The nature of light is wave and corpuscular properties of light. Corpuscular properties of light

Over the past hundred years, science has made great strides in studying the structure of our world, both at the microscopic and macroscopic levels. The amazing discoveries brought to us by special and general theories of relativity, quantum mechanics still excite the minds of the public. However, any educated person needs 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 not subject to intuitive everyday perception.

Corpuscles and waves

For the first time, dualism was discovered in the study of light, which behaved depending on the conditions in completely different ways. On the one hand, it turned out that light is an optical electromagnetic wave. On the other hand, there is a discrete particle (the chemical action of light). Initially, scientists believed that these two views are 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 is 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.

Experiment with two slits

Photon diffraction is a clear demonstration of dualism. The detector of charged particles is a photographic plate or a luminescent screen. Each individual photon was marked by a flare or point flash. The combination of such marks gave an interference pattern - the alternation of weakly and strongly illuminated stripes, which is a characteristic of wave diffraction. This is explained by such a concept as corpuscular-wave dualism. The famous physicist and Nobel laureate Richard Feynman said that matter behaves on a small scale 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 versions alternately. To date, it has been absolutely proven that both properties manifest themselves completely simultaneously.

corpuscular wave

How to explain such behavior of matter? The wave that is inherent in corpuscles (particles) is called the de Broglie wave, 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 only determines the probability that a particle is at different points in space at different times. Simply put, a de Broglie wave is a probability. Thus, an 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. A photon is a quantum of an electromagnetic field, a positron and an electron are of an electron-positron field, a meson is a quantum of a meson field, and so on. The interaction between wave fields is explained by the exchange between them by some intermediate particles, for example, during electromagnetic interaction, photons are exchanged. This directly implies another confirmation that the wave processes described by de Broglie are absolutely real physical phenomena. And corpuscular-wave 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 manifests itself in the so-called tunnel effect, that is, when photons penetrate through the energy barrier. This phenomenon is due to the excess of the average value by the momentum of the particle at the moment of the antinode of the wave. With the help of tunneling, it was possible to develop a variety of electronic devices.

Interference of light quanta

Modern science speaks about the interference of photons as mysteriously as about the interference of electrons. It turns out that a photon, which is an indivisible particle, can simultaneously pass through any path open to itself and interfere with itself. If we take into account that the corpuscular-wave dualism of the properties of a substance and a photon are a wave that covers many structural elements, then its divisibility is not excluded. This contradicts the previous views on the particle as an elementary indivisible formation. Possessing a certain mass of motion, a photon forms a longitudinal wave associated with this motion, 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 splits into two components, which interfere with each other; the photon wave travels along two paths and forms an interference pattern. It was experimentally found that an interference pattern is also created when single charged photons pass through the interferometer in turn. This confirms the thesis that each individual photon interferes with itself. This is especially clear when taking into account the fact that light (not coherent and not monochromatic) is a collection of photons that are emitted by atoms in mutually unrelated and random processes.

What is light?

A light wave is an electromagnetic non-localized field that is distributed over space. The electromagnetic field of the wave has a volumetric energy density, which 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, due to the universality of such a phenomenon as wave-particle duality, are properties of an electromagnetic wave. For example, in the phenomena of interference and diffraction and in 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 proved that a single photon is not an electromagnetic pulse. It cannot be divided into beams with beam splitters, as shown by the French physicists Aspe, Roger and Grangier.

Light also has corpuscular properties, which are manifested in the Compton effect and in the photoelectric effect. A photon can behave like a particle that is absorbed by whole objects that are much smaller than its wavelength (for example, an atomic nucleus). In some cases, photons can generally be considered point objects. It makes no difference from what position to consider the properties of light. In the field of color vision, a stream of light can perform the functions of both a wave and a particle-photon as an energy quantum. An object point focused on a retinal photoreceptor, such as the cone membrane, can allow the eye to form its own filtered value as the main spectral light beams and sort them by wavelength. According to the values of the quantum energy, in the brain, the subject point will be translated into the sensation of color (focused optical image).

Introduction 2

1. Wave properties of light 3

1.1 Dispersion 3

1.2 Interference 5

1.3 Diffraction. Young's experience 6

1.4 Polarization 8

2. Quantum properties of light 9

2.1 Photoelectric effect 9

2.2 Compton effect 10

Conclusion 11

List of used literature 11

Introduction

The first ideas of ancient scientists about what light is 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 a large number of 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 a luminous object. This point of view was held by Lucretius, Democritus.

At the same time, Euclid formulated the law of rectilinear propagation of light. He wrote: "The rays emitted by the eyes propagate along a straight path."

However, later, already in the Middle Ages, such an idea of the nature of light loses its meaning. Fewer and fewer scientists follow these views. And by the beginning of the XVII century. these points of view can be considered already forgotten.

In the 17th century, almost simultaneously, two completely different theories about what light is and what its nature is began to develop.

One of these theories is associated with the name of Newton, and the other with the name of Huygens.

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 (substance transfer).

According to Huygens' ideas, light is a stream of waves propagating in a special, hypothetical medium, ether, which fills all space and penetrates into all bodies.

Both theories have existed in parallel for a long time. None of them could win a decisive victory. Only the authority of 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.

On the basis of the corpuscular theory, it was difficult to explain why light beams, crossing in space, do not act on each other in any way. After all, light particles must collide and scatter.

The wave theory explained this easily. Waves, for example, on the surface of water, freely pass through each other without 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. Under the corpuscular theory, the rectilinear propagation of light is simply a consequence of the law of inertia.

Such an uncertain position regarding the nature of light persisted until the beginning of the 19th century, when the phenomena of light diffraction (enveloping light around obstacles) and light interference (intensification or weakening of illumination when light beams were superimposed on each other) were discovered. These phenomena are inherent exclusively in wave motion. It is impossible to explain them with the help of corpuscular theory. Therefore, it seemed that the wave theory had won a final and complete victory.

Such confidence was especially strengthened when Maxwell showed in the second half of the 19th century that light is a special case of electromagnetic waves. Maxwell's work laid the foundations for the electromagnetic theory of light.

After the experimental discovery of electromagnetic waves by Hertz, there was no doubt that light behaves like a wave during propagation.

However, in the late 19th century, ideas about the nature of light began to change radically. It suddenly turned out that the rejected corpuscular theory is still relevant to reality.

When emitted and absorbed, light behaves like a stream of particles.

Discontinuous, or, as they say, quantum properties of light have been discovered. An unusual situation has arisen: the phenomena of interference and diffraction can still be explained by considering light as a wave, and the phenomena of radiation and absorption by considering light as a stream of particles. These two seemingly incompatible ideas about the nature of light in the 30s of the 20th century were successfully combined in a new outstanding physical theory of quantum electrodynamics.

1. Wave properties of light

1.1 Dispersion

Being engaged in the improvement of telescopes, Newton drew attention to the fact that the image given by the lens is colored at the edges. He became interested in this and was the first to investigate the diversity of light rays and the resulting color features, which no one had even known before (words from the inscription on Newton's grave) Newton's basic experiment was ingeniously simple. Newton guessed to send a light beam of small cross section to a prism. A beam of sunlight entered the darkened room through a small hole in the shutter. Falling on a glass prism, it refracted and gave on the opposite wall an elongated image with iridescent alternation of colors. Following the centuries-old tradition that the rainbow was considered to consist of seven primary colors, Newton also identified seven colors: purple, blue, cyan, green, yellow, orange and red. Newton called the rainbow strip itself a spectrum.

Closing the hole with red glass, Newton observed only a red spot on the wall, closing it with blue-blue, etc. It followed from this that it was not the prism that colored the white light, as previously assumed. The prism does not change the color, but only decomposes it into its component parts. White light has a complex structure. It is possible to distinguish beams of various colors from it, and only their joint action gives us the impression of a white color. In fact, if using a second prism rotated 180 degrees relative to the first. Collect all the beams of the spectrum, then again you get white light. If we single out any part of the spectrum, for example, green, and force the light to pass through another prism, we will no longer get a further change in color.

Another important conclusion that Newton came to was formulated by him in a treatise on Optics as follows: Light beams that differ in color differ in the degree of refraction Violet rays are most strongly refracted, red ones are less than others. The dependence of the refractive index of light on its color is called dispersion (from the Latin word Dispergo, I scatter).

Newton further improved his observations of the spectrum in order to obtain purer colors. After all, the round colored spots of the light beam that passed through the prism partially overlapped each other. Instead of a round hole, a narrow slit (A) was used, illuminated by a bright source. Behind the slit was a lens (B) that produced an image on the screen (D) in the form of a narrow white stripe. If a prism (C) is placed in the path of the rays, then the image of the slit will be stretched into a spectrum, a colored strip, the color transitions in which from red to violet are similar to those observed in a rainbow. Newton's experience is shown in Fig. 1

If you cover the gap with colored glass, i.e. If you direct colored light at a prism instead of white light, the image of the slit will be reduced to a colored rectangle located at the corresponding place in the spectrum, i.e. depending on the color, the light will deviate to different angles from the original image. The described observation shows that rays of different colors are refracted differently by a prism.

Newton verified this important conclusion by many experiments. The most important of them consisted in determining the refractive index of rays of different colors extracted from the spectrum. For this purpose, a hole was cut in the screen on which the spectrum is obtained; by moving the screen, it was possible to release a narrow beam of rays of one color or another through the hole. This method of highlighting homogeneous rays is more perfect than highlighting with colored glass. Experiments have shown that such a selected beam, refracted in the second prism, no longer stretches the strip. Such a beam corresponds to a certain refractive index, the value of which depends on the color of the selected beam.

Thus, Newton's main experiments contained two important discoveries:

1. Light of different colors is characterized by different refractive indices in a given substance (dispersion).

2. White is a collection of simple colors.

Knowing that white light has a complex structure, one can explain the amazing variety of colors in nature. If an object, for example, a sheet of paper, reflects all the rays of various colors falling on it, then it will appear white. By covering the paper with a layer of paint, we do not create light of a new color, but retain some of the existing light on the sheet. Only red rays will now be reflected, the rest will be absorbed by a layer of paint. Grass and tree leaves appear green to us because of all the sun's rays falling on them, they reflect only green ones, absorbing the rest. If you look at the grass through red glass, which transmits only red rays, it will appear almost black.

We now know that different colors correspond to different wavelengths of light. Therefore, Newton's first discovery can be formulated as follows: the refractive index of matter depends on the wavelength of light. It usually increases as the wavelength decreases.

1.2 Interference

The interference of light was observed for a very long time, but they just did not realize it. Many have seen the interference pattern when they had fun blowing soap bubbles or watching

In the 17th century, almost simultaneously, two completely different theories about what light is and what its nature is began to develop. 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 (substance transfer).

According to the ideas of H. Huygens, light is a stream of waves propagating in a special, hypothetical medium - ether, which fills all space and penetrates into all bodies.

Both theories have existed in parallel for a long time. 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.

On the basis of the corpuscular theory, it was difficult to explain why light beams, crossing in space, do not act on each other in any way. After all, light particles must collide and scatter.

The wave theory explained this easily. Waves, for example, on the surface of water, freely pass through each other without mutual influence.

Such an uncertain position regarding the nature of light persisted until the beginning of the 19th century, when the phenomena of light diffraction (enveloping light around obstacles) and light interference (intensification or weakening of illumination when light beams were superimposed on each other) were discovered. These phenomena are inherent exclusively in wave motion. It is impossible to explain them with the help of corpuscular theory. The wave properties of light also include dispersion of light, polarization. Therefore, it seemed that the wave theory had won a final and complete victory.

Such confidence was especially strengthened when D. Maxwell showed in the second half of the 19th century that light is a special case of 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 light behaves like a wave during propagation. However, at the beginning of the 20th century, ideas about the nature of light began to change radically. It suddenly turned out that the rejected corpuscular theory is still relevant to reality. When emitted and absorbed, light behaves like a stream of particles. The wave properties of light could not explain the patterns of the photoelectric effect.

An unusual situation has arisen. The phenomena of interference, diffraction, polarization of light from ordinary light sources irrefutably testify to the wave properties of light. However, even in these phenomena, under appropriate conditions, light exhibits corpuscular properties. In turn, the regularities of the thermal radiation of bodies, the photoelectric effect and others undeniably indicate that light behaves not as a continuous, extended wave, but as a stream of "clots" (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 (with a speed c), then we come to the conclusion that both wave and corpuscular properties are simultaneously inherent in light. But in some phenomena, under certain conditions, either wave or corpuscular properties play the main role and light can considered either as a wave or as 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 micro-object 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 a mass m. Any particle with momentum was associated with a wave process with a wavelength \(~\lambda = \dfrac(h)(p)\) . For particles that have 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 had no experimental confirmation at that time. But it was a powerful revolutionary impetus to the development of new ideas about the nature of material objects. Over the course of several years, a number of outstanding physicists of the 20th century - W. Heisenberg, E. Schrödinger, P. Dirac, N. Bohr and others - developed the theoretical foundations of a new science, which was called quantum mechanics.

The first experimental confirmation of de Broglie's hypothesis was obtained in 1927 by American physicists K. Devisson and L. Germer. They found that an electron beam scattered by a nickel crystal produced a distinct diffraction pattern similar to that produced by short-wavelength X-rays scattered by the crystal. In these experiments, the crystal played the role of a natural diffraction grating. The position of the diffraction maxima was used to determine the wavelength of the electron beam, which turned out to be in full agreement with the de Broglie formula.

The following year, 1928, the English physicist J. Thomson (the son of J. Thomson, who had discovered the electron 30 years earlier) received a new confirmation of de Broglie's hypothesis. In his experiments, Thomson observed the diffraction pattern that occurs when an electron beam passes through a thin polycrystalline gold foil. On a photographic plate mounted behind a foil, concentric light and dark rings were clearly observed, the radii of which changed with a change in the electron velocity (i.e., wavelength) according to de Broglie.

In subsequent years, the experiment of J. Thomson 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 proved that the wave properties are inherent not only to a large set of electrons, but also to each electron separately.

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 phenomenon of nature, a general property of 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 grain of dust with a mass of 10 -9 g, moving at a speed of 0.5 m / s, corresponds to a de Broglie wave with a wavelength of about 10 -21 m, i.e., approximately 11 orders of magnitude smaller than the size of atoms. This wavelength lies outside the region accessible to observation. 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 microobjects.

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 micro-objects do not manifest themselves simultaneously, they complement each other, only their combination characterizes the micro-object completely. This is the formula formulated by the famous Danish physicist N. Bohr complementarity principle. It can be conditionally said 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 into the region of maxima recorded on a photographic plate. But the process of getting electrons to 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 that an electron will fall into one place or another. Thus, the description of the state of a micro-object and its behavior can only be given on the basis of probability theory.

De Broglie waves are not electromagnetic waves and have no analogy among all types of waves studied in classical physics, because they are not emitted by any source of waves and are not related 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.

30.12.2015. 14:00

Many who begin to learn physics, both in their school years and in higher educational institutions, sooner or later face questions about light. First, what I dislike 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 the effects that contradict this explanation. This is already a kind of rule of interpretation - Well, what about this and that? Honey, listen, we're talking about something else right now, just ignore it. After all, within the framework of this question, everything beats? Well, nice.

The next "Schrödinger's Cat" for any knowledge is CWD (corpuscular wave dualism). When the state of a photon (a particle of light) or an electron can be described by both wave effects and corpuscular (particles). As for the phenomena indicating the wave properties of matter, everything is more or less clear, except for one thing - the medium in which this very wave is transmitted. But regarding the 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 a wave nature? Well, this was facilitated by open effects and experiments with daylight. For example, such a concept as the spectrum of light, (the visible spectrum of light) where, depending on the wavelength and, accordingly, the frequency, the color of the spectrum changes from red to purple, and then we see it with our imperfect eye. Everything behind it and in front of it refers to infrared, radio radiation, ultraviolet, gamma radiation, and so on.

Pay attention to the picture above, which shows the spectrum of electromagnetic radiation. Depending on the frequency of the wave of electromagnetic manifestation, it can be both gamma radiation and visible light and not only, for example, it can even be a radio wave. But what is most surprising in all this, only the visible spectrum of light, so insignificant in the entire frequency range, for some reason, SUDDENLY and only exclusively to it, are 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 fluctuations do not exhibit corpuscular properties. Only partly, the concept of "gamma quantum" is applied to gamma radiation, but more on that later.

And what actual phenomena or effects confirm the presence of corpuscular properties, even if only in the visible spectrum of light? And here the most surprising begins.

According to official science, the corpuscular properties of light are confirmed by two well-known effects. For the discovery and explanation of these effects, the Nobel Prizes in physics were awarded to Albert Einstein (photo-effect), Arthur Compton (Compotne effect). It should be noted with the question - why the photo effect does not bear the name of Albert Einstein, because it was for him that he received the Nobel Prize? And everything is very simple, this effect was discovered not by him, but by another talented scientist (Alexander Becquerel 1839), Einstein only explained the effect.

Let's start with the photo effect. Where, according to physicists, is there evidence that light has corpuscular properties?

The photoelectric effect is a phenomenon due to which electrons are emitted by a substance when it is 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 the photon is just 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. That is why the concept of a quantum of light or a corpuscle was born. But here we should focus on what is "intensity" in this particular case. After all, solar panels still produce more electricity with an increase in the amount of light falling on the surface of the photocell. For example, when we talk about the intensity of sound, we mean the amplitude of its vibrations. The larger the amplitude, the more energy the acoustic wave carries and the more power is needed to create such a wave. In the case of light, such a concept is completely absent. According to today's ideas in 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 scrutiny. Or they are simply invented in support of any hypothesis, which is most likely the case.

As for the Compton scattering of light (the Compoton effect), it is not at all clear how, on the basis of this effect, it is concluded that light is a particle and not a wave.

In general, in fact, today physics does not have a concrete confirmation that the photon particle is full-fledged and exists in the form of a particle in principle. There is a certain quantum which is characterized by a frequency gradient and no more. And what is most interesting, 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 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 fly from atom to atom, the value of which is several times greater than this distance?

But today, physics does not hesitate to operate with the concept of quantum, photon or particle in relation to light. Just not paying attention to the fact that it does not fit into the standard model that describes matter and the laws by which it exists.

The main characteristics of light as a wave process are the frequency n and the wavelength l. The corpuscular properties of light are characterized by photons. Each photon has energy

e f = hn, (5.1)

and momentum

. (5.3)

Formula (5.3) establishes the connection between the wave and corpuscular properties of light.

In this regard, an assumption arose that the dual nature is inherent not only in light, but also in particles of matter, in particular, an electron. In 1924, Louis de Broglie put forward the following hypothesis: a wave process is associated with an electron, the wavelength of which is equal to

where h = 6.63 × 10 –34 J×s is Planck's constant, m is the electron mass, v is the electron velocity.

Calculations have shown that the wavelength associated with a moving electron is of the same order as the wavelength of X-rays (10–10 ¸ 10–13 m).

It can be seen from de Broglie's formula (5.4) that the wave properties of particles are significant only in those cases in which the value of Planck's constant h cannot be neglected. If under the conditions of this problem we can assume that h ® 0, then both l®0 and the wave properties of particles can be neglected.

5.2. Experimental substantiation of corpuscular-wave dualism

De Broglie's hypothesis received experimental confirmation in the experiments of K. Davisson and L. Germer (1927), P.S. Tartakovsky (1927), L.M. Biberman, N.G. Sushkin and V.A. Fabrikant (1949) and others.

In the experiments of Davisson and Germer (Fig. 5.1), electrons from an electron gun were directed in a narrow beam to a nickel crystal, the structure of which is well known.

Fig.5.1. Diagram of Davisson and Germer's experiment

The electrons reflected from the crystal surface hit a receiver connected to a galvanometer. The receiver moved along an arc and caught electrons reflected at different angles. The more electrons entered the receiver, the greater the current was recorded by the galvanometer.

It turned out that at a given angle of incidence of the electron beam and a change in the potential difference U, which accelerates the electrons, the current I did not change monotonously, but had a number of maxima (Fig. 5.2).

Fig.5.2. Dependence of the current strength on the accelerating potential difference in the experiments of Davisson and Germer

The resulting graph indicates that the reflection of electrons occurs not at any, but at strictly defined values of U, i.e. at strictly defined velocities v of electrons. This dependence could be explained only on the basis of ideas about electron waves.

To do this, we express the electron velocity in terms of the accelerating voltage:

and find the de Broglie wavelength of the electron:

(5.6)

For electron waves reflected from a crystal, as well as for X-rays, the Wulf-Braggs condition must be satisfied:

2d sinq = kl, k = 1,2,3,..., (5.7)

where d is the crystal lattice constant, q is the angle between the incident beam and the crystal surface.

Substituting (5.6) into (5.7), we find those values of the accelerating voltage that correspond to the reflection maxima, and, consequently, to the maximum current through the galvanometer:

(5.8)

The values of U calculated by this formula at q=const are in excellent agreement with the results of the experiments of Davisson and Germer.

In the experiments of P.S. Tartakovsky, the crystal was replaced by a thin film of a polycrystalline structure (Fig. 5.3).

Fig.5.3. Scheme of experiments P.S. Tartakovsky

The electrons scattered by the film produced diffraction circles on the screen. A similar picture was observed in the scattering of x-rays by polycrystals. The de Broglie wavelength l of electrons can be determined from the diameters of the diffraction circles. If l is known, then the diffraction pattern makes it possible to judge the structure of the crystal. This method of studying the structure is called electron diffraction.

L.M. Biberman, N.G. Sushkin and V.A. Fabrikant carried out experiments on the diffraction of single, successively flying electrons. Individual electrons hit different points on the screen, seemingly randomly scattered. However, upon scattering of a large number of electrons, it was found that the points of electron impact on the screen are distributed in such a way that they form maxima and minima, i.e. with a long exposure, the same diffraction pattern was obtained, which gives an electron beam. This indicates that each individual electron has wave properties.

Diffraction phenomena were observed in experiments not only with electrons, but also with protons, neutrons, atomic and molecular beams.