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 guided by the idea of accounting for the laws, more or less complex and numerous, of the most diverse phenomena perceptible to the senses (macroscopic phenomena), by means of laws that are essentially simpler and fewer in number, governing microscopic complexes (molecules and atoms) conceived as constituting macroscopic bodies.
The investigation into the constitution of bodies thus encompasses a twofold process: 1) the analysis of bodies into their microscopic constituents, thereby implicating the problem of determining the nature and laws of such constituents; 2) synthesis, through which the macroscopic laws are derived in their variety and with their limitations.
Hence the importance of the question, which, viewed in this way, includes within itself the problem of reducing the diverse appearances of macroscopic natural phenomena to a higher unity and of determining the scope and true significance of the laws that govern them.
Summary:
I. The Kinetic Theory of Heat
II. Brownian Motion and the Determination of Avogadro’s Number
III. The Atomic Nature of Electricity and the Existence of the Electron
IV. Radioactive Phenomena and the Constitution of the Atom
V. Quantization of Energy and the Structure of the Atom
VI. X-Rays and the Periodic Table of the Elements
VII. The Constitution of the Nucleus; Isotopes; the Equivalence of Matter and Energy
VIII. The Dual Aspect of Matter and Radiation as Particles and Waves
IX. Energy.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 the molecular agitation. These hypotheses were revived in the 17th century by Gassendi and later by Daniel Bernoulli, who made the first quantitative applications in deducing Boyle’s law on the pressure of gases. A further impetus to the atomic conception came from the discovery of the fundamental laws governing chemical phenomena, which were very naturally interpreted through atomic and molecular hypotheses. Thus, the notions of “atom” and “molecule” were clarified (v. CHEMISTRY). The laws of reactions between substances in the gaseous state then led Avogadro to 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 concept of molecular weight (v. CHEMISTRY) and, in this way, the ratios between the masses of the molecules of various substances.The first approach to the question of the absolute dimensions of atoms, and thus to the true value of the atomic hypothesis, was provided by the study of gases through the so-called kinetic theory of heat. This theory was suggested by the following observations: in mechanical phenomena directly observable, a superficial investigation generally appears to show that part of the mechanical energy involved is lost; in reality, this energy is not lost but is transformed into the internal energy of the bodies in which mechanical work has been expended. Indeed, an increase in temperature can be observed in such bodies, as if a quantity of heat proportional to the dissipated work had been supplied (first principle of thermodynamics, or principle of the equivalence of work and heat: V. THERMOLOGY).
The first principle of thermodynamics strongly suggests the idea that heat is a particular form of mechanical energy (an idea that, in more or less clear form, had been entertained by atomists before the discovery of the first principle). Indeed, if one seeks to examine closely how macroscopic mechanical energy appears as such to give rise, for example, to increases 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 (e.g., 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 previously calm body of water: initially, relatively long and broad waves are observed; among these, waves of ever-decreasing wavelength progressively tend to predominate until every motion has disappeared.
A direct analytical examination of this energy transformation process shows that if matter had a continuous structure, the process of fragmenting energy into ever more numerous and minute motions would never end.
The atomic structure of matter, however, sets a limit to the further fragmentation and disorganization of the internal energy of bodies: indeed, if matter is composed of simple, indivisible elementary particles, and no internal motion of these simple particles can occur, then the smallest motions that can take place in matter must be the translational motions of the individual elementary corpuscles.
In the early atomic theories, it was supposed that the atoms themselves were the elementary particles; today it is known that this hypothesis is not exact, yet for the purposes of considerations on the kinetic nature of heat, as will be seen, atoms can be regarded precisely as simple particles, and thus the viewpoint of the founders of the kinetic theory can be considered fundamentally correct. The great importance of this observation will be seen later.
The standpoint of the kinetic theory of heat can therefore be stated as follows: 1) the molecules and atoms forming a body possess disordered motions, meaning precisely that the motion of each corpuscle is, to a large extent, independent of the motions of the other particles constituting the body. The energy associated with such motions is disorganized internal energy; 2) the temperature of bodies depends on this disorganized internal energy: hence, to give or absorb heat means to transfer or absorb energy in a disorganized form; 3) consequently, temperature and related quantities (e.g., pressure in a gas) can be defined only for large aggregates of atoms or molecules: indeed, the notion of the disorganization of a molecule’s motion is relative only to the motions of the other molecules. In other words: temperature, pressure, etc., are statistical quantities that can be defined only for ensembles of very many atoms, i.e., for macroscopic bodies, just as, for example, the average mortality rate is a statistical quantity definable only for a collection of many living individuals (v. PROBABILITY).
The bodies to which the concepts of kinetic theory are most readily applicable, and which were historically the first to be studied from this perspective, are gases. Indeed, in gases, the motion of each molecule can be considered almost entirely independent of the motion of the others, as it is said, the interaction between molecules is practically negligible (at the limit for so-called perfect gases, it is zero).
Since the molecules of a gas are consequently not bound together by forces (except for gravity, which is generally negligible), they will tend, because of the disordered motions by which they are animated, to move apart in all directions. As is well known, it follows that the gas occupies all the space available to it; moreover, the molecules, striking against the walls of the container holding the gas, exert on them a pressure that is the resultant effect of all the collisions occurring per unit time on a unit surface.
As the temperature increases, the liveliness of molecular motion increases, and, as a consequence, it became possible to derive the experimental laws of gases (Boyle’s law, Gay-Lussac’s law, etc.) in their quantitative expression from the pressure exerted on the foundations of previous concepts; the average speed of molecules in relation to temperature was determined (a speed later confirmed by Stern in the present century with very precise direct measurements, and which at ordinary temperatures turns out to be on the order of several hundred meters per second); a quantitative theory was given for the phenomena of diffusion, gas viscosity, and heat conduction (v. TERMOLOGIA) by introducing the important concept of mean free path, i.e., the average distance traveled in a straight line by gas molecules between two consecutive collisions; it was demonstrated (a highly notable result) that Avogadro’s hypothesis is a consequence of the fundamental assumptions of the kinetic theory; and finally, the most important result was reached (Maxwell) according to which the translational kinetic energy of molecules, due to thermal agitation, is on average distributed among the various molecules independently of their size (rotational kinetic energy is also simply related to translational energy). This principle (the principle of the equipartition of energy) allowed for a theory of the specific heats of gases, with results that were entirely satisfactory and in agreement with experience. Lastly (and together with the principle of the equipartition of energy, this may be considered the most important result of the kinetic theory), it became possible to determine Avogadro’s number N (i.e., the number of atoms contained in a gram-atom) by measurements of gas viscosity and of the deviations of real gases from ideal gas behavior (v. TERMOLOGIA). Using data for argon, it was found that:
\[ N = 6.22 \cdot 10^{23} \]
It was also found, as a measure of the atomic diameter (again for argon),
\[ D = 2.8 \cdot 10^{-8} \, \text{cm}. \]
II. BROWNIAN MOTION AND THE DETERMINATION OF AVOGADRO’S NUMBER
The determination of Avogadro’s number N is of the greatest importance, not only because it provides the key to atomic dimensions, but also because this determination furnishes the foundation for the experimental evidence of atomic theories.
The method indicated for measuring N, which, as has been said, was the first to be followed, was beset by arbitrary and difficult-to-evaluate assumptions (such as the assumption of the spherical shape of molecules), and therefore could not be considered sufficient to provide the required experimental demonstration. Indeed, even the proponents of kinetic theories, despite their brilliant successes, were unwilling to grant their theories much more credence than working hypotheses. However, a much more direct and, moreover, fundamentally sounder evidence was obtained by another route.
It has already been noted that the existence of atoms implies that the further subdivision of mechanical energy (or any organized energy) 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 dependent only on temperature, can be regarded in a sense as an indirect but reliable confirmation of atomic structure. Now, such agitation, which eludes direct sensory examination, can indeed be revealed by sufficiently refined experimental means, and is known as “Brownian motion” (from its discoverer, the botanist Brown).
If one examines under a microscope with high magnification a suspension of very fine particles in a fluid (e.g., a so-called colloidal solution), one can observe that the particles present are in a state of irregular and often very lively motion; the characteristics of such motion are quite different from those of ordinary macroscopic motion. In fact, these are not organized collective movements caused by external disturbances (movements which, moreover, can be recognized and may even occur, but which disappear after some time if appropriate precautions are taken). Brownian motion remains unchanged for any duration of observation and is independent of all precautions taken to protect the system from external perturbing 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 that are independent of each other in both magnitude and direction; the direction and magnitude of the velocity of each particle changes continuously in a completely irregular manner; in a word, Brownian motion appears to be governed by the law of chance.
Brownian motion stands in contrast to the usual behavior of macroscopic bodies; when analyzed thermodynamically, it appears as a phenomenon analogous to the spontaneous passage of heat from a colder to a warmer 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 kinetic theory of matter, namely that the laws of the macroscopic world are no more than approximate and deducible as limiting cases—often by means of probability calculations—from the laws of the microscopic world.
How is Brownian motion interpreted in light of kinetic theories? It has already been said that pressure in a fluid is generated by the numerous random impacts of molecules; the forces due to pressure and pressure differences therefore arise from such impacts. If, then, one immerses in a fluid a body so small that the number of impacts it receives from the fluid molecules in an appreciable time is not very large, it is quite possible that in that small interval of time it receives relatively many more impacts from one side than from the opposite side: it will thus be driven by an appreciable force for an appreciable time. Since the impacts are entirely random, this force will continually change direction, and the motion will be entirely irregular.
If, on the other hand, one immerses in the fluid a relatively large body, this, given its considerable inertia, will practically not be affected by forces that continually change direction, and no appreciable motion will be observed; hence it appears macroscopically that in a fluid at equilibrium the pressure is uniform.
The confirmation of this way of interpreting Brownian phenomena—and at the same time of the correctness of the kinetic theory of gases—is provided by the following fact of the greatest importance: by studying Brownian phenomena, it is possible by various methods to arrive at the determination of Avogadro’s number, and the results are found to be consistent with one another and in excellent agreement with the determination based on the measurement of gas viscosity, which was mentioned earlier.
The average of the determinations made by Perrin, who in the first decade of this century carried out the first fundamental measurements in question, is
\[ N = 6.8 \cdot 10^{23} \]
After such a result, it is very difficult to deny the accuracy of the atomic theory of matter. As Perrin himself points out, one need only consider that, a priori, in the study of Brownian phenomena any value between zero and infinity might have resulted.
It is impossible to describe all the methods employed for the determination of N by measurements on Brownian phenomena; to give an idea of them, one of these may be mentioned, particularly simple and significant: if a small mirror is attached to an extremely fine quartz thread, the mirror, as a result of Brownian movement, performs very small oscillations which can be observed by reflecting light upon the mirror itself. It can be shown that under these conditions the average kinetic energy of the mirror's movement must be one-third of the average kinetic energy of a molecule at the same temperature, and this energy is inversely proportional to the Avogadro number N.
On the other hand, the average energy of the 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 carried out by Gerlach and Kappler, and gave a result in good agreement with other measurements.
It should be noted that Brownian movement can be observed in all measuring instruments comprising highly sensitive moving parts, and since it is absolutely ineliminable, it constitutes a limit to the sensitivity of measuring devices.
Thus it has been seen that the kinetic theory of heat makes it possible to define the fundamental concepts of the atomic theory of the structure of matter and to provide a first, though not entirely sufficient, experimental evidence.
This evidence is fully achieved through the study of Brownian movement, which can be quantitatively interpreted 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 regarded as indivisible particles: now, however, discoveries concerning the atomicity of electricity, radioactivity, etc., have shown that atoms are composite particles; despite this, the kinetic theory is not thereby invalidated, and the reason for this 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 through the solution a constant quantity of electricity equal to 96,500 coulombs. Since, on the other hand, according to Faraday's laws, the quantity of electrolyte decomposed is strictly proportional to the quantity of electricity carried, independently of any other circumstance (and therefore, in particular, for quantities of electrolyte however small), by extrapolating this law down to the atoms, it must be concluded (Helmholtz and Stoney) that each monovalent atom carries through the electrolyte a constant charge, precisely equal to 96,500 coulombs divided by the number of atoms contained in a gram-atom, i.e., divided by the Avogadro number.In the phenomenon of electrolysis, therefore, electric charges are shown to be all multiples of an elementary charge and of the 96,500 coulombs: N. Assuming for N the value 6.04 × 10^23, it follows that
\[ e = 4.80 \times 10^{-10} \, \text{esu C.G.S.} \]
The atomicity of electricity is manifested not only in the phenomenon of electrolysis, but as a general property of electric charges, i.e., all electric charges that appear in any phenomenon must be regarded as whole multiples of the quantity of electricity e. This fact, directly observable when sufficiently sensitive devices are used, 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. The details of these experiments cannot be entered into here; suffice it to say that Millikan succeeded in measuring the electric charge carried by a droplet of a non-volatile substance and in demonstrating that this charge is always an integral multiple of a constant quantity.
The elementary quantity of electricity thus determined was found to be 4.8 × 10^-10 esu. As can be seen, the agreement with the value determined by the previous method, based on knowledge of the Avogadro number, is truly excellent. Further experiments carried out by Millikan's method and with particular care have 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 existence of such particles was demonstrated by determining the ratio between their charge and their mass, which 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 (an hypothesis which further experiments showed to be in accordance with the truth), it was possible in this way to deduce the mass of such a particle, which proved to be about 1/186th that of the hydrogen atom.
The particles in question were called electrons. Electrons were later found in numerous other phenomena, such as, for example, thermionic emission, consisting in the emission of electrons by hot bodies, the photoelectric effect (emission of electrons from matter under the action of radiation), etc.
Now, since electrons are found in the discharge in very rarefied gases, whatever the nature of the electrodes and the gas interposed, and since, for example, the photoelectric effect occurs for any substance (it being sufficient to use light of sufficiently high frequency), it becomes natural to conclude that electrons form a general constituent of matter. It was soon possible to gather evidence that electrons are among the constituents of atoms. It is well known, in fact, that light radiations have an electromagnetic nature. They must therefore be emitted by electric charges in motion. Since the motion of electric charges is disturbed by a magnetic field, it could be foreseen that the characteristic spectra emitted by substances in the gaseous state (v. OPTICS) 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 variation in frequency of the spectral lines emitted depends on the ratio between the charge and the mass of the emitting electric charges. It is possible in this way to determine this ratio by purely optical measurements. The following fundamental result was obtained: the ratio in question is equal to that between the charge and the mass of the electron. It must therefore be concluded that the electric charges which emit the characteristic spectral lines of bodies in the gaseous state are electrons.
On the other hand, among the characteristic spectra there are those of the elements (it is indeed possible to base on this fact an extremely sensitive method of chemical analysis which has made possible, among other things, the determination of the elements present in the stars). It must therefore be admitted that such spectra are characteristic of atoms, and hence that electrons are constituents of atoms. Thus the hypothesis that atoms were simple particles was disproved. This most important result will be discussed further shortly.
It should also be recalled here that electrons are responsible for the high electrical conductivity of metals: within metals, one must think that there are electrons which, in a first approximation at least, can be considered as free, i.e., not stably bound to any atom. 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, these electrons can then begin to move, giving rise to an electric current. Now, the existence of free electrons within metals can be demonstrated by direct experiments: if, in fact, a piece of metal is subjected to a strong acceleration, the free electrons, by virtue 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 has been obtained for electrons by other methods (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 (i.e., making them electrically conductive by stripping electrons from their molecules). Such substances were called radioactive. Studies on radioactive substances received a great impetus following the discovery made by the Curies of a particularly radioactive element, which was called radium.Through 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, β, and γ radiations.
The α radiation consists of particles with extremely high velocity, positively charged (as can be shown by deflecting them in a magnetic field), whose electric charge is equal to twice the elementary charge, and whose mass is equal to about four times the mass of the hydrogen atom.
These particles can be detected by various means that allow them to be distinguished and counted one by one (e.g., Wilson cloud chamber, Geiger counters; the Wilson cloud chamber allows photographing the “tracks” of these particles).
From photographs taken with the Wilson cloud chamber, it can be observed, for example, that these are particles all having the same properties: their mass is determined by measuring the ratio between their charge and their mass using methods analogous to those used for electrons. The charge of these particles can also be measured directly by collecting them in a Faraday cup and counting their number (it should be noted that this measurement can be considered a new determination of Avogadro’s number and is in agreement with previous ones). An α particle can be considered a twice-ionized helium atom: if it captures two electrons, it is transformed into a neutral helium atom, as was directly demonstrated experimentally. The β radiation, on the other hand, consists of high-energy electrons and is studied by means analogous to those used for the α particles. The γ rays are electrically neutral and, as was demonstrated, of the same nature as light but with an extremely high frequency.
Moreover, it was demonstrated that the emission of these radiations is accompanied by a disintegration of the atoms and a consequent transformation of radioactive elements into other elements. Thus, it was directly proven that atoms are composite particles, and the problem arose of determining their structure. This problem was fundamentally solved by Rutherford, who used α particles precisely as a means of investigation.
As has been said, it was known that electrons must be part of the atom; since electrons are negatively charged and atoms are neutral, there must certainly be positive charges within the atom. The problem was to determine how these positive charges were distributed, together with which the main mass of the atom must be considered, given that the mass of the electrons is negligible. Now, the presence of positive charges in the atom must cause the deflection of α particles when they pass through matter (scattering of α particles).
From the magnitude of this phenomenon, it is even possible to infer 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 region whose radius is on the order of \(10^{-13}\) cm and therefore extremely smaller than the radius of the atom itself (on the order of \(10^{-8}\) cm).
As a consequence of this fundamental discovery, Rutherford proposed his famous atomic model: according to this model (which in its essential concepts can be considered in accordance with reality), the atom consists of a central “nucleus” with a radius on the order of \(10^{-12}\) cm, containing the positive charge and almost the entire mass of the atom, and of electrons, in a number sufficient to neutralize the positive charge of the nucleus, orbiting the nucleus like planets around the sun.
V. ENERGY QUANTIZATION AND ATOMIC STRUCTURE
Several serious difficulties were raised against Rutherford’s atomic model, which, upon closer examination, were nothing more than a particular aspect of a fundamental difficulty encountered when attempting to apply the laws of classical mechanics and electrodynamics (which are approximately valid for macroscopic bodies) to the study of atomic structure. This difficulty can be summarized in the following contradiction: the kinetic theory of heat leads to results in agreement with experience as long as it is assumed that atoms behave as if they were indivisible particles, whereas radioactive and optical phenomena (e.g., the Zeeman effect) show that atoms are composite particles.The solution to this apparent contradiction was found by introducing a new concept into physics: the concept of energy quantization, which was introduced by Planck at the beginning of the present century in the study of an entirely different phenomenon (the so-called “blackbody” radiation law) and proved to be highly fruitful in solving the problem at hand (Bohr).
According to Planck’s idea, radiation can be emitted or absorbed only in “indivisible quanta of energy,” proportional to the frequency of the radiation itself.
The proportionality constant, the “universal quantum of action,” is a universal constant equal to \(6.55 \cdot 10^{-27}\) erg·sec, and was determined by Planck by comparing his blackbody radiation law with experimental data (in doing so, Planck was also able to determine Avogadro’s number appearing in his law, finding a result in agreement with other measurements).
The “quantum of action h,” or Planck’s constant, was also determined by other methods; Einstein showed that the photoelectric effect, which could not be explained in any way on the basis of classical electrodynamics, could conversely be well explained by Planck’s hypothesis, and in this way he was able to determine the constant h independently in agreement with Planck’s results.
Einstein himself and later Debye applied this concept to the theory of the specific heats of solids at very low temperatures, with very satisfactory results.
But the application of Planck’s hypotheses, which proved most fruitful, was made by Bohr in his explanation of the optical spectra emitted by atoms and of atomic structure. Since, according to Planck’s idea, radiation can only be emitted in discrete quanta by atoms, an atom that emits a quantum of radiation will have, in its final state (after emission), an energy differing from that of its initial state by precisely the energy of the emitted quantum, which depends solely on its frequency. Since each atom can emit only certain specific frequencies (those of its characteristic spectrum), it follows that each atom can possess only certain discrete energies, whose differences correspond to the radiation quanta that the atom can emit. This is essentially the idea from which Bohr started. It is important to note that this concept allows the apparent contradiction between the kinetic theory of heat and the fact that atoms are not simple particles to be overcome. Indeed, if the energy of atoms can assume only discrete values, there will be a finite difference between the lowest possible energy (the ground state) and the next higher level. If this difference, as is found in reality at not too high temperatures, is much greater than the average energy that can be exchanged in a collision between two atoms in thermal motion, it is clear that the atom will normally remain in the ground state and cannot transition to the next level; that is, its internal energy cannot vary due to collisions, just as if the atom were an indivisible particle.
It should be noted that Bohr thus not only overcame the difficulties encountered by Rutherford but also provided an immediate explanation for the general structure of the characteristic spectra emitted by elements, which had remained entirely mysterious under classical electrodynamics. Moreover, by introducing a particular quantization hypothesis (later refined by Sommerfeld), he was able to calculate a priori the frequencies emitted by the hydrogen atom and ionized helium, obtaining results in remarkable agreement with experimental data.
VI. X-RAYS AND THE PERIODIC TABLE OF THE ELEMENTS
The quantum theory made it possible to explain in a relatively simple way the natural classification of chemical elements (Mendeleev’s periodic table), transforming Mendeleev’s empirical classification (v. CHIMICA) into a rational one and accounting at the same time for the relationship between this classification and the law of characteristic X-ray spectra discovered by Moseley.The fundamental concept of this rational classification is as follows: atoms are composed of a positively charged nucleus and a certain number of electrons surrounding II. The nuclear charge is an integer multiple Z of the elementary electric charge “e”; the number of electrons (in a neutral atom) is also equal to Z; the number Z is called the “atomic number.”
Now, practically all chemical properties and at least most physical properties of elements depend exclusively on the atomic number Z. Therefore, elements can be rationally classified by arranging them in order of increasing atomic number.
As already mentioned, a great contribution to this classification came from the study of the characteristic spectra of X-rays. These rays, discovered by Röntgen, are of the same nature as light radiation.
The proof of this fact was provided by Laue. It is well known that to demonstrate the wave nature of light, one can use diffraction experiments (v. OPTICS), among which particularly notable are those performed with gratings, which allow an absolute and very precise measurement of the wavelengths of light.
However, under ordinary experimental conditions, optical gratings are not suitable for demonstrating the wave nature of X-rays or measuring their wavelengths, because the spacing between their lines is not sufficiently small.
Laue observed that nature provides other structures that can serve this purpose: crystals. Indeed, according to the fundamental hypothesis of crystallography, crystals are composed of atoms (of the kind present in the chemical composition of the crystal), arranged at regular intervals, forming a true spatial lattice (in reality, the atoms in a crystal are not stationary but oscillate around the lattice points due to thermal agitation). The distance between successive atoms in a crystal can be calculated using Avogadro’s number and is on the order of 10^-8 cm. It was therefore predicted that, by directing X-rays at a crystal, diffraction phenomena analogous to those observed with light and optical gratings would occur. The experiment fully confirmed this prediction, providing experimental proof of the wave nature of X-rays and the validity of views on the structure of crystalline bodies. Definitive confirmation came when diffraction phenomena of X-rays were also observed using optical gratings under special conditions (grazing incidence). This led to an absolute measurement of the wavelength of X-rays, and by comparison with experiments on crystals, it was possible to determine the absolute distances between atoms in crystals, yielding results in agreement with those predicted by Avogadro’s number.
Thus, a true X-ray spectroscopy analogous to optical spectroscopy was established, and it was shown that each element, like it emits a characteristic optical spectrum, also emits a characteristic X-ray spectrum. The information provided by these spectra is particularly valuable because, whereas optical spectra are emitted by electrons farthest from the nucleus, X-ray spectra are emitted by electrons closest to the nucleus and thus are more directly influenced by the nuclear charge, so that their frequencies depend in a simple way on this charge, i.e., on the atomic number (Moseley’s law). This property of X-rays also makes it possible to discover and identify unknown elements, placing them in their correct position in the periodic table.
With this rational criterion for classifying elements established, it became possible, by applying the quantization conditions of Bohr and Sommerfeld and a principle concerning electron behavior discovered by Pauli (the exclusion principle), to demonstrate that electrons in each atom are distributed in various “electron shells,” starting from those closest to the nucleus (the innermost shell) to the outermost ones.
It was also shown that chemically homologous elements (those in the same column of Mendeleev’s table; V. CHIMICA) have similar arrangements of electrons in their outermost shell; thus, the explanation for the periodicity in chemical and spectroscopic properties, empirically observed, was found.
VII. THE CONSTITUTION OF THE NUCLEUS; ISOTOPES; THE EQUIVALENCE OF MASS AND ENERGY
It has been seen that the properties of the atom depend substantially on the atomic number, i.e., on the nuclear charge, and thus directly or indirectly on the nucleus.The chemical species of an atom is defined by its nuclear charge; transmutations involving a change from one chemical species to another
According to Einstein’s principle, a certain mass corresponds to a given energy, which is precisely the difference between the sum of the masses of free protons and neutrons and that of the nucleus.
It should be noted that this is not a mere induction or hypothesis. As has already been mentioned, it is possible to induce nuclear transmutations in various ways, for example by bombarding nuclei with particles or neutrons; other transmutations are obtained by bombarding with protons, γ-rays, or other particles.
In this way, it is possible to induce in nuclei reactions that are in a certain sense analogous to ordinary chemical reactions, and in which, as in chemical reactions, there can be a release or absorption of specific quantities of energy; in nuclear reactions, however, the energies involved in each elementary process are normally incomparably greater than those involved in chemical reactions.
Now, these energies are precisely determined, and it can be observed that every transfer of energy to the exterior is accompanied by a decrease in the mass of the reacting system, which exactly matches that predicted on the basis of Einstein’s equivalence relation, and vice versa. Nuclear reactions thus provide an unquestionable experimental proof of the equivalence between mass and energy.
Among nuclear reactions, the so-called “fission” of uranium and thorium has assumed enormous practical importance because it has enabled the utilization of nuclear energy.
VIII. THE DUAL PARTICLE AND WAVE ASPECT OF MATTER AND RADIATION
Reference has been made to the successes achieved by Planck’s idea (quantization of energy) in various fields of physics. It must now be said that for some time this idea also raised very serious difficulties.The principal difficulty concerned the nature of electromagnetic radiation. In certain phenomena, this radiation behaves not only as if it were simply emitted or absorbed in indivisible quanta, as Planck’s hypothesis suggested, but also as if it had to propagate in the form of “energy granules” (photons), each equal to a Planck energy quantum: this behavior, for example, seemed evident in the scattering of radiation by free electrons, an effect (the Compton effect) that can indeed be described as an elastic collision between a photon and an electron.
On the other hand, there are phenomena (interference, diffraction, etc.) that are entirely incompatible with the hypothesis that radiation consists of corpuscles, even if these corpuscles travel at the speed of light and possess the properties of ordinary particles.
This contradiction was resolved through the work of several physicists (De Broglie, Heisenberg, Schrödinger, Born, Jordan, Dirac, Bohr), which led to a profound revolution in the fundamental concepts of physics.
First, it was established that the dual particle and wave aspect is not peculiar to radiation but is also characteristic of matter: this consequence of the theory was verified experimentally in a direct manner by observing diffraction phenomena produced by crystals on electrons, analogous to the diffraction phenomena observed with X-rays (diffraction phenomena were later observed for heavy particles as well); the conditions of quantization formulated by Bohr and Sommerfeld, which had remained somewhat arbitrary, were deduced and refined as consequences valid in limited and particular cases of the more general theory; criteria of an exactly quantitative nature were thus successfully applied to the theory of atomic structure, where the old Bohr-Sommerfeld theory had failed quantitatively and had only provided qualitative indications; the nature of the forces binding atoms together in molecules was elucidated, i.e., the nature of chemical forces; a unified theory of both the wave effects and the corpuscular effects of radiation was developed. Finally, various new phenomena were predicted and subsequently confirmed by experiment, among which may be mentioned the existence of the positive electron (equal in mass to the negative electron but with a positive charge), which was found in artificial radioactivity and cosmic radiation, and a remarkable phenomenon concerning these particles, in which it is possible to observe the transformation of a photon (a quantum of radiant energy) into a pair of electrons, one positive and one negative.
This phenomenon is a case of the transformation of energy into matter: it can be observed experimentally, as can the converse phenomenon, the annihilation of an electron pair with the production of γ-quanta.
These transformations of matter into energy and energy into matter occur in accordance with Einstein’s law, of which they constitute a further brilliant direct confirmation.
All these successes were achieved through the recognition of the untenability of the hypothesis of physical determinism, at least as classically conceived, and of the essentially probabilistic nature of physical laws. Thus, the concept was reaffirmed and refined that the laws of classical and macroscopic physics are only approximate laws, deducible as limiting cases, in which Planck’s constant can be considered negligible, 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 amount 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 (the first law of thermodynamics), which made it possible to formulate the fundamental principle of the conservation of energy: at the basis of this principle is the conception that the various forms in which energy appears phenomenologically (mechanical energy, thermal energy, electromagnetic energy, chemical energy, etc.) are all equivalent to one another and can be transformed into one another.
Since the distinction between the different forms of energy must in this way be considered phenomenological, for every isolated physical system only the total energy can be defined in an exact and general manner; this total energy remains constant, as has already been said, over 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 entirely general validity.
(v.) inasmuch as it asserts the absolute superiority of the spiritual world over matter.
However, it can also be developed in a particular or methodical form for a single problem or aspect of philosophy: for example, ethical materialism (hedonism, utilitarianism [v.]) posits pleasure or utility as the principle of morality (as the subject of consciousness), but does not prescribe a materialistic interpretation of the world; biological materialism holds that vital phenomena in corporeal beings are generated by mechanical and chemical processes of inorganic matter, but does not exclude the presence of spiritual life. A comprehensive materialistic system finds itself unable to achieve full coherence, both because it cannot avoid attributing to itself, as an intellectual system, some difference from material processes, and because the definition of the concept of matter is itself formal and therefore not deducible from matter. Materialistic systems are in reality formally corresponding to epochs of spiritual fatigue or decline, or due to the prevalence of empirical knowledge and progress. Their constant error is that while they propose the principle of matter as contrary to the metaphysics of form, it is nevertheless a metaphysical principle that goes beyond sensory experience and is never fully justified by II. Indeed, there is a metaphysical materialism in the description of the spiritual world and of the world in terms of material images, as in the life of geology, which is characteristic of primitive Greek and Eastern cosmogonies and of the subsequent theories that follow or reproduce them.
Ancient materialism is still very close to these forms of naive metaphysics, although inspired by scientific and juridical interests. It is distinguished into atomistic and pneumatological. Atomistic materialism is represented by the school of Abdera (Leucippus, Democritus [v.], 5th–4th centuries B.C.) and by the school of Epicurus ([v.], 3rd century B.C.–2nd century A.D.). They agree in identifying matter with bodies, and these with indivisible atoms or corpuscles, moved by perpetual motion in empty space. The weight of the atoms determines their downward motion, and this is the same necessity (ἀνάγκη) that governs all events (v. ATOMISM). The ancient atomism is credited with formulating the principle of the conservation of matter and the canons of scientific research with empirical method, although these are also found developed or accepted by other schools. Characteristic of its stance in religious and social matters is the view that deities exist only as corporeal entities, that the universal mechanism of necessity excludes providence, that religion as a relationship between man and God is useless and harmful and superstitious; that the soul, according to Epicurus, dies with the body, and therefore there is no afterlife or underworld (according to Democritus, the soul had weak survivals subject to the laws of bodies); that civilization is formed by aggregations of material and utilitarian interests, and to these are owed social order and the progress of the arts. In this, many evolutionary views of the ancients are confusedly adopted and reworked (adaptation of species; origins of language and of social contract): but above all, there emerges from the inconsistencies of the doctrine and the aridity of reason a poetic melancholy, a veiled pessimism about the fate of imagination and human life, which inspires the work of Lucretius and his imitators.
Pneumatological materialism is represented by the Stoic school (3rd century B.C.–2nd century A.D.; V. STOICISM). It appeals, through rational revision of hylozoism (v.), to the idea of a single primitive matter (the fiery νευρός), identical with the divine principle, which generates and permeates all things, maintaining their life and animation, particularizing its own universal law and energy into laws and productive principles of individual existences, recognizing itself in human reason, and reabsorbing everything into the periodic consummation and renewal of the world (ἀποκατάστασις). The Stoics thus proposed the identity of matter and form, and therefore of necessity and freedom, of fact and providence, of experience and reason: but for polemical reasons (idealization of wisdom, formalism of moral law, religious sense of cosmic order) they failed to eliminate dualism from their doctrine; indeed, they justified it logically in the contrast between activity and passivity, λόγος and πάθος. Their materialism therefore did not take the path of science, but that of quietism (v.) and return to metaphysics.
Affiliated with Hellenic schools and largely derived from them are the Eastern materialistic schools. In Indian philosophy: the systems of Nyāya and Vaiśeṣika (3rd century B.C., scholastic expositions of the 3rd century A.D.) reorganize atomistic theories within categorical schemes; the heterodox tendencies, no less ancient, of the Lokāyatas and Cārvākas, propose respectively sensism and hedonism. In the Persian world, Manichaeism (3rd century A.D.) gives rise to the abstract and rigorous dualism between spirit and matter, which allowed the systematic survival of physical and ethical materialism, as a doctrine parallel to that of spiritual life, in the heresies of the Middle Ages (v. CATHARS).
With the triumph of Christianity, the danger that materialism could ever become a definitive system ceased, a danger still immanent in post-Aristotelian schools. There are, however, Christian heresies of a materialistic nature, for example, that of Montanus (v. martyr in 175) followed by Tertullian (v.) in his final phase; which attributed a material substance even to the soul. In medieval Christianity (12th century) there is the pantheistic materialism of Amalric of Bena (identity of creator and creatures, unity of the essence of all beings) and David of Dinant (who almost foolishly posited God as the first matter: Sum. Theol., 1°, q. 3, a. 8, c); and logical materialism, or the theory of the indifference of the most general and substantial concepts to the differences of individual, species, and genus concepts (Adelard of Bath, Walter of Mortagne), not without some scientific reference to Democritean atomism, known through the Arabs and Constantine the African (11th century). With the first rebirth of culture in the West, Epicureanism returned to vogue for juridical and literary reasons (Frederick II of Swabia, Guido Cavalcanti), and this vogue continued in Humanism (Lorenzo Valla): but the new Epicureanism tended to reconcile itself with finalism or theism, so much so that even Albert the Great considered Anaxagoras as Epicurean. In the materialistic tendencies of the Renaissance, however, hylozoism and pantheism prevail (Pomponazzi, Telesio, Libertinism).
Modern materialism begins in the 17th century, with the molecular theory of matter, which renewed the corpuscular theory and the atomic hypothesis of the ancients. This theory is developed in connection with the mechanical doctrine of nature in dualistic systems (Galilei, Descartes, Newton), but it is also supported, apart from religious problems, as a systematic principle of natural philosophy, by notable thinkers such as Pierre Gassendi (1592–1655), Thomas Hobbes (1588–1679), and Robert Boyle (1627–91), whose tendency may be designated as physical materialism. Gassendi, in the name of Epicurus, re-established against Descartes and his attempted synthesis of atomic theories with the new rational mechanics, the classical corpuscular theory, seeking to explain the free will of atoms as deriving from their individual properties. Hobbes maintained that the corpuscular theory alone, with its mechanism, is sufficient to explain the origin of living beings and sensitive consciousness. Boyle combined the atomic hypothesis with the magnetic and chemical properties of atoms, which he had discovered. He was the first to give (De ipsa natura, 1682) a non-metaphysical definition of matter on purely scientific grounds. The philosophical current thus formed finally received the name of materialism (materialism by Pierre Bayle in his Dictionnaire historique et critique (1695–97; 2nd ed. 1702); and Berkeley set out to destroy it by denying the existence of matter. But it continued to develop in that form throughout the 18th century in association with deism, beginning with John Toland (Letters to Serena, 1704: Motion essential to matter). It thus found singular expressions in that century: the Cartesio sobre el alma (1713) by J. G. Westphal and J. D. Hocheisel; the Histoire naturelle de l'âme (1745) and L'homme machine by Julien Offray de La Mettrie; the Essai de cosmologie (1750) by Pierre Moreau de Maupertuis (1698–1759), who asked whether atoms themselves might be sentient, and whether sentience is not an “epiphenomenon” of the brain; the Pensées sur l'interprétation de la nature (1754) by Diderot, and the treatise De la nature by J. B. Robinet (1735–1820).
In the second half of the 18th century, however, the tendency to unify materialism and atheism dominates, represented by the Système de la nature of d’Holbach (1774) and the Encyclopédie des Sans-Dieu of Pierre Maréchal (1800). This is countered by physiological and ideological materialism, inspired by the sensism of Condillac (Traité des systèmes, 1749), with its doctrine of psychic phenomena as organic reactions to physical phenomena (Charles Bonnet, 1720–93; Claude Adrien Helvétius, 1715–73; Pierre Cabanis [v.], 1757–1808). This allows for a genesis of life superior to matter, and for the formation of consciousness, starting from elementary phenomena such as the irritability of tissues and sensation as an internal reaction to impressions. A parallel trend is represented by English associationist materialism, which considered (David Hartley, 1705–57) sensations and ideas as “motions of the soul,” entirely similar and parallel to the vibrations of the nervous system and subject to the same type of mechanical necessity; and proposed (Joseph Priestley [1733–1804], Free discussion of the doctrines of materialism, 1778) to study psychic phenomena in their corresponding physical phenomena and according to the same physical law of attraction and repulsion. This was later brought to logical perfection and materialistic conclusions by James Mill (1773–1836: Analysis of the phenomena of the human mind, 1829). Spinozism was also interpreted in that period in a materialistic-pantheistic sense (H. de Boulainvilliers, H. Heydenreich).
At the beginning of the 19th century, with the predominance of idealism, the ideologists (v. IDEOLOGIA) came to accept, albeit cautiously and with varying opposition, Kantian criticism, which regards “physical matter” and the scientific principles related to it as postulates derived from intellectual categories, while sensible matter is merely the inseparable content of intuitive form, and its existence in itself is unknowable. Yet it cannot be Kant (v.) attributes to the matter of knowledge, both intuitive and intellectual, a limiting function on knowledge, which the subsequent transcendental and absolute idealism had to attempt to overcome: and this idealism did not succeed in entirely replacing traditional spiritualism, of Cartesian inspiration and dualistic in its background.
Dialectical materialism (v.) arose instead in the mid-19th century, as a negation of Hegel’s absolute idealism, and gave rise to historical materialism. The economic materialism that followed from it, and through the work of the same authors, identified “value” with productive labor and defined artistic and intellectual values as “surplus value” (v. VALORE). Dialectical, historical, and economic materialism, after varying fortunes in the 19th century, are still conjoined in the socialism and communism of the 20th century, as at their origins. Attempts have been made repeatedly to trace them back to Kantian criticism, unifying matter and the sensible form of practice in a single act, but Marxists fail to overcome the initial sophism of the “inversion” of the idea into its content or matter, since this is comprehensible only insofar as it is within the idea itself.
Psycho-physical materialism (A. Weber, L. Fechner, H. Helmholtz, H. Hertz) arose in the first half of the 19th century through the extension of the experimental method and the advances of physical sciences to associationist psychology and to Spinozist materialism: Fechner linked it with a pantheistic vision of the universe. It tends predominantly to demonstrate that there are constant and quantitative relations between physical phenomena and psychic phenomena in accordance with the law of the conservation of energy (L. Meyer, 1840). With the development of new atomic theories (C. Avogadro, P. Gay-Lussac), evolutionary cosmogony (P. R. Laplace, H. L. Helmholtz), and zoogony (K. Vogt, R. Virchow), mechanical-biological materialism also resurged in the mid-century (K. Vogt, Küchenlatein und Wissenschaft, 1854; K. Moleschott [v.], Kreislauf des Lebens, 1852; L. Büchner [v.], Kraft und Stoff, 1855), in which atomic matter constitutes the substratum of organized and organic material forms, the forces required to produce them are traced back to phenomena of matter or to an initial dualism, and any autonomy of psychic life in relation to the functions of the brain is denied. This new dogmatic materialism could not help but conclude with a certain skepticism regarding the limits of scientific knowledge (P. Du Bois-Reymond) and the possibility of excluding teleology (F. Überweg). Corresponding to this in the social sciences are Max Stirner’s ethical atomism (Der Einzige, 1845) and determinism.
In the second half of the 19th century, in connection with the predominance of the evolutionary method in the natural sciences (C. Darwin, H. Spencer) and the electromagnetic theories of matter (W. I. Rankine, J. Maxwell, W. Ostwald), the monistic (energetic, evolutionary) conception gained ascendancy. It substituted for the classical concept of atomic matter that of an indeterminate matter as primitive or fundamental energy, diffused throughout, from which the formation of atomic and molecular nuclei would derive, and which would continue to produce subsequent evolutionary phenomena. This hypothesis, which also inverts the traditional relationship between force and matter, was adopted even in psychology with the theory of Mind-Stuff (psychic matter; V. Taine). It would theoretically be reconcilable with spiritualistic systems, since energy is rather form than matter; but so far it has inspired monistic systems akin to pantheism and decidedly materialistic. Such were the evolutionary cosmogonies of Ernst Haeckel and Ernesto Morselli at the end of the last century, and that of contemporary quantum physics by Max Planck, which returns to uniting energy with a primitive quantity of nuclear value.
The initial error of monism was precisely that of attributing to the atom a primitive and cross-grained existence, and this error is repeated even in modern activistic and energetic forms. Neither the atom nor the instant, neither the elements of extended matter nor those of physical forces or energies are the act of life. Still more evident is their radical insufficiency to account for the forms of spiritual life (truth, freedom, duty), which, by their ideal value of universality and necessity, are essentially irreducible to the mere empirical becoming in space and time in which every monism (v. ATHEISM; ATOMISM; DUALISM; MONISM; and individual thinkers cited) resolves and concludes itself.
SANTINO CARAMELLA