CONSTITUTION OF MATTER
The problem of the constitution of matter is undoubtedly one of the fundamental scientific questions: indeed, research concerning this issue has been guided by the idea of explaining the laws—more or less complex and numerous—of the highly diverse phenomena that fall under the senses (macroscopic phenomena) through the essentially simpler and fewer laws governing microscopic complexes (molecules and atoms), conceived as the constituents of macroscopic bodies.
The investigation into the constitution of bodies thus comprises a dual process: 1) the analysis of bodies into their microscopic constituents, thereby involving 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, encompasses the problem of reducing the diverse appearances of macroscopic natural phenomena to a higher unity and of determining the scope of validity and the true meaning 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 atomicity 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 elements
VII. The constitution of the nucleus; isotopes; the equivalence between matter and energy
VIII. The dual corpuscular and wave-like aspect of matter and radiation
IX. Energy.I. THE KINETIC THEORY OF HEAT
As is well known, already the ancients (Leucippus, Democritus) had some intuition regarding the atomic structure of matter and molecular agitation. These hypotheses were revived in the 17th century by Gassendi and then by Daniel Bernoulli, who made the first quantitative applications of them to deduce 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 precisely defined (v. CHIMICA). The laws of reactions between substances in the gaseous state then suggested to Avogadro his famous hypothesis: equal volumes of gases at the same pressure and temperature contain the same number of molecules. This hypothesis allowed for the determination of the notion of molecular weight (v. CHIMICA) and, in this way, the ratios between the masses of the molecules of various substances.The first approach to addressing the question of the absolute dimensions of atoms, and thus 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 that fall under direct observation, it generally appears upon a coarse examination that a 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 dissipated. Indeed, an increase in temperature can be observed in such bodies, as if a quantity of heat proportional to the amount of dissipated work had been supplied (first principle of thermodynamics, or principle of the equivalence between work and heat: V. TERMOLOGIA).
The first principle of thermodynamics strongly suggests 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). Indeed, if one attempts to closely examine the way in which macroscopic mechanical energy disappears as such to give rise, for example, to increases in temperature in some bodies, it is possible to observe that this phenomenon occurs through a fragmentation of the energy of collective movements into energy of disordered movements (e.g., vibrations) of increasingly 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 body of water initially at rest: first, relatively long and wide waves are observed; among them, progressively shorter wavelengths tend to predominate, until all apparent motion disappears.
The direct analytical examination of this phenomenon of energy transformation shows that if matter had a continuous structure, the process of fragmenting energy into increasingly numerous and minute movements would never end.
The atomic structure of matter, however, gives rise to a limit to the successive fragmentation and disorganization of the internal energy of bodies: indeed, if matter is constituted by simple elementary particles, not further divisible, no internal movement of these simple particles being possible, it must be admitted that the smallest movements that can occur in matter are precisely the translational movements of the individual elementary corpuscles.
In the early atomic theories, it was assumed that the atoms themselves were the elementary particles; today it is known that this hypothesis is not exact, but for the purposes of considerations on the kinetic nature of heat, for reasons that will be seen, atoms can be considered precisely as simple particles, and thus the viewpoint of the founders of the kinetic theory itself can be deemed fundamentally correct. The great importance of this observation will be seen later.
The perspective of the kinetic theory of heat can therefore be precisely stated as follows: 1) the molecules and atoms that form a body are endowed with disordered movements, and by this it is precisely meant that the movement of each corpuscle is, to a very considerable degree, independent of the movements of the other particles constituting the body. The energy related to such movements is "disorganized internal energy"; 2) the temperature of bodies depends on disorganized internal energy: to give (or absorb) heat means nothing other than to give or absorb energy in a disorganized form; 3) as a consequence, temperature and dependent quantities (e.g., the pressure in a gas) can be defined only for numerous complexes of atoms or molecules: indeed, the notion of the disorganization of the movement of a molecule is relative only to the movement of the other molecules. In other words: temperature, pressure, etc., are statistical quantities that can be defined only for ensembles of very many atoms, that is, for macroscopic bodies, just as, for example, the average mortality rate is a statistical quantity definable only for an ensemble 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. Indeed, 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 (at the limit, for so-called perfect gases, null).
Since the molecules of the gas are not, as a consequence, bound to each other by forces (with the exception of gravity, generally negligible), they will tend, due to the disordered movements by which they are animated, to move apart in all directions: it follows, as is well known, that the gas occupies all the space made available to it; it also follows that the molecules, by striking the walls of the container holding the gas, exert on them a pressure that is the resultant effect of all the impacts occurring in the unit of time on the unit of surface.
By increasing the temperature, the liveliness of molecular movement increases, and, consequently, the pressure.
On the basis of the preceding concepts, it is possible to rediscover the experimental laws of gases (Boyle's law, Gay-Lussac's law, etc.) in their quantitative expression. The average velocity of molecules in relation to temperature was determined (a velocity later confirmed by highly precise direct quantitative measurements in the present century by Stern, and which, at usual temperatures, was found to be on the order of several hundred meters per second). A quantitative theory of diffusion phenomena, gas viscosity, and heat conduction (v. TERMOLOGIA) was developed by introducing the important concept of the mean free path—that is, the average distance traveled in a straight line by gas molecules between two consecutive collisions. It was demonstrated (a notably significant result) that Avogadro's hypothesis is a consequence of the fundamental assumptions of kinetic theory. Finally, an extremely important result (Maxwell) was reached, according to which the translational kinetic energy of molecules, due to thermal agitation, is distributed on average among the different molecules independently of their size (even rotational kinetic energy is simply related to translational energy). This principle (the principle of equipartition of energy) allowed for the development of the theory of specific heats of gases, with entirely satisfactory results in agreement with experience. Lastly (and, together with the principle of equipartition of energy, this may be considered the most important result of kinetic theory), it became possible to determine Avogadro's number N (that is, the number of atoms contained in one gram-atom) through measurements of gas viscosity and deviations of real gases from ideal gas behavior (v. TERMOLOGIA). Using data related to Argon, the following was found:
N = 6.22 · 10²³
Furthermore, the diameter of the atom (again for Argon) was determined as:
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 remarkable importance, not only because it provides the key to atomic dimensions, but also because such determination furnishes the foundation for the experimental evidence of atomic theories.The method indicated for measuring N, which, as mentioned, was the first to be followed, could not be considered sufficient to provide the required experimental demonstration due to the arbitrary and difficult-to-evaluate hypotheses it contains (such as the hypothesis of the spherical shape of molecules). Indeed, even the proponents of kinetic theories, despite their brilliant successes, were not inclined to grant their theories much more credibility than working hypotheses. However, far more direct evidence, grounded moreover on the fundamental concepts of kinetic theory, has been achieved by another route.
It has already been observed that the existence of atoms implies that the successive fractionation of mechanical energy (or otherwise organized energy) that dissipates 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 solely a function of temperature, can be considered in a certain sense an indirect but sure observation of atomic structure. Now, such agitation, which escapes direct sensory examination, can indeed be revealed by sufficiently refined experimental investigation methods and is known as "Brownian motion" (after its discoverer, the botanist Brown).
If one examines under a microscope with strong magnification a suspension of very minute particles in a fluid (e.g., a so-called colloidal solution), one can observe that the particles therein appear to be in a state of irregular and often highly vigorous motion: the characteristics of this kind of motion are quite different from those of ordinary macroscopic movements. Indeed, it is not a matter of organized collective movements caused by external disturbances (movements that are, moreover, easily recognizable and may also occur but disappear after some time if appropriate precautions are taken). Brownian motion remains unaltered for any duration of observation and independently of all precautions taken to protect the system from external perturbing influences; in any case, it is clearly distinguishable from movements due to external causes by the following two facts: particles, however close, have velocities independent of one another in both magnitude and direction; the direction and magnitude of each particle's velocity change continuously in a wholly irregular manner; Brownian motion appears, in a word, governed by the law of chance.
"Brownian motion appears in contrast with the common 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 one. Brownian motion is therefore the direct experimental confirmation of the conception that constitutes the profound foundation of studies on the constitution of matter, according to which the laws of the macroscopic world are merely approximate and deducible as limiting cases, often through the calculus of probabilities, from the laws of the microscopic world."
How is the mechanism of Brownian motion interpreted in light of kinetic theories? It has already been stated that pressure is generated in a fluid by the innumerable collisions of molecules: the forces due to pressures and pressure differences are therefore attributable to such collisions. If, then, a body so minute that the number of collisions it receives from the fluid's molecules in an appreciable time is not very large is immersed in a fluid, it may well happen that in that certain small time interval it receives relatively many more collisions from one side than from the opposite side: it will therefore be impelled to move by an appreciable force for an appreciable time. Since the phenomenon of collisions is entirely random, this force will continuously change direction, and the motion will be wholly irregular.
If, conversely, a relatively large body is immersed in the fluid, this body, given its considerable inertia, will practically not feel the effects of forces that continuously change direction, and no appreciable motion will be observed, whence it appears macroscopically that in a fluid at equilibrium the pressure is uniform.
Confirmation of this way of interpreting Brownian phenomena, and at the same time of the accuracy of the kinetic theory of gases, is provided by the following fact of great importance: through the study of Brownian phenomena, it is possible by various means to arrive at the determination of Avogadro's number, and the results found are in agreement with one another and in what can be considered excellent agreement with the determination based on the measurement of gas viscosity, which was previously mentioned.
The average of Perrin's determinations, who in the first decade of this century carried out the first fundamental measurements in question, is
N = 6.8 · 10²³
After this result, it is very difficult to deny the accuracy of the atomic theory of matter. Indeed, as Perrin himself observes, 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 through measurements on Brownian phenomena; to give an idea, one particularly simple and significant method is mentioned: if a small mirror is attached to a very fine quartz fiber, the mirror, due to Brownian motion, performs very small oscillations that can be observed by reflecting light off the mirror itself. It can be demonstrated that under such conditions, the average kinetic energy of the mirror's motion must be one-third of the average kinetic energy of a molecule at the same temperature, and this energy is inversely proportional to Avogadro's 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 ascend to the determination of the number N. The experiment was conducted by Gerlach and Kappler, yielding a result in good agreement with other measurements.
It should be noted that Brownian motion can be observed in all measuring instruments comprising highly sensitive mobile equipment, and being absolutely ineliminable, it constitutes a limit to the sensitivity of measuring devices.
It has thus been seen that the kinetic theory of heat allows the definition of the fundamental concepts of the atomic theory of the structure of matter and provides a first, though not entirely sufficient, experimental evidence thereof.
Such evidence is fully achieved through the study of Brownian motion, which can be quantitatively interpreted on the basis of the concepts formulated in kinetic theory and constitutes its direct experimental verification.
In all the considerations made in 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, kinetic theory is not invalidated, and the reason for this fact will be clarified when discussing the atomicity of energy.
### 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 transports a constant quantity of electricity through the solution, equal to 96,500 Coulombs. Since, moreover, according to Faraday’s laws, the quantity of electrolyte decomposed is rigorously proportional to the quantity of electricity transported, regardless of any other circumstance (and thus, in particular, for however small quantities of electrolyte), by extrapolating this law to the level of atoms, one must conclude (Helmholtz and Stoney) that each monovalent atom carries with it through the electrolyte a constant charge, precisely equal 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, electric charges are shown to be all multiples of an elementary charge "e" equal to 96,500 Coulombs : N. Assuming for N the value 6.04 × 10²³, it follows that:
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 electric charges that appear in any phenomenon must be considered integer multiples of the quantity of electricity "e." This fact, directly verifiable when working with sufficiently sensitive devices, allows for 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. It is not possible to enter into the details of such experiments; 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 such charge is always an integer multiple of a constant quantity.
The elementary quantity of electricity thus determined was found to be 4.8 × 10⁻¹⁰ e.s.u. As can be seen, the agreement with the value determined by the previous method and based on the knowledge of Avogadro’s number is truly excellent. Further experiments conducted with Millikan’s method and with particular care led to an even better agreement.
On the other hand, through the study of discharge in extremely rarefied gases, Thomson succeeded in demonstrating the existence of negatively charged particles with a mass much smaller than that of the lightest atom (the hydrogen atom). The demonstration of the existence of such particles was achieved 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 (a hypothesis that further experiments proved to be true), it was possible to derive the mass of such a particle in this way, which turned out to be approximately 1,860 times smaller than that of the hydrogen atom.
The particles in question were called "electrons." Electrons were subsequently found in numerous other phenomena, such as, for example, the thermionic effect, consisting of the emission of electrons by hot bodies, and the photoelectric effect (emission of electrons from matter under the action of radiation), etc.
Now, since electrons are found in the discharge of highly rarefied gases, regardless of the nature of the electrodes and the interposed gas, and since, for example, the photoelectric effect occurs in any substance (provided light of sufficiently high frequency is used), it becomes natural to conclude that electrons form a general constituent of matter. It was soon possible to gather proof that electrons are among the constituents of atoms. It is well known, in fact, 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, it was possible to predict 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 due to insufficient experimental means, was later effectively discovered by Zeeman. Now, as theory can show, the variation 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 through purely optical measurements. This fundamental result was obtained: the aforementioned ratio is equal to that between the charge and the mass of the electron. It must therefore be concluded that the electric charges emitting 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, which has allowed, among other things, the determination of the elements present in stars). Therefore, it must be admitted that such spectra are characteristic of atoms, and thus that electrons are constituents of atoms. The hypothesis that atoms were simple particles thus collapsed. This most important result will be returned to shortly.
It should also be recalled here that electrons are responsible for the high electrical conductivity of metals: inside metals, in fact, it must be thought that there exist electrons which, at least in first approximation, can be considered free, that is, not stably bound to any atom. These electrons, under the action of the electric field established inside the metal when a certain potential difference is maintained between two points of it, can then be set in motion, giving rise to the electric current. Now, the existence of free electrons inside metals can be demonstrated through direct experiments: if, in fact, a piece of metal is subjected to a strong acceleration, the free electrons, due to their inertia, will shift inside 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. Indeed, the same ratio obtained for electrons through other methods was found (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 possess the property of spontaneously emitting radiations capable of ionizing gases (that is, rendering them electrically conductive by stripping electrons from their molecules). These substances were called radioactive. Studies on radioactive substances gained great momentum following the discovery by the Curie spouses of a particularly radioactive element, which was named 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 named alpha (α) radiations, beta (β) radiations, and gamma (γ) radiations.
Alpha 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 charge, and whose mass is approximately 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 chamber, Geiger counters: the Wilson chamber allows photographing the "tracks" of these particles).
From photographs taken with the Wilson chamber, it can be observed, for example, that these are particles all possessing 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 within a Faraday well and counting their number (note that this measurement can be considered a new determination of Avogadro's number and is in agreement with previous ones). An alpha particle can be considered a helium atom twice ionized: if it captures two electrons, it transforms into a neutral helium atom, as was demonstrated experimentally in a direct manner. Beta radiation, on the other hand, consists of high-energy electrons and is studied with means analogous to those used for particles. Gamma rays are electrically neutral and, as was demonstrated, of the same nature as light, but of extremely high frequency.
Furthermore, it was demonstrated that the emission of these radiations is accompanied by a disintegration of 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 resolved by Rutherford, who used alpha particles as a means of investigation.
As mentioned, it was known that electrons must be part of the atom; since electrons are negatively charged and atoms are neutral, positive charges certainly exist within the atom. The problem was to determine how these positive charges were distributed, with which the principal mass of the atom was also thought to be associated, given that the mass of electrons is negligible. Now, the presence of positive charges in the atom must produce the deflection of alpha particles when they pass through matter ("scattering of alpha particles").
From the extent of this phenomenon, it is indeed possible to infer the distribution of 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 to 10⁻¹⁵ 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 celebrated model of the atom: according to this model (which in its essential concepts can be considered conforming to reality), the atom consists of a central "nucleus" with a radius on the order of 10⁻¹² cm, containing 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 planets around the sun.
V. QUANTIZATION OF ENERGY AND STRUCTURE OF THE ATOM
Several serious difficulties were raised against Rutherford's atomic model, which, upon closer consideration, were merely a particular aspect of a fundamental difficulty encountered when attempting to apply the laws of classical mechanics and electrodynamics—valid (approximately) for macroscopic bodies—to the study of atomic structure. This difficulty can be summarized in the following contradiction: the kinetic theory of heat yields results in agreement with experience as long as atoms are assumed to behave as if they were indivisible particles, whereas radioactive and optical phenomena (Zeeman effect, etc.) demonstrate that atoms are composite particles.The solution to this apparent contradiction was found through the introduction of a new concept in physics: 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 proved highly fruitful in resolving the problem under discussion (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 proportionality constant, the "universal quantum of action," is a universal constant equal to 6.55 × 10⁻²⁷ erg·sec, determined by Planck by comparing his blackbody radiation law with experimental data (Planck also succeeded in determining, in the same manner, Avogadro's number, which appears in his law, obtaining a result in agreement with other measurements).
The "quantum of action h," or Planck's constant, was also determined through other means; Einstein showed that the photoelectric effect, which appeared entirely inexplicable on the basis of classical electrodynamics, could instead be perfectly explained by Planck's hypothesis, and in this way independently determined the constant h in agreement with Planck's own results.
Einstein himself and later Debye applied it to the theory of specific heats of solids at very low temperatures, with highly satisfactory results.
However, the most fruitful application of Planck's hypotheses was made by Bohr in explaining the optical spectra emitted by atoms and the structure of the atom. Since, according to Planck's idea, radiation can only be emitted in discrete quanta by atoms, the atom emitting a quantum of radiation will have an energy, in its final state (after emission), that must differ from the energy of its initial state precisely by the energy of the emitted quantum, which depends solely on its frequency. Since each atom can emit only certain specific frequencies (the frequencies of its characteristic spectrum), it follows that each atom can possess only certain specific energies, whose differences are equal to the quanta of radiation that the atom can emit. This is essentially the idea from which Bohr started. It is very important to note that this idea allows overcoming the apparent contradiction between the kinetic theory of heat and the fact that atoms are not simple particles. Indeed, if the energy of atoms can assume only discrete values, there will exist a certain finite difference between the lowest value that such energy can take (fundamental level) and the immediately subsequent value. Now, if this difference is, as is found to be the case in reality at not excessively high temperatures, much greater than the energy that on average can be transferred in a collision between two atoms in thermal agitation, it is clear that the atom must normally be in the fundamental level and cannot transition to the next level, meaning its internal energy cannot vary due to collisions, just as if the atom were an indivisible particle.
It should be noted that Bohr not only succeeded in overcoming the difficulties encountered by Rutherford but also found an immediate explanation for the general structure of the characteristic spectra emitted by elements, which had remained entirely mysterious on the basis of classical electrodynamics. Moreover, starting from 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 truly extraordinary agreement with experimental data.
VI. X-RAYS AND THE PERIODIC TABLE OF ELEMENTS
Quantum ideas made it possible to account in a relatively simple manner for the natural classification of chemical elements (Mendeleyev’s periodic table), transforming Mendeleyev’s empirical classification (v. CHIMICA) into a rational one, and simultaneously explaining the relationship between this classification and the law of characteristic X-ray spectra of elements discovered by Moseley.The fundamental concept of this rational classification is as follows: it has been stated that atoms are composed of a positively charged nucleus and a certain number of electrons surrounding 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 an electrically neutral state) is also equal to Z; the number Z is called the "atomic number."
Now, practically all chemical properties and at least a large part of the physical properties of elements depend exclusively on the atomic number Z. Elements can therefore be classified rationally by arranging them in order of increasing atomic number.
As previously mentioned, a great aid to this classification came from the study of characteristic X-ray spectra. These rays, discovered by Röntgen, are of the same nature as light radiation.
The demonstration of this fact was provided by Laue. It is known that, to demonstrate the wave nature of light, one can resort to diffraction experiments (v. OTTICA), among which those performed with gratings are particularly notable, allowing for an absolute and very precise measurement of the wavelengths of light radiation.
However, optical gratings are not suitable under ordinary experimental conditions for demonstrating the wave nature of X-rays and measuring their wavelength because the distance between their lines is not sufficiently small.
On the other hand, as Laue observed, there exist in nature gratings that can be used for such measurements: these are crystals. Indeed, according to the fundamental hypothesis of crystallography, crystals are composed of atoms (of the species of elements entering into the chemical composition of the crystal), which are arranged at regular distances from one another, thus forming a true spatial lattice (in reality, the atoms of the crystal are not stationary but oscillate due to thermal agitation around the nodes of the crystal lattice). The distance between successive atoms in a crystal can be calculated based on Avogadro’s number and is of the order of 10⁻⁸ cm. Laue then predicted that by directing X-rays onto a crystal, diffraction phenomena analogous to those observed with light and optical gratings could be observed. The experiment fully confirmed this prediction, thus providing experimental proof of the wave nature of X-rays and the correctness of views on the structure of crystalline bodies. Definitive confirmation was later obtained when diffraction phenomena of X-rays were also observed using optical gratings, employed with a particular technique (grazing incidence). This led to an absolute measurement of the wavelength of X-rays and, by comparison with experiments conducted with crystals, allowed for the absolute measurement of distances between atoms in crystals, yielding results in agreement with those predicted based on Avogadro’s number.
It thus became 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, also emits a characteristic X-ray spectrum. Now, the information provided by this spectrum is particularly valuable because, while optical spectra are emitted by the outermost electrons, X-ray spectra are emitted by the electrons closest to the nucleus, and thus are more directly affected by the nuclear charge, so that their frequencies depend in a simple manner on this nuclear charge, that is, on the atomic number (Moseley’s law). This property of X-rays has also made it possible to discover and identify previously unknown elements, classifying them in their correct place in the periodic table of elements.
Having thus found the rational criterion for classifying elements, it became possible, by applying the Bohr-Sommerfeld quantization conditions and a principle concerning the behavior of electrons discovered by Pauli (exclusion principle), to demonstrate that electrons in each atom are distributed in various electronic "rings," starting from the electrons closest to the nucleus (innermost rings) to the outermost electrons.
It was also demonstrated that chemically homologous elements (found in the same column of Mendeleyev’s table; V. CHIMICA) have their outermost electrons arranged in a similar manner; thus, the explanation for the periodicity in chemical and spectroscopic behaviors, empirically discovered, was found.
VII. THE CONSTITUTION OF THE NUCLEUS; ISOTOPES; THE EQUIVALENCE BETWEEN MATTER AND ENERGY
It has been seen that the properties of the atom depend essentially on the atomic number, that is, 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 that imply a transformation from one chemical species to another (radioactive transmutations) are therefore nuclear transmutations. The great interest in studying the structure of the nucleus is thus understood.
In this regard, it must first be noted that it was discovered, first for radioactive elements and later also for non-radioactive ones (Aston), that atoms with the same atomic number but different atomic weights can exist; that is, nuclei with the same charge but different masses can exist. This was observed by measuring the charge-to-mass ratio of ions (electrically charged atoms) of the same element using methods substantially analogous to those used to measure the charge-to-mass ratio of electrons; these methods were so perfected as to constitute a direct means of "weighing" atoms with great precision.
Elements having the same atomic number but different masses were called isotopes.
The most notable result obtained by Aston regarding isotopes was the following: the mass of each isotope can be expressed by a nearly integer number if the mass of the oxygen atom is taken as 16.
This result immediately suggested the hypothesis that the nuclei of different elements were composed of a different number of identical particles.
This hypothesis was later refined and assumed definitive value with the discovery of a new type of particle, which can, up to now, be considered elementary, having the following fundamental properties: a mass comparable to that of the hydrogen atom (slightly greater), no electric charge, and dimensions of the order of those of the hydrogen nucleus. This particle was called the "neutron," and in essence, apart from the electric charge, it can be considered entirely analogous to the nucleus of hydrogen (which had previously been called the "proton"); indeed, according to modern views, the proton and neutron must be considered the same particle (the so-called "heavy particle" or "nucleon") in two different states.
Neutrons can be detected essentially in two ways: a) through collisions of these particles with protons, observing the recoiling protons (so-called recoil protons); b) by observing the transformations that such particles can induce in nuclei.
In this regard, it should be noted that Rutherford had already succeeded, by striking nuclei with α particles, in producing artificial disintegration. Later, Joliot and Curie demonstrated that, still using α particles, certain nuclei could be rendered radioactive (artificial radioactivity). Fermi showed that, using neutrons, this phenomenon could be observed with an extremely higher frequency. This phenomenon can therefore serve to detect neutrons.
Following the discovery of neutrons, it was understood that all nuclei must be considered as composed exclusively of neutrons and protons in varying numbers, specifically a number of protons equal to the atomic number and a number of neutrons equal to the atomic weight (relative to oxygen = 16) minus the atomic number.
However, it must be observed that if the masses of all the protons and neutrons that make up a nucleus are summed, a mass somewhat greater than that of the nucleus is obtained. This fact does not constitute a difficulty; rather, 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. RELATIVISMO). According to this view, every quantity of energy possesses a mass proportional to it and vice versa.
Now, since the nuclei of elements existing in nature are highly stable complexes, this means that the particles constituting them (protons and neutrons) are bound together by considerable forces, and a certain amount of work must be supplied to separate them. This amount 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 free protons and neutrons and that of the nucleus.
It should be noted that this is not merely an induction or hypothesis. Indeed, it has already been mentioned that nuclear transmutations can be induced in various ways, for example, by bombarding nuclei with α particles or neutrons; other transmutations are obtained by bombarding with protons, γ rays, or other particles.
Thus, "reactions" can be induced in nuclei that are in some ways analogous to ordinary chemical reactions, and in which, as in chemical reactions, the development or absorption of certain quantities of energy can occur. However, in nuclear reactions, the energies involved per elementary process are normally incomparably greater than those involved in chemical reactions.
Now, these energies are precisely determinable, and it can then be observed 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 based on Einstein's equivalence relation and vice versa. Nuclear reactions thus 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 enormous practical importance because it has enabled the utilization of nuclear energy.
VIII. THE DUAL CORPUSCULAR 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 this idea also raised, for some time, very serious difficulties.Perhaps the principal among these difficulties concerned the nature of electromagnetic radiation. Indeed, in certain phenomena, this radiation behaves not only as if it were emitted or absorbed in indivisible quanta, as Planck's hypothesis required, but also as if it propagated in the form of "granules" of energy (photons), each equal to a quantum of Planck's energy: this behavior, for example, could appear evident in the scattering of radiation by free electrons, an effect (the Compton effect) that can be precisely described as an elastic collision between a photon and an electron.
On the other hand, there exist phenomena (interference, diffraction, etc.) that are entirely incompatible with the hypothesis that radiation consists of corpuscles, even if traveling at the speed of light, but possessing the properties of ordinary corpuscles.
This contradiction was overcome thanks to the work of several physicists (De Broglie, Heisenberg, Schrödinger, Born, Jordan, Dirac, Bohr), which led to a profound revolution in the fundamental conceptions of physics.
First, it was established that the duality of corpuscular and wave aspects is not peculiar to radiation but is also characteristic of matter: this consequence of the theory was experimentally verified in a direct manner by observing diffraction phenomena produced by crystals on electrons, analogous to the diffraction phenomena found with X-rays (diffraction phenomena were later observed also for heavy particles); the quantization conditions of Bohr and Sommerfeld, which had remained somewhat arbitrary, were derived and specified as consequences valid in particular and limited cases of the more general theory; thus, exact quantitative criteria were successfully applied to the theory of atomic constitution where the old theory of Bohr and Sommerfeld had failed quantitatively and provided only qualitative indications; the nature of the forces binding atoms together in the molecule, i.e., chemical forces, was discovered; a unified theory of both the wave and corpuscular effects of radiation was given. Finally, various new phenomena were predicted, later confirmed by experience, among which the existence of the positive electron (equal in mass to the negative electron but with a positive charge) is recalled, which was found in artificial radioactivity and cosmic radiation, and an interesting phenomenon concerning these particles was predicted, 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 the transformation of energy into matter: it can be observed experimentally, as can the opposite phenomenon, the annihilation of a pair of electrons 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 unsustainability of the hypothesis of physical determinism, at least as classically conceived, and of the essentially probabilistic meaning of physical laws. Thus, the concept was reaffirmed and specified that the laws of classical and macroscopic physics are merely approximate laws, deducible as limiting cases, when Planck's constant can be considered null, of 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 precisely defined and to reveal its fundamental importance in physics with the discovery of the equivalence between heat and mechanical work (first principle of thermodynamics), which allowed the enunciation of the fundamental principle of the conservation of energy: at the foundation of this principle lies the conception that the various 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 into each other.
Since the distinction between the different forms of energy must thus be considered phenomenological in character, for every isolated physical system one can define in an exact and general manner only the total energy, which, as already stated, remains constant 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 merged with that of the conservation of mass into a single principle of entirely general validity.