30.12.2015. 14:00
Many who begin to learn physics as in school years and in higher educational institutions, sooner or later they face questions regarding light. Firstly, what I don’t like most about the physics we know today. So this is the interpretation of some concepts, with an absolutely calm facial expression and not paying attention to other phenomena and effects. That is, with the help of some laws or rules they try to explain certain phenomena, but at the same time they try not to notice effects that contradict this explanation. This is already a kind of rule for conducting interpretation - Well, what about this and that? Honey, listen, we're talking about something else now, just don't pay attention. After all, within the framework of this question, everything is beating? Well, that's nice.
The next "Schrödinger's Cat" for any knowledge is KVD (corpuscular wave dualism). When the state of a photon (particle of light) or an electron can be described by both wave effects and corpuscular (particles). As for phenomena indicating the wave properties of matter, everything is more or less clear, except for one thing - the medium in which this same wave is transmitted. But regarding corpuscular properties and especially the presence of such “particles” of light as photons, I have a lot of doubts.
How did people know that light has wave nature? Well, this was facilitated by open effects and experiments with daylight. For example, such a concept as the spectrum of light (visible spectrum of light) where, depending on the wavelength and, accordingly, frequency, the color of the spectrum changes from red to violet, which is what we see with our imperfect eyes. Everything that is behind and in front of it belongs to infrared, radio radiation, ultraviolet, gamma radiation, and so on.
Notice how the picture above shows the spectrum of electromagnetic radiation. Depending on the frequency of the wave of an electromagnetic manifestation, it can be either gamma radiation or visible light and not only, for example, it can even be a radio wave. But what is most surprising in all this is that only the visible spectrum of light, so insignificant in the entire frequency range, for some reason, SUDDENLY and only exclusively, is attributed the properties of particles - photons. For some reason, only the visible spectrum exhibits corpuscular properties. You will never hear about the corpuscular properties of radio waves or, say, gamma radiation; these vibrations do not exhibit corpuscular properties. The concept of “gamma quantum” is only partially applied to gamma radiation, but more on that later.
And what actual phenomena or effects confirm the presence, even if only of the visible spectrum of light, of corpuscular properties? And this is where the most amazing thing begins.
If you believe official science, the corpuscular properties of light are confirmed by two well-known effects. For the discovery and explanation of these effects, Nobel Prizes in physics were awarded to Albert Einstein (photo effect) and Arthur Compton (Compton effect). It should be noted that the question is why the photo effect is not named after Albert Einstein, because it was for him that he received Nobel Prize? And everything is very simple, this effect was discovered not by him, but by another talented scientist (Alexandre Becquerel 1839), Einstein only explained the effect.
Let's start with the photo effect. Where, according to physicists, is there confirmation that light has corpuscular properties?
The photo effect is a phenomenon due to which a substance emits electrons when exposed to light or any other electromagnetic radiation. In other words, light is absorbed by matter and its energy is transferred to electrons, causing them to move in an orderly manner, thus turning into electrical energy.
In fact, it is not clear how physicists came to the conclusion that the so-called photon is a particle, because in the phenomenon of the photoelectric effect it is established that electrons fly out to meet photons. This fact gives an idea of the incorrect interpretation of the phenomenon of the photo effect, since it is one of the conditions for the occurrence of this effect. But according to physicists, this effect shows that a photon is a particle only due to the fact that it is completely absorbed, and also due to the fact that the release of electrons does not depend on the intensity of irradiation but solely on the frequency of the so-called photon. This is why the concept of a light quantum or corpuscle was born. But here we should focus on what “intensity” is in this particular case. After all, solar panels still produce more electricity when the amount of light incident on the surface of the photocell increases. For example, when we talk about the intensity of sound, we mean the amplitude of its vibrations. The greater the amplitude, the greater the energy the acoustic wave carries and the greater the power required to create such a wave. In the case of light, such a concept is completely absent. According to today's understanding of physics, light has a frequency, but no amplitude. Which again raises a lot of questions. For example, a radio wave has amplitude characteristics, but visible light, whose waves are, say, slightly shorter than radio waves, has no amplitude. All this described above only says that such a concept as a photon is, to put it mildly, vague, and all phenomena indicating its existence as their interpretation do not stand up to criticism. Or they are simply invented in support of some hypothesis that this is most likely the case.
As for Compton scattering of light (Compoton effect), it is not at all clear how, based on this effect, the conclusion is made that light is a particle and not a wave.
In general, in fact, today physics does not have concrete confirmation that the photon particle is complete and exists in the form of a particle in principle. There is a certain quantum that is characterized by a frequency gradient and nothing more. And what’s most interesting is that the dimensions (length) of this photon, according to E=hv, can be from several tens of microns to several kilometers. And all this does not confuse anyone when using the word “particle” to refer to a photon.
For example, a femtosecond laser with a pulse length of 100 femtoseconds has a pulse (photon) length of 30 microns. For reference, in a transparent crystal the distance between atoms is approximately 3 angstroms. Well, how can a photon whose magnitude is several times greater than this distance fly from atom to atom?
But today physics does not hesitate to operate with the concept of quantum, photon or particle in relation to light. Simply not paying attention to the fact that it does not fit into the standard model describing matter and the laws by which it exists.
Over the past hundred years, science has made great strides in studying the structure of our world at both the microscopic and macroscopic levels. The amazing discoveries brought to us by the special and general theories of relativity and quantum mechanics still excite the minds of the public. However, anyone educated person it is necessary to understand at least the basics of modern scientific achievements. One of the most impressive and important points is wave-particle duality. This is a paradoxical discovery, the understanding of which is beyond the reach of intuitive everyday perception.
Corpuscles and waves
Dualism was first discovered in the study of light, which behaved completely differently depending on conditions. On the one hand, it turned out that light is an optical electromagnetic wave. On the other hand, a discrete particle ( chemical action Sveta). Initially, scientists believed that these two ideas were mutually exclusive. However, numerous experiments have shown that this is not the case. Gradually, the reality of such a concept as wave-particle duality became commonplace. This concept provides the basis for studying the behavior of complex quantum objects that are neither waves nor particles, but only acquire the properties of the latter or the former depending on certain conditions.
Double slit experiment
Photon diffraction - visual demonstration dualism. The detector of charged particles is a photographic plate or a fluorescent screen. Each individual photon was marked by illumination or a spot flash. The combination of such marks gave an interference pattern - alternation of weakly and strongly illuminated stripes, which is a characteristic of wave diffraction. This is explained by such a concept as wave-particle duality. Famous physicist and Nobel laureate Richard Feynman said that matter behaves on small scales in such a way that it is impossible to feel the “naturalness” of quantum behavior.
Universal dualism
However, this experience is valid not only for photons. It turned out that dualism is a property of all matter, and it is universal. Heisenberg argued that matter exists in both forms alternately. Today it has been absolutely proven that both properties appear completely simultaneously.
Corpuscular wave
How can we explain this behavior of matter? The wave that is inherent in corpuscles (particles) is called the de Broglie wave, named after the young aristocratic scientist who proposed a solution to this problem. It is generally accepted that de Broglie's equations describe a wave function, which, squared, determines only the probability that the particle is in different time at different points in space. Simply put, the de Broglie wave is a probability. Thus, equality was established between the mathematical concept (probability) and the real process.
Quantum field
What are corpuscles of matter? By and large, these are quanta of wave fields. Photon - quantum electromagnetic field, positron and electron - electron-positron, meson - quantum of meson field, and so on. The interaction between wave fields is explained by the exchange of certain intermediate particles between them, for example, during electromagnetic interaction there is an exchange of photons. From this directly follows another confirmation that the wave processes described by de Broglie are absolutely real physical phenomena. And wave-particle dualism does not act as a “mysterious hidden property” that characterizes the ability of particles to “reincarnate.” It clearly demonstrates two interrelated actions - the movement of an object and the wave process associated with it.
Tunnel effect
The wave-particle duality of light is associated with many other interesting phenomena. The direction of action of the de Broglie wave appears during the so-called tunnel effect, that is, when photons penetrate through the energy barrier. This phenomenon is caused by the particle momentum exceeding the average value at the moment of the wave antinode. Tunneling has made it possible to develop many electronic devices.
Interference of light quanta
Modern science speaks about the interference of photons in the same mysterious way as about the interference of electrons. It turns out that a photon, which is an indivisible particle, can simultaneously pass along any path open to itself and interfere with itself. If we take into account that the wave-particle duality of the properties of matter and the photon are a wave that covers many structural elements, then its divisibility is not excluded. This contradicts previous views of the particle as an elementary indivisible formation. Possessing a certain mass of movement, the photon forms a longitudinal wave associated with this movement, which precedes the particle itself, since the speed of the longitudinal wave is greater than that of the transverse electromagnetic wave. Therefore, there are two explanations for the interference of a photon with itself: the particle is split into two components, which interfere with each other; The photon wave travels along two paths and forms an interference pattern. It was experimentally discovered that an interference pattern is also created when single charged particles-photons are passed through the interferometer in turn. This confirms the thesis that each individual photon interferes with itself. This is especially clearly seen when taking into account the fact that light (neither coherent nor monochromatic) is a collection of photons that are emitted by atoms in interconnected and random processes.
What is light?
A light wave is an electromagnetic non-localized field that is distributed throughout space. The electromagnetic field of a wave has a volumetric energy density that is proportional to the square of the amplitude. This means that the energy density can change by any amount, that is, it is continuous. On the one hand, light is a stream of quanta and photons (corpuscles), which, thanks to the universality of such a phenomenon as particle-wave duality, represent the properties of an electromagnetic wave. For example, in the phenomena of interference and diffraction and scales, light clearly exhibits the characteristics of a wave. For example, a single photon, as described above, passing through a double slit creates an interference pattern. With the help of experiments, it was proven that a single photon is not an electromagnetic pulse. It cannot be divided into beams with beam splitters, as the French physicists Aspe, Roger and Grangier showed.
Light also has corpuscular properties, which manifest themselves in the Compton effect and the photoelectric effect. A photon can behave like a particle that is absorbed entirely by objects whose dimensions are much smaller than its wavelength (for example, atomic nucleus). In some cases, photons can generally be considered point objects. It makes no difference from what position we consider the properties of light. In the field of color vision, a stream of light can act as both a wave and a particle-photon as an energy quantum. A spot focused on a retinal photoreceptor, such as the cone membrane, can allow the eye to form its own filtered value as the main spectral rays of light and sort them into wavelengths. According to the quantum energy values, in the brain the object point will be translated into a sensation of color (focused optical image).
Wave and corpuscular properties of elementary particles
Wave properties of light
It has long been known that light has wave properties. Robert Hooke, in his work Micrographia (1665), compares light to the propagation of waves. Christian Huygens published his Treatise on Light in 1690, in which he developed the wave theory of light. It is interesting that Newton, who was familiar with these works, in his treatise on optics convinces himself and others that light consists of particles - corpuscles. Newton's authority for some time even prevented recognition wave theory Sveta. This is all the more surprising since Newton not only heard about the work of Hooke and Huygens, but also himself designed and manufactured an instrument on which he observed the phenomenon of interference, known today to every schoolchild under the name “Newton’s Rings.” The phenomena of diffraction and interference are simply and naturally explained in the wave theory. He, Newton, had to change himself and resort to “inventing hypotheses” of very vague content in order to make the corpuscles move properly.
Newton achieved his greatest success as a scientist in explaining the motion of planets using the laws of mechanics he discovered. Naturally, he tried to use these same laws to explain the movement of light, but in order for this to become possible, light must necessarily consist of corpuscles. If light consists of particles, then the laws of mechanics apply to them, and in order to find the laws of their motion, it remains only to find out what forces act between them and matter. Explaining such diverse phenomena as the motion of planets and the propagation of light using the same principles is a monumental task, and Newton could not deny himself the pleasure of searching for a solution. Modern science does not recognize Newton's corpuscular theory, however, since the publication of Einstein's work on the photoelectric effect, light is generally considered to consist of photon particles. Newton was not mistaken in the fact that the movement of the planets and the propagation of light are governed by certain general principles that were unknown to him.
Let us recall the most well-known experiments, instruments and devices in which the wave nature of light is most clearly manifested.
1. "Newton's rings".
2. Interference of light as it passes through two holes.
3. Interference of light when reflected from thin films.
4. Various instruments and devices: Fresnel biprism, Fresnel mirrors, Lloyd mirror; interferometers: Michelson, Mach-Zehnder, Fabry-Perot.
5. Diffraction of light by a narrow slit.
6. Diffraction grating.
7. Poisson's spot.
All these experiments, instruments, devices or phenomena are well known, so we will not dwell on them. I would like to remind you of just one interesting detail related to the name “Poisson’s spot”. Poisson was an opponent of the wave theory. Considering Fresnel's method, he came to the conclusion that if light is a wave, then there should be a bright spot in the center of the geometric shadow of an opaque disk. Considering that this conclusion was absurd, he put forward it as a convincing objection to the wave theory. However, this absurd prediction was experimentally confirmed by Aragon.
Corpuscular properties of light
Since 1905, science has known that light is not only a wave, but also a stream of particles - photons. It all started with the discovery of the photoelectric effect.
The photoelectric effect was discovered by Hertz in 1887.
1888 - 1889 the phenomenon was experimentally studied by Stoletov.
1898 Lenard and Thompson discovered that the particles emitted by light are electrons.
The main problem that the photoelectric effect posed to scientists was that the energy of electrons ejected from a substance by light does not depend on the intensity of the light incident on the substance. It depends only on its frequency. The classical wave theory could not explain this effect.
1905 Einstein gave a theoretical explanation of the photoelectric effect, for which he received the Nobel Prize in 1921.
According to Einstein's assumption, light consists of photons, the energy of which depends only on frequency and is calculated using Planck's formula: . Light can remove an electron from a substance if the photon has enough energy to do so. In this case, the number of photons that fall on the illuminated surface does not matter. Therefore, the intensity of light does not matter for the onset of the photoelectric effect.
When explaining the photoelectric effect, Einstein used Planck's famous hypothesis. Planck once suggested that light is emitted in portions - quanta. Now Einstein suggested that light, moreover, is absorbed in portions. This assumption was sufficient to explain the photoelectric effect. Einstein, however, goes further. He assumes that light is distributed in portions or photons. There was no experimental basis for such a statement at that time.
The most direct confirmation of Einstein's hypothesis was provided by Bothe's experiment.
In Bothe's experiment, a thin metal foil F was placed between two gas-discharge counters Sch. The foil was illuminated by a weak beam of X-rays, under the influence of which it itself became a source of X-ray radiation. Secondary photons were captured by Geiger counters. When the counter was triggered, the signal was transmitted to the mechanisms M, which made a mark on the moving belt L. If the secondary radiation was emitted in the form of spherical waves, then both counters would have to trigger simultaneously. However, experience showed that the marks on the moving tape were located completely independently of each other. This could only be explained in one way: secondary radiation occurs in the form of individual particles that can fly either in one or in the opposite direction. Therefore, both counters cannot operate simultaneously.
Compton experience
In 1923, Arthur Holly Compton, an American physicist, while studying the scattering of X-rays by various substances, discovered that in the rays scattered by the substance, along with the original radiation, there were rays with a longer wavelength. This behavior of X-rays is only possible from a quantum mechanical point of view. If X-rays consist of quantum particles, then these particles, when colliding with electrons at rest, should lose energy, just as a fast-flying ball loses energy when colliding with a stationary one. The flying ball, having lost energy, slows down. A photon cannot slow down; its speed is always equal to the speed of light; in fact, it itself is light. But since the photon energy is equal to , the photon reacts to the collision by decreasing its frequency.
Let the energy and momentum of the photon before the collision be:
;
Energy and momentum of a photon after scattering by an electron:
;
.
Energy of an electron before colliding with a photon:
Its momentum before the collision is zero - the electron is at rest before the collision.
After the collision, the electron gains momentum and its energy increases accordingly: 
. The last relation is obtained from the equality: 
.
Let us equate the energy of the system before the collision of a photon with an electron to the energy after the collision.
The second equation is obtained from the law of conservation of momentum. In this case, of course, we should not forget that momentum is a vector quantity.
;
Let's transform the energy conservation equation
,
and square the right and left sides
.
We equate the resulting expressions for the squared electron momentum
, from where we get: 
. As usual,
let us introduce the notation 
.
The quantity is called the Compton wavelength of the electron and is denoted . Given these notations, we can write an expression that represents the theoretical derivation of Compton's experimental result: 
.
De Broglie's hypothesis and the wave properties of other particles
In 1924, de Broglie hypothesized that photons were no exception. Other particles, according to de Broglie, should also have wave properties. Moreover, the connection between energy and momentum, on the one hand, and wavelength and frequency, on the other hand, should be exactly the same as for electromagnetic photons.
For photons, . According to de Broglie's assumption, a wave of matter with a frequency and wavelength should be associated with a particle 
.
What kind of wave is this and what is it about physical meaning, de Broglie could not say. Today it is generally accepted that the de Broglie wave has a probabilistic meaning and characterizes the probability of finding a particle at various points in space.
The most interesting thing about this is that the wave properties of particles were discovered experimentally.
In 1927, Davisson and Jammer discovered diffraction of electron beams when reflected from a nickel crystal.
In 1927, son J.J. Thomson and, independently, Tartakovsky obtained a diffraction pattern when an electron beam passed through metal foil.
Subsequently, diffraction patterns were also obtained for molecular beams.
The characterization of the state of electrons in an atom is based on the position of quantum mechanics about the dual nature of the electron, which simultaneously has the properties of a particle and a wave.
For the first time, the dual particle-wave nature was established for light. Studies of a number of phenomena (radiation from hot bodies, the photoelectric effect, atomic spectra) led to the conclusion that energy is emitted and absorbed not continuously, but discretely, in separate portions (quanta). The assumption of energy quantization was first made by Max Planck (1900) and substantiated by Albert Einstein (1905): the quantum energy (∆E) depends on the radiation frequency (ν):
∆E = hν, where h = 6.63·10 -34 J·s – Planck’s constant.
Equating the photon energy hν to its total energy mс 2 and taking into account that ν = с/λ, we obtain a relation expressing the relationship between the wave and corpuscular properties of the photon:
In 1924 Louis de Broglie suggested that the dual corpuscular-wave nature is inherent not only in radiation, but also in any material particle: each particle having mass (m) and moving with speed (υ) corresponds to a wave process with wavelength λ:
λ = h / mυ (55)
The smaller the particle mass, the longer the wavelength. Therefore, it is difficult to detect the wave properties of macroparticles.
In 1927, American scientists Davisson and Germer, Englishman Thomson and Soviet scientist Tartakovsky independently discovered electron diffraction, which was experimental confirmation of the wave properties of electrons. Later, diffraction (interference) of α-particles, neutrons, protons, atoms and even molecules was discovered. Currently, electron diffraction is used to study the structure of matter.
One of the principles of wave mechanics lies in the wave properties of elementary particles: uncertainty principle (W. Heisenberg 1925): for small atomic-scale bodies it is impossible to simultaneously accurately determine the position of a particle in space and its speed (momentum). The more precisely the coordinates of a particle are determined, the less certain its speed becomes, and vice versa. The uncertainty relation has the form:
where ∆х is the uncertainty in the position of the particle, ∆Р x is the uncertainty in the magnitude of the momentum or velocity in the x direction. Similar relationships are written for the y and z coordinates. The quantity ℏ included in the uncertainty relation is very small, therefore for macroparticles the uncertainties in the values of coordinates and momenta are negligible.
Consequently, it is impossible to calculate the trajectory of an electron in the field of a nucleus; one can only estimate the probability of its presence in the atom using wave function ψ, which replaces the classical concept of trajectory. The wave function ψ characterizes the amplitude of the wave depending on the coordinates of the electron, and its square ψ 2 determines the spatial distribution of the electron in the atom. In the simplest version, the wave function depends on three spatial coordinates and makes it possible to determine the probability of finding an electron in atomic space or its orbital . Thus, atomic orbital (AO) is the region of atomic space in which the probability of finding an electron is greatest.
Wave functions are obtained by solving the fundamental relation of wave mechanics - equationsSchrödinger (1926) :
(57)
where h is Planck’s constant, is a variable value, U is the potential energy of the particle, E is the total energy of the particle, x, y, z are the coordinates.
Thus, the quantization of the microsystem energy follows directly from the solution of the wave equation. The wave function completely characterizes the state of the electron.
The wave function of a system is a function of the state of the system, the square of which is equal to the probability density of finding electrons at each point in space. It must satisfy standard conditions: be continuous, finite, unambiguous, and vanish where there is no electron.
An exact solution is obtained for the hydrogen atom or hydrogen-like ions; various approximations are used for multielectron systems. The surface that limits the probability of finding an electron or electron density to 90–95% is called the boundary surface. The atomic orbital and electron cloud density have the same boundary surface (shape) and the same spatial orientation. The atomic orbitals of an electron, their energy and direction in space depend on four parameters - quantum numbers : main, orbital, magnetic and spin. The first three characterize the motion of an electron in space, and the fourth - around its own axis.
Quantum numbern – The main thing . It determines the energy level of an electron in an atom, the distance of the level from the nucleus, and the size of the electron cloud. Accepts integer values from 1 to ∞ and corresponds to the period number. From the periodic table for any element, by the period number, you can determine the number of energy levels of the atom, and which energy level is the outer one. The more n, the greater the energy of interaction between the electron and the nucleus. At n= 1 hydrogen atom is in the ground state, at n> 1 – excited. If n∞, then the electron has left the atomic volume. The ionization of the atom has occurred.
For example, the element cadmium Cd is located in the fifth period, which means n=5. In its atom, electrons are distributed in five energy levels(n = 1, n = 2, n = 3, n = 4, n = 5); the fifth level will be external (n = 5).
Since the electron has, along with the properties of a wave and the properties of a material particle, it, having a mass m, a speed of movement V, and being at a distance from the nucleus r, has an angular momentum: μ = mVr.
Momentum is the second (after energy) characteristic of an electron and is expressed through a secondary (azimuthal, orbital) quantum number.
Orbital quantum numberl- determines the shape of the electron cloud (Fig. 7), the energy of the electron at the sublevel, and the number of energy sublevels. Accepts values from 0 to n– 1. Except for numerical values l It has letter designations. Electrons with the same value l form a sublevel.
In each quantum level, the number of sublevels is strictly limited and equal to the layer number. Sublevels, like energy levels, are numbered in order of their distance from the nucleus (Table 26).
The first ideas of ancient scientists about what light was were very naive. There were several points of view. Some believed that special thin tentacles come out of the eyes and visual impressions arise when they feel objects. This point of view had big number followers, among whom were Euclid, Ptolemy and many other scientists and philosophers. Others, on the contrary, believed that the rays are emitted by a luminous body and, reaching the human eye, bear the imprint of the luminous object. This point of view was held by Lucretius and Democritus.
In the 17th century, almost simultaneously, two completely different theories about what light is and what its nature is. One of these theories is associated with the name of I. Newton, and the other with the name of H. Huygens.
I. Newton adhered to the so-called corpuscular theory of light, according to which light is a stream of particles coming from a source in all directions (matter transfer).
According to the ideas of H. Huygens, light is a stream of waves propagating in a special, hypothetical medium - ether, filling all space and penetrating into all bodies.
Both theories long time existed in parallel. None of them could win a decisive victory. Only the authority of I. Newton forced the majority of scientists to give preference to the corpuscular theory. The laws of light propagation, known at that time from experience, were more or less successfully explained by both theories.
Based on the corpuscular theory, it was difficult to explain why light beams, intersecting in space, do not act on each other. After all, light particles must collide and scatter.
The wave theory easily explained this. Waves, for example, on the surface of water, pass freely through each other without exerting mutual influence.
However, the rectilinear propagation of light, leading to the formation of sharp shadows behind objects, is difficult to explain based on the wave theory. With the corpuscular theory, the rectilinear propagation of light is simply a consequence of the law of inertia.
This uncertainty regarding the nature of light persisted until early XIX century, when the phenomena of light diffraction (light bending around obstacles) and light interference (increasing or weakening of illumination when light beams are superimposed on each other) were discovered. These phenomena are inherent exclusively to wave motion. They cannot be explained using corpuscular theory. The wave properties of light also include light dispersion and polarization. Therefore, it seemed that the wave theory had won a final and complete victory.
This confidence became especially stronger when D. Maxwell showed in the second half of the 19th century that there is light special case electromagnetic waves. The works of D. Maxwell laid the foundations of the electromagnetic theory of light. After the experimental discovery of electromagnetic waves by G. Hertz, there was no doubt that when light propagates, it behaves like a wave. However, at the beginning of the 20th century, ideas about the nature of light began to change radically. Unexpectedly, it turned out that the rejected corpuscular theory was still related to reality. When emitted and absorbed, light behaves like a stream of particles. The wave properties of light could not explain the laws of the photoelectric effect.
An unusual situation has arisen. The phenomena of interference, diffraction, polarization of light from conventional light sources irrefutably indicate the wave properties of light. However, even in these phenomena, under appropriate conditions, light exhibits corpuscular properties. In turn, the laws of thermal radiation of bodies, the photoelectric effect and others indisputably indicate that light behaves not as a continuous, extended wave, but as a flow of “clumps” (portions, quanta) of energy, i.e. like a stream of particles - photons.
Thus, light combines the continuity of waves and the discreteness of particles. If we take into account that photons exist only when moving (at speed c), then we come to the conclusion that light simultaneously has both wave and corpuscular properties. But in some phenomena, under certain conditions, either wave or corpuscular properties play the main role and light can consider either a wave or particles (corpuscles).
The simultaneous presence of wave and corpuscular properties in objects is called wave-particle duality.
Wave properties of microparticles. Electron diffraction
In 1923, the French physicist L. de Broglie put forward a hypothesis about the universality of wave-particle duality. De Broglie argued that not only photons, but also electrons and any other particles of matter, along with corpuscular ones, also have wave properties.
According to de Broglie, each microobject is associated, on the one hand, with corpuscular characteristics - energy E and momentum p, and on the other hand, wave characteristics - frequency ν and wavelength λ .
The corpuscular and wave characteristics of micro-objects are related by the same quantitative relationships as those of a photon:
\(~E = h \nu ;\;\;\; p = \dfrac(h \nu)(c) = \dfrac(h)(\lambda)\) .
De Broglie's hypothesis postulated these relationships for all microparticles, including those that have mass m. Any particle with momentum was associated with a wave process with a wavelength \(~\lambda = \dfrac(h)(p)\) . For particles with mass,
\(~\lambda = \dfrac(h)(p) = \dfrac(h \cdot \sqrt(1 - \dfrac(\upsilon^2)(c^2)))(m \cdot \upsilon)\) .
In the nonrelativistic approximation ( υ « c)
\(~\lambda = \dfrac(h)(m \cdot \upsilon)\) .
De Broglie's hypothesis was based on considerations of the symmetry of the properties of matter and did not have experimental confirmation at that time. But it was a powerful revolutionary impetus for the development of new ideas about the nature of material objects. For several years whole line outstanding physicists XX century - W. Heisenberg, E. Schrödinger, P. Dirac, N. Bohr and others - developed theoretical basis new science, which was called quantum mechanics.
The first experimental confirmation of de Broglie's hypothesis was obtained in 1927 by American physicists K. Davison and L. Germer. They discovered that a beam of electrons scattered by a nickel crystal produced a distinct diffraction pattern similar to that produced by the scattering of short-wave X-rays by the crystal. In these experiments, the crystal played the role of a natural diffraction grating. By position diffraction maxima The wavelength of the electron beam was determined, which turned out to be in full accordance with de Broglie's formula.
The following year, 1928, the English physicist J. Thomson (son of J. Thomson, who discovered the electron 30 years earlier) received new confirmation of de Broglie’s hypothesis. In his experiments, Thomson observed the diffraction pattern that appears when an electron beam passes through a thin polycrystalline gold foil. On a photographic plate installed behind the foil, concentric light and dark rings were clearly observed, the radii of which changed with the electron speed (i.e., wavelength) according to de Broglie.
In subsequent years, J. Thomson's experiment was repeated many times with the same result, including under conditions when the electron flow was so weak that only one particle could pass through the device at a time (V.A. Fabrikant, 1948). Thus, it was experimentally proven that wave properties are inherent not only in a large collection of electrons, but also in each electron individually.
Subsequently, diffraction phenomena were also discovered for neutrons, protons, atomic and molecular beams. Experimental proof of the presence of wave properties of microparticles led to the conclusion that this is a universal natural phenomenon, general property matter. Consequently, wave properties must also be inherent in macroscopic bodies. However, due to the large mass of macroscopic bodies, their wave properties cannot be detected experimentally. For example, a speck of dust weighing 10 -9 g moving at a speed of 0.5 m/s corresponds to a de Broglie wave with a wavelength of the order of 10 -21 m, i.e. approximately 11 orders of magnitude smaller than the size of atoms. This wavelength lies outside the observable region. This example shows that macroscopic bodies can only exhibit corpuscular properties.
Thus, de Broglie’s experimentally confirmed hypothesis of wave-particle duality radically changed the ideas about the properties of micro-objects.
All micro-objects have both wave and corpuscular properties, however, they are neither a wave nor a particle in the classical sense. Different properties of microobjects do not appear simultaneously, they complement each other, only their totality characterizes the microobject completely. This is the formula formulated by the famous Danish physicist N. Bohr principle of complementarity. We can roughly say that micro-objects propagate like waves and exchange energy like particles.
From the point of view of wave theory, the maxima in the electron diffraction pattern correspond to the highest intensity of de Broglie waves. A large number of electrons fall in the region of the maxima recorded on the photographic plate. But the process of electrons getting into different places on a photographic plate is not individual. It is fundamentally impossible to predict where the next electron will fall after scattering; there is only a certain probability of the electron hitting one place or another. Thus, a description of the state of a microobject and its behavior can only be given on the basis of probability theory.
De Broglie waves are not electromagnetic waves and have no analogies among all types of waves studied in classical physics, because they are not emitted by any wave sources and do not relate to the propagation of any field, such as electromagnetic or any other. They are associated with any moving particle, regardless of whether it is electrically charged or neutral.
