inside the atom. The problem was to determine how these positive charges were distributed, with which the principal mass of the atom had also to be thought connected, given that the mass of the electrons is negligible. Now the presence of positive charges in the atom must produce the deflection of α particles when these pass through the m. ("diffusion of α particles").
From the magnitude of this phenomenon it is even possible to trace back to the distribution of the positive charges in the atom. Rutherford was thus able to demonstrate that the positive charges of each atom are concentrated in a zone whose radius is of the order of 10⁻¹³ . 10⁻¹⁵ cm. and therefore extremely smaller than the radius of the atom itself (of the order of 10⁻⁸ cm.).
As a consequence of this fundamental discovery of his, Rutherford proposed his celebrated model of the atom: the atom consists, according to this model (which in its essential concepts can be considered conformable to reality), of a central "nucleus" of radius of the order of 10⁻¹² cm., comprising the positive charge and almost all the mass of the atom, and of electrons, in such number as to neutralize the positive charge of the nucleus, gravitating around the nucleus like the planets around the sun.
V. QUANTIZATION OF ENERGY AND STRUCTURE OF THE ATOM
Against Rutherford's atomic model several serious difficulties were raised, which, on close consideration, were but a particular aspect of a fundamental difficulty encountered when one tries to apply the laws of classical mechanics and electrodynamics, valid (approximately) for macroscopic bodies, to the study of the structure of atoms. This difficulty can be summed up in the following contradiction: the kinetic theory of heat leads to results in agreement with experience as long as one admits that atoms behave as if they were indivisible particles, whereas radioactive and optical phenomena (Zeeman effect, etc.) show that atoms are composite particles.
The solution of this apparent contradiction could be found through the introduction of a new concept into physics, the concept of the quantization of energy, which was introduced by Planck at the beginning of the present century, in the study of an entirely different phenomenon (the law of so-called "black" radiation), and which proved most fruitful in the solution of the problem with which we are dealing (Bohr).
According to Planck's idea, radiation can be emitted or absorbed in "indivisible quanta of energy, proportional to the frequency of the radiation itself."
The constant of proportionality, the "universal quantum of action," is a universal constant equal to 6.55 . 10⁻²⁷ erg sec., and was determined by Planck from the comparison of his law of black radiation with experience (Planck succeeded at the same time in determining in this way also the Avogadro number that appears in his law, finding a result in agreement with other measurements).
The "quantum of action h," or Planck's constant, was determined also by other means; Einstein showed that the photoelectric effect, which did not appear in any way interpretable on the basis of classical electrodynamics, could on the contrary be very well explained by Planck's hypothesis, and he succeeded in this way in determining independently the constant h in agreement with Planck's own results.
Einstein himself and then Debye made an application of it to the theory of the specific heats of solid bodies at very low temperatures, with very satisfactory results.
But the application of perhaps greatest fruitfulness of Planck's hypotheses was made by Bohr in the explanation of the optical spectra emitted by atoms and of the structure of the atom. Since, according to Planck's idea, radiation can be emitted by atoms only in discrete quanta, the atom that emits a quantum of radiation will have an energy, in the final state (after the radiation has been emitted), which must differ from the energy of the initial state by exactly the energy of the emitted quantum, which depends only on its frequency. Since each atom can emit only certain determined frequencies (the frequencies of the characteristic spectrum), it follows that each atom can have only certain determined energies, whose differences are equal to the quanta of radiation that the atom can emit. This is substantially the idea from which Bohr started. It is very important to note that this idea makes it possible to overcome the apparent contradiction between the kinetic theory of heat and the fact that atoms are not simple particles. In fact, if the energy of atoms can assume only discrete values, there will exist a certain finite difference between the lowest value that this energy can assume (ground level) and the immediately following value. Now if this difference is, as is in fact found in reality, at not too high temperatures, much greater than the energy that on average can be transferred in a collision between two atoms in the motion of thermal agitation, it is clear that the atom must normally be in the ground level and cannot pass to the next level, that is, its internal energy cannot vary as a result of collisions, just as if the atom were an indivisible particle.
It should be noted that Bohr thus succeeded not only in overcoming the difficulties into which Rutherford had fallen, but also in finding an immediate explanation of the general structure of the characteristic spectra emitted by the elements, which on the basis of classical electrodynamics had remained entirely mysterious. Not only that, but starting from a particular hypothesis of his own regarding quantization, later perfected by Sommerfeld, he succeeded in calculating a priori the frequencies emitted by the hydrogen atom and by ionized helium, finding results in truly extraordinary agreement with the experimental ones.
VI. X-RAYS AND THE PERIODIC TABLE OF THE ELEMENTS
Quantum ideas made it possible to account in a relatively simple way for the natural classification of the chemical elements (Mendeleev's periodic table), transforming Mendeleev's empirical classification (v. CHIMICA) into a rational classification, and at the same time accounting for the relation that exists between this classification and the law of the characteristic X-ray spectra of the elements discovered by Moseley.
The fundamental concept of this rational classification is the following: it has been said that atoms are composed of a positively charged nucleus and a certain number of electrons located around the nucleus. The charge of the nucleus is an integer multiple Z of the elementary electric charge "e"; the number of electrons (for the atom in the electrically neutral state) is also equal to Z; the number Z is called the "atomic number."
Now, practically all the chemical properties and at least a large part of the physical properties of the elements depend exclusively on the atomic number Z. The elements can therefore be rationally classified by arranging them in order of increasing atomic number.
As already mentioned, great assistance to this classification was given by the study of the characteristic X-ray spectra. Such rays, discovered by Röntgen, are of the same nature as luminous radiations.
The demonstration of this fact was given by Laue. It is well known that, in order to demonstrate the wave nature of light, one can have recourse to diffraction experiments (v. OTTICA), among which particularly noteworthy are those performed with gratings, which allow an absolute and very precise measurement of the wavelengths of luminous radiations.
Optical gratings, however, do not lend themselves under ordinary experimental conditions to the demonstration of the wave nature of X-rays and to the measurement of their wavelength, because the distance between their lines is not sufficiently small.
There exist in nature, on the other hand, as Laue observed, gratings that can lend themselves to such measurements: these are crystals. In fact, according to the fundamental hypothesis of crystallography, crystals are made up of atoms (of the species of the elements that enter into the chemical composition of the crystal), which are arranged at regular distances from one another, and thus form a true spatial lattice (in reality the atoms of the crystal are not still but oscillate due to thermal agitation around the nodes of the crystal lattice). The distance between successive atoms of a crystal can be calculated on the basis of Avogadro's number and turns out to be of the order of 10⁻⁸ cm. Laue then predicted that, by causing X-rays to fall on a crystal, diffraction phenomena could be observed, analogous to those observed with light and optical gratings. Experiment fully confirmed this prediction, thus achieving an experimental demonstration of the wave nature of X-rays and of the correctness of the views concerning the structure of crystalline bodies. The definitive confirmation came, then, when it became possible to observe diffraction phenomena of X-rays also by means of optical gratings, used with a particular expedient (grazing incidence). In this way an absolute measurement of the wavelength of X-rays was reached, and therefore, by comparison with the experiments performed with crystals, it was possible to arrive at the absolute measurement of the distances between the atoms of crystals, with results found to be in agreement with those predicted on the basis of Avogadro's number.
It was thus possible to establish a true X-ray spectroscopy analogous to optical spectroscopy, and in this way it was demonstrated that each element, just as it emits a characteristic spectrum of optical frequencies, likewise emits a characteristic spectrum of X-rays. Now, the information given by this spectrum is particularly valuable, because while optical spectra are emitted by the electrons farthest from the nucleus, X-ray spectra are emitted by the electrons closest to the nucleus, and therefore are more directly affected by the effect of the nuclear charge, so that their frequencies depend in a simple way on this nuclear charge, that is, on the atomic number (Moseley's law). This property of X-rays also made it possible to discover and identify elements still unknown, classifying them in their proper place in the periodic table of the elements.
Having thus found the rational criterion for classifying the elements, it was possible, by applying the Bohr-Sommerfeld quantization conditions and a principle concerning the behavior of electrons discovered by Pauli (exclusion principle), to demonstrate that the electrons are distributed in each atom in various electronic "shells," starting from the electrons closest to the nucleus (deeper shells) up to the outermost electrons.
It was also demonstrated that chemically homologous elements (which are found in the same column of Mendeleev's table; v. CHIMICA) have the electrons located in the outermost shell arranged in a similar way; thus the explanation was found for the periodicity in chemical and spectroscopic behavior that had been found empirically.
VII. THE CONSTITUTION OF THE NUCLEUS; ISOTOPES; THE EQUIVALENCE BETWEEN MATTER AND ENERGY
It has been seen that the properties of the atom depend substantially on the atomic number, that is, on the nuclear charge, and therefore, directly or indirectly, on the nucleus.
The chemical species of an atom is defined by its nuclear charge; the transmutations that involve a transformation from one chemical species to another (radioactive transmutations) are therefore nuclear transmutations. One therefore understands the great interest that the study of the structure of the nucleus holds.
In this regard it must first of all be noted that it was discovered first for the radioactive elements and then also for the non-radioactive ones (Aston) that atoms can exist having the same atomic number and different atomic weight; that is, nuclei can exist having the same charge but different mass. This could be seen by measuring the ratio between the charge and the mass of the ions (electrically charged atoms) of one and the same element with methods substantially analogous to those used to measure the ratio between the charge and the mass of electrons; these methods were perfected to such a degree as to constitute a direct means for "weighing" atoms, of very great precision.
The elements having the same atomic number and different mass were called isotopes.
The most remarkable result obtained by Aston regarding isotopes was the following: the mass of each isotope can be expressed by an almost integer number if the mass of the oxygen atom is taken as equal to 16.
This result immediately suggested the hypothesis that the nuclei of the different elements were composed of a different number of particles equal to one another.
This hypothesis was made more precise, and took on definitive value, with the discovery of a new type of particle, which can, up to now, be considered an elementary particle, having the following fundamental properties: mass comparable to that of the hydrogen atom (just slightly greater), zero electric charge, and dimensions of the order of those of the hydrogen nucleus. This particle was called the "neutron," and in substance it can be considered, apart from the electric charge, entirely analogous to the hydrogen nucleus (which had previously already been called the "proton"); indeed, according to modern views, proton and neutron must be considered the same particle (the so-called "heavy particle" or "nucleon") in two different states.
Neutrons can be detected substantially in two ways: a) by means of the collisions of these particles against protons, observing the protons that rebound (the so-called recoil protons); b) by observing the transformations that such particles can induce in nuclei.
In this last connection it should be observed that Rutherford had already succeeded, by striking nuclei with α particles, in producing artificial disintegration. Later Joliot and Curie demonstrated that, again using α particles, certain nuclei can be made radioactive (artificial radioactivity). Fermi demonstrated that, using neutrons, this phenomenon can be observed with an extremely higher frequency. This phenomenon can therefore serve to reveal neutrons.
Following the discovery of neutrons, it was understood that all nuclei must be considered composed exclusively of neutrons and protons in different numbers, and precisely of a number of protons equal to the atomic number and a number of neutrons equal to the atomic weight (referred to oxygen = 16) minus the atomic number.
It should be observed, however, that if one adds up the masses of all the protons and all the neutrons that form part of a nucleus, one obtains a mass somewhat greater than the mass of the nucleus. This fact does not constitute a difficulty; on the contrary, it is a brilliant experimental confirmation of the consequence deduced by Einstein from the theory of relativity, regarding the equivalence between mass and energy (v. RELATIVITÀ). According to this view, every quantity of energy possesses a mass proportional to it and vice versa.
Now, since the nuclei of the elements that exist in nature are very stable complexes, this means that the particles that constitute them (protons and neutrons) are bound to one another by considerable forces, and it is necessary, in order to separate them, to supply them with a certain quantity of work. This quantity of work, that is, quantity of energy, is equivalent, by Einstein's principle, to a certain mass, which is precisely the difference between the sum of the masses of the free protons and neutrons and that of the nucleus.
It should be noted that this is not a simple induction or hypothesis. In fact, it has already been mentioned that it is possible to provoke nuclear transmutations in various ways, e.g., by bombarding nuclei with α particles or with neutrons; other transmutations are obtained by bombarding with protons, or with γ rays or with other particles.
One can thus provoke in nuclei "reactions" in a certain way analogous to ordinary chemical reactions, and in which, as in chemical reactions, there can be a release or absorption of determined quantities of energy; in nuclear reactions, however, the energies brought into play for each elementary process are as a rule incomparably greater than the energies brought into play in chemical reactions.
Now these energies are exactly determinable, and one can then ascertain that every release of energy to the outside is accompanied by a decrease in the mass of the reacting system, which coincides perfectly with that predicted on the basis of Einstein's equivalence relation, and vice versa. Nuclear reactions therefore provide an undoubted experimental proof of the equivalence between mass and energy.
Among nuclear reactions, the so-called "fission" of uranium and thorium has assumed an enormous practical importance because it has permitted the utilization of nuclear energy.
VIII. THE DUAL CORPUSCULAR AND WAVE ASPECT OF MATTER AND OF RADIATION
Mention has been made of the successes obtained by Planck's idea (quantization of energy) in various fields of physics. It must now be said that it also raised very serious difficulties for a considerable time.
The principal perhaps of these difficulties concerned the nature of electromagnetic radiation. In fact, in certain phenomena this radiation behaves not only as if it were simply emitted or absorbed in indivisible quanta, as Planck's hypothesis required, but also as if it had to propagate in the form of "granules" of energy (photons), each equal to a Planck quantum of energy: this behavior, for example, could seem evident in the scattering of radiation by free electrons, which effect (Compton effect) can indeed be described as an elastic collision between a photon and an electron.
On the other hand, there exist phenomena which (interference, diffraction, etc.) are entirely incompatible with the hypothesis that radiation consists of corpuscles, even if traveling at the speed of light, but having the properties of ordinary corpuscles.
This contradiction could be overcome through the work of several physicists (De Broglie, Heisenberg, Schrödinger, Born, Jordan, Dirac, Bohr), which led to a profound upheaval in the fundamental conceptions of physics.
First of all it was established that the duality of corpuscular and wave aspect is not peculiar to radiation, but is proper also to matter: this consequence of the theory was verified experimentally in a direct way by observing diffraction phenomena produced by crystals on electrons, analogous to the diffraction phenomena encountered with X-rays (diffraction phenomena were later observed also for heavy particles); the quantization conditions of Bohr and Sommerfeld were deduced and made precise, conditions which had in truth remained somewhat arbitrary, as consequences valid in limiting and particular cases of the more general theory; thus criteria that were exactly quantitative were successfully applied to the theory of the constitution of atoms, where quantitatively the old theory of Bohr and Sommerfeld had fallen short and had given only qualitative indications; the nature of the forces that bind atoms to one another in the molecule, that is, of chemical forces, was found; a single theory was given of both the wave effects and the corpuscular effects of radiation. Finally, various new phenomena were predicted, later confirmed by experience, among which is remembered the existence of the positive electron (equal in mass to the negative electron, but with positive charge), which was found in artificial radioactivity and in cosmic radiation, and an interesting phenomenon was predicted that concerns these particles, and in which it is possible to observe the transformation of a photon (quantum of radiant energy) into a pair of electrons, one positive and one negative.
This phenomenon is a case of transformation of energy into matter: it can be observed experimentally, as can also the opposite phenomenon, the annihilation of a pair of electrons with the production of γ quanta.
These transformations of matter into energy and of energy into matter occur in conformity with Einstein's law, of which they constitute a further brilliant direct confirmation.
All these successes were obtained through the recognition of the untenability of the hypothesis of physical determinism, at least as it was classically conceived, and of the essentially probabilistic meaning of physical laws. Thus the concept was reaffirmed and made precise that the laws of classical and macroscopic physics are nothing but approximate laws, deducible as limiting cases, in the case in which Planck's constant can be considered zero, from the quantum laws.
IX. ENERGY
Energy is a physical quantity, a function of the state of the physical system under consideration, constant for every isolated system, transformable into work and measured by the quantity of work to which it is equivalent.
The notion of energy began to be clarified and to reveal its fundamental importance in physics with the discovery of the equivalence between heat and mechanical work (first law of thermodynamics), which made it possible to state the fundamental principle of the conservation of energy: at the foundation of this principle lies the conception that the different forms in which energy phenomenologically appears (mechanical energy, thermal energy, electromagnetic energy, chemical energy, etc.) are all equivalent to one another and can be transformed one into another.
Since the distinction between the different forms of energy must thus be considered to be of a phenomenological character, for every isolated physical system only the total energy can be defined in an exact and general way, and it proves to be constant, as has already been said, in the course of time (principle of the conservation of energy).
With the discovery of the equivalence between mass and energy, the principle of the conservation of energy has merged with that of the conservation of mass into a single principle of wholly general validity.