Dualism of wave and corpuscular properties of radiation. Wave-particle duality

Wave-particle duality– the property of any microparticle to detect signs of a particle (corpuscle) and a wave. The wave-particle duality is most clearly manifested in elementary particles. An electron, a neutron, a photon, under some conditions, behave like well-localized material objects (particles) in space, moving with certain energies and impulses along classical trajectories, and in others, like waves, which is manifested in their ability to interfere and diffraction. Thus, an electromagnetic wave, scattering on free electrons, behaves like a stream of individual particles - photons, which are quanta of the electromagnetic field (Compton effect), and the momentum of the photon is given by the formula p = h/λ, where λ is the length of the electromagnetic wave, and h is Planck’s constant . This formula in itself is evidence of dualism. In it, on the left is the momentum of an individual particle (photon), and on the right is the wavelength of the photon.

The duality of electrons, which we are accustomed to consider as particles, is manifested in the fact that when reflected from the surface of a single crystal, a diffraction pattern is observed, which is a manifestation of the wave properties of electrons. The quantitative relationship between the corpuscular and wave characteristics of an electron is the same as for a photon: р = h/λ (р is the momentum of the electron, and λ is its de Broglie wavelength). Wave-particle duality is the basis of quantum physics.

Wave (fur) is a process always associated with a material environment that occupies a certain volume in space.

64. De Broglie waves. Electron diffraction Wave properties of microparticles. The development of ideas about the corpuscular-wave properties of matter received in the hypothesis about the wave nature of the movement of microparticles. Louis de Broglie, from the idea of symmetry in nature for particles of matter and light, attributed to any microparticle a certain internal periodic process (1924). Combining the formulas E = hν and E = mc 2, he obtained a relation showing that any particle has its own : λ B = h/mv = h/p, where p is the momentum of the wave-particle. For example, for an electron with an energy of 10 eV, the de Broglie wavelength is 0.388 nm. Subsequently, it was shown that the state of a microparticle in quantum mechanics can be described by a certain complex wave function coordinates Ψ(q), and the squared modulus of this function |Ψ| 2 defines the probability distribution of coordinate values. This function was first introduced into quantum mechanics by Schrödinger in 1926. Thus, the de Broglie wave does not carry energy, but only reflects the “phase distribution” of some probabilistic periodic process in space. Consequently, the description of the state of microworld objects is probabilistic nature, in contrast to objects of the macroworld, which are described by the laws of classical mechanics.

To prove de Broglie's idea about the wave nature of microparticles, the German physicist Elsasser proposed using crystals to observe electron diffraction (1925). In the USA, K. Davisson and L. Germer discovered the phenomenon of diffraction when an electron beam passes through a plate of nickel crystal (1927). Independently of them, the diffraction of electrons passing through metal foil was discovered by J.P. Thomson in England and P.S. Tartakovsky in the USSR. Thus, de Broglie’s idea about the wave properties of matter found experimental confirmation. Subsequently, diffraction, and therefore wave, properties were discovered in atomic and molecular beams. Not only photons and electrons, but also all microparticles have particle-wave properties.

The discovery of the wave properties of microparticles showed that such forms of matter as field (continuous) and matter (discrete), which from the point of view of classical physics were considered qualitatively different, under certain conditions can exhibit properties inherent in both forms. This speaks of the unity of these forms of matter. A complete description of their properties is possible only on the basis of opposing, but complementary, ideas.

Introduction

Almost simultaneously, two theories of light were put forward: Newton's corpuscular theory and Huygens' wave theory.

According to the corpuscular theory, or theory of outflow, put forward by Newton at the end of the 17th century, luminous bodies emit tiny particles (corpuscles) that fly straight in all directions and, when they enter the eye, cause a sensation of light.

According to the wave theory, a luminous body causes elastic vibrations in a special medium filling the entire cosmic space - the world ether - that propagate in the ether like sound waves in the air.

At the time of Newton and Huygens, most scientists adhered to Newton's corpuscular theory, which quite satisfactorily explained all light phenomena known at that time. The reflection of light was explained similarly to the reflection of elastic bodies upon impact with a plane. The refraction of light was explained by the action of large attractive forces on the corpuscles from a denser medium. Under the influence of these forces, which manifest themselves, according to Newton's theory, when approaching a denser medium, the light corpuscles received acceleration directed perpendicular to the boundary of this medium, as a result of which they changed the direction of movement and at the same time increased their speed. Other light phenomena were explained similarly.

Subsequently, new observations that appeared did not fit into the framework of this theory. In particular, the inconsistency of this theory was discovered when the speed of propagation of light in water was measured. It turned out to be not more, but less than in the air.

At the beginning of the 19th century, Huygens' wave theory, not recognized by his contemporaries, was developed and improved by Young and Fresnel and received universal recognition. In the 60s of the last century, after Maxwell developed the theory of the electromagnetic field, it turned out that light is electromagnetic waves. Thus, the wave mechanistic theory of light was replaced by the wave electromagnetic theory. Light waves (visible spectrum) occupy the range of 0.4–0.7 µm on the electromagnetic wave scale. Maxwell's wave theory of light, which treats radiation as a continuous process, was unable to explain some of the newly discovered optical phenomena. It was supplemented by the quantum theory of light, according to which the energy of a light wave is emitted, distributed and absorbed not continuously, but in certain portions - light quanta, or photons - which depend only on the length of the light wave. Thus, according to modern concepts, light has both wave and corpuscular properties.

Interference of light

Waves that create oscillations at every point in space with a phase difference that does not change over time are called coherent. The phase difference in this case has a constant, but, generally speaking, different value for different points in space. It is obvious that only waves of the same frequency can be coherent.

When several coherent waves propagate in space, the oscillations generated by these waves strengthen each other at some points and weaken each other at others. This phenomenon is called wave interference. Waves of any physical nature can interfere. We will look at the interference of light waves.

Sources of coherent waves are also called coherent. When a certain surface is illuminated by several coherent light sources, alternating light and dark stripes generally appear on this surface.

Two independent light sources, for example two electric lamps, are not coherent. The light waves they emit are the result of the addition of a large number of waves emitted by individual atoms. The emission of waves by atoms occurs randomly, and therefore there are no constant relationships between the phases of the waves emitted by two sources.

When the surface is illuminated by incoherent sources, the pattern of alternating light and dark stripes characteristic of interference does not appear. The illumination at each point turns out to be equal to the sum of the illumination created by each of the sources separately.

Coherent waves are produced by splitting a beam of light from one source into two or more separate beams.

Interference of light can be observed when illuminating a transparent plate of variable thickness, in particular a wedge-shaped plate, with monochromatic (one-color) rays. The observer's eye will receive waves reflected from both the front and back surfaces of the plate. The result of interference is determined by the phase difference between the two waves, which gradually changes with the thickness of the plate. The illumination changes accordingly: if the difference in the path of the interfering waves at a certain point on the surface of the plate is equal to an even number of half-waves, then at this point the surface will appear light; if the phase difference is an odd number of half-waves, it will appear dark.

When a plane-parallel plate is illuminated by a parallel beam, the phase difference of the light waves reflected from its front and rear surfaces is the same at all points - the plate will appear uniformly illuminated.

Around the point of contact of a slightly convex glass with a flat one, when illuminated with monochromatic light, dark and light rings are observed - the so-called Newton's rings. Here, the thinnest layer of air between both glasses plays the role of a reflective film, having a constant thickness along concentric circles.

Diffraction of light.

A light wave does not change the geometric shape of the front when propagating in a homogeneous medium. However, if light propagates in an inhomogeneous medium, in which, for example, there are opaque screens, areas of space with a relatively sharp change in the refractive index, etc., then a distortion of the wave front is observed. In this case, a redistribution of the intensity of the light wave occurs in space. When illuminating, for example, opaque screens with a point source of light at the boundary of the shadow, where, according to the laws of geometric optics, there should be an abrupt transition from shadow to light, a number of dark and light stripes are observed; part of the light penetrates into the region of the geometric shadow. These phenomena relate to the diffraction of light.

So, diffraction of light in the narrow sense is the phenomenon of light bending around the contour of opaque bodies and light entering the region of a geometric shadow; in a broad sense, any deviation in the propagation of light from the laws of geometric optics.

Sommerfeld's definition: diffraction of light is understood as any deviation from rectilinear propagation if it cannot be explained as a result of reflection, refraction or bending of light rays in media with a continuously changing refractive index.

If the medium contains tiny particles (fog) or the refractive index changes noticeably over distances of the order of the wavelength, then in these cases we talk about light scattering and the term “diffraction” is not used.

There are two types of light diffraction. By studying the diffraction pattern at an observation point located at a finite distance from an obstacle, we are dealing with Fresnel diffraction. If the observation point and the light source are located so far from the obstacle that the rays incident on the obstacle and the rays going to the observation point can be considered parallel beams, then we talk about diffraction in parallel rays - Fraunhofer diffraction.

The theory of diffraction considers wave processes in cases where there are any obstacles in the path of wave propagation.

Using the theory of diffraction, problems such as noise protection using acoustic screens, the propagation of radio waves over the Earth's surface, the operation of optical instruments (since the image given by a lens is always a diffraction pattern), surface quality measurements, the study of the structure of matter, and many others are solved. .

Polarization of light

The phenomena of interference and diffraction, which served to substantiate the wave nature of light, do not yet provide a complete picture of the nature of light waves. New features are revealed to us by the experience of passing light through crystals, in particular through tourmaline.

Let's take two identical rectangular tourmaline plates, cut so that one of the sides of the rectangle coincides with a certain direction inside the crystal, called the optical axis. Let's put one plate on top of the other so that their axes coincide in direction, and pass a narrow beam of light from a lantern or the sun through the folded pair of plates. Since tourmaline is a brown-green crystal, the trace of the transmitted beam will appear on the screen as a dark green speck. Let's start rotating one of the plates around the beam, leaving the second one motionless. We will find that the trace of the beam becomes weaker, and when the plate is rotated 90 0, it will completely disappear. With further rotation of the plate, the passing beam will again begin to intensify and reach its previous intensity when the plate rotates 180 0, i.e. when the optical axes of the plates are again parallel. With further rotation of the tourmaline, the beam weakens again.

All observed phenomena can be explained if the following conclusions are drawn.

1) Light vibrations in the beam are directed perpendicular to the line of propagation of light (light waves are transverse).

2) Tourmaline is capable of transmitting light vibrations only when they are directed in a certain way relative to its axis.

3) In the light of a lantern (sun), transverse vibrations of any direction are presented and, moreover, in the same proportion, so that no one direction is predominant.

Conclusion 3 explains why natural light passes through tourmaline to the same extent in any orientation, although tourmaline, according to conclusion 2, is only able to transmit light vibrations in a certain direction. The passage of natural light through tourmaline causes the transverse vibrations to be selected only those that can be transmitted by tourmaline. Therefore, light passing through tourmaline will be a set of transverse vibrations in one direction, determined by the orientation of the tourmaline axis. We will call such light linearly polarized, and the plane containing the direction of oscillation and the axis of the light beam - the plane of polarization.

Now the experiment with the passage of light through two successively placed tourmaline plates becomes clear. The first plate polarizes the light beam passing through it, leaving it to oscillate in only one direction. These vibrations can pass through the second tourmaline completely only if their direction coincides with the direction of the vibrations transmitted by the second tourmaline, i.e. when its axis is parallel to the axis of the first. If the direction of vibrations in polarized light is perpendicular to the direction of vibrations transmitted by the second tourmaline, then the light will be completely delayed. If the direction of vibrations in polarized light makes an acute angle with the direction transmitted by tourmaline, then the vibrations will be only partially transmitted.

Light dispersion

Newton turned to the study of colors observed in the refraction of light in connection with attempts to improve telescopes. In an effort to obtain the best quality lenses possible, Newton became convinced that the main drawback of images was the presence of colored edges. Newton made his greatest optical discoveries through his study of coloration during refraction.

The essence of Newton's discoveries is illustrated by the following experiments (Fig. 1) the light from a lantern illuminates a narrow hole S (slit). Using a lens L, the image of the slit is obtained on the screen MN in the form of a short white rectangle S`. By placing a prism P on the path, the edge of which is parallel to the slit, we find that the image of the slit will shift and turn into a colored stripe, the color transitions in which from red to violet are similar to those observed in a rainbow. Newton called this rainbow image a spectrum.

If you cover the gap with colored glass, i.e. if you direct colored light instead of white light to the prism, 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 at different angles from the original image S`. The described observations show that rays of different colors are refracted differently by a prism.

Newton verified this important conclusion through many experiments. The most important of them was to determine the refractive index of rays of different colors isolated from the spectrum. For this purpose, a hole was cut in the screen MN 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 isolating uniform rays is more advanced than isolating using colored glass. Experiments have discovered that such a separated beam, refracted in a 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.

The experiments described show that for a narrow colored beam isolated from the spectrum, the refractive index has a very definite value, while the refraction of white light can only be approximately characterized by one value of this index. Comparing similar observations, Newton concluded that there are simple colors that do not decompose when passing through a prism, and complex colors, which represent a set of simple ones that have different refractive indices. In particular, sunlight is a combination of colors that is decomposed with the help of a prism, giving a spectral image of the slit.

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 color is a collection of simple colors.

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 a substance depends on the wavelength of light.

It usually increases as the wavelength decreases.

Planck's hypothesis

In an effort to overcome the difficulties of classical theory in explaining the radiation of a heated solid, the German physicist Max Planck in 1900. expressed a hypothesis that marked the beginning of a true evolution in theoretical physics. The meaning of this hypothesis is that the energy reserve of an oscillatory system in equilibrium with electromagnetic radiation cannot take on any value. The energy of elementary systems that absorb and radiate electromagnetic waves must necessarily be equal to an integer multiple of some specific amount of energy.

The minimum amount of energy that a system can absorb or emit is called an energy quantum. The energy of the quantum E must be proportional to the oscillation frequency v:

E= hv .

Proportionality factor h in this expression is called Planck's constant. Planck's constant is

6,6261937 . 10 -34 J . With

Planck's constant is sometimes called the quantum of action. Note that the dimension h coincides with the dimension of angular momentum.

Based on this new idea, Planck obtained the law of energy distribution in the spectrum, which is in good agreement with experimental data. The good agreement of the theoretically predicted law with experiment was a thorough confirmation of Planck's quantum hypothesis.

Discovery of the photoelectric effect

Planck's quanta hypothesis served as the basis for explaining the phenomenon of the photoelectric effect, discovered in 1887. German physicist Heinrich Hertz.

The phenomenon of the photoelectric effect is detected by illuminating a zinc plate connected to the rod of an electrometer. If a positive charge is transferred to the plate and rod, then the electrometer does not discharge when the plate is illuminated. By imparting a negative electrical charge to the plate, the electrometer discharges as soon as ultraviolet radiation hits the plate. This experiment proves that negative electrical charges can be released from the surface of a metal plate under the influence of light. Measuring the charge and mass of the particles ejected by the light showed that these particles were electrons.

There are several types of photoeffects: external and internal photoeffects, valve photoeffects and a number of other effects.

The external photoelectric effect is the phenomenon of electrons being ejected from a substance under the influence of light incident on it.

The internal photoelectric effect is the appearance of free electrons and holes in a semiconductor as a result of the breaking of bonds between atoms due to the energy of light incident on the semiconductor.

The gate photoelectric effect is the occurrence under the influence of light of an electromotive force in a system containing contact between two different semiconductors or a semiconductor and a metal.

Laws of the photoelectric effect

The quantitative laws of the photoelectric effect were established by the outstanding Russian physicist Alexander Grigorievich Stoletov (1839 - 1896) in 1888 - 1889. Using a vacuum glass balloon with two electrodes (Fig. 2), he studied the dependence of the current in the balloon on the voltage between the electrodes and the lighting conditions of the electrode.

In a vacuum cylinder there are two metal electrodes A and K, to which voltage is applied. The polarity of the electrodes and the voltage applied to them can be changed using the center-tapped potentiometer R. When the potentiometer slider is to the left of the midpoint, minus is applied to electrode A, and plus is applied to electrode K. The voltage applied between the electrodes is measured with a voltmeter V. Electrode K is irradiated with light through a window covered with quartz glass. Under its influence, electrons (called photoelectrons) are pulled out of this electrode, which fly to electrode A and form a photocurrent, recorded by a milliammeter mA.

In the described installation, using electrodes made of different metals for each illuminated

substances, it is possible to obtain the current-voltage characteristics of the external photoelectric effect (i.e., the dependence of the photocurrent strength I on the voltage U between the electrodes) at different values of the incident light energy flux.

Two such characteristics are presented in (Fig. 3).

The following patterns and laws of the external photoelectric effect have been experimentally established.

1. In the absence of voltage between the electrodes, the photocurrent is non-zero. This means that photoelectrons have kinetic energy when they leave.

2. As U increases, the photocurrent I gradually increases, because an increasing number of photoelectrons reach the anode.

3. When a certain accelerating voltage U n is reached between the electrodes, all electrons knocked out from the cathode reach the anode and the strength of the photocurrent ceases to depend on the voltage. Such a photocurrent, the strength of which does not increase with increasing voltage, is called saturation photocurrent. If the number of photoelectrons emitted from the illuminated metal per unit time is n e, then the strength of the saturation photocurrent

I n = D q / D t = Ne / D t = n e

Therefore, by measuring the strength of the saturation current, it is possible to determine the number of photoelectrons emitted in one second.

4. The strength of the saturation photocurrent is directly proportional to the flux of light energy incident on the metal (the first law of the photoelectric effect):

I n = g F

Here g is the proportionality coefficient, called the photosensitivity of the substance. Consequently, the number of electrons ejected from a substance in one second is directly proportional to the flow of light energy incident on this substance.

5. Due to the initial kinetic energy, electrons can do work against the forces of the retarding electric field. Therefore, photocurrent also exists in the region of negative voltages from 0 to U 3 (electrode A is connected to the “minus” of the current source). Starting from a certain delay voltage U 3, the photocurrent stops. In this case, the work of the retarding electric field A e = eU 3 is equal to the maximum initial kinetic energy of photoelectrons W km. =mv m 2 /2:

A e = W k.m. ; e U 3 = mv m 2 /2

V m = 2e U 3 / m

Thus, by measuring the retardation voltage U 3, it is possible to determine the maximum initial kinetic energy and the maximum initial speed of photoelectrons.

6. The value of the retarding voltage, and therefore the maximum kinetic energy and maximum speed of photoelectrons does not depend on the intensity of the incident light, but depends on its frequency (the second law of the photoelectric effect).

7. For each substance there is a certain frequency value v k (and, therefore, wavelength l k), such that at frequencies v smaller incident light v k (i.e., light wavelengths greater than l k), the photoelectric effect is not observed (third law of the photoelectric effect). Frequency v k (and wavelength l k) is called the red limit of the photoelectric effect. For example, when a zinc plate is irradiated with visible light, even at a very high intensity, the photoelectric effect does not occur, whereas when it is irradiated with ultraviolet light, even at a very low intensity, a photoelectric effect is observed.

8. From the beginning of irradiation of the metal with light until the start of the emission of photoelectrons, time t passes<10 -9 с. Следовательно, фотоэффект безынерционен. Если частота падающего света v > v k, then the emission of photoelectrons occurs almost instantly. If v < v Therefore, no matter how long the metal is illuminated, the photoelectric effect is not observed.

Photons

In relativistic physics (the theory of relativity) it is shown that mass m and energy W are interrelated:

W = mc 2

Therefore, energy quantum Wф=h v electromagnetic radiation corresponds to mass

m f = W f / c 2 = h v / c 2

Electromagnetic radiation, and therefore the photon, exists only when propagating at a speed With. This means that the rest mass of the photon is zero.

Photon, having mass m f and moving with speed With, has momentum

p f = m f c = h v / c

The photon also has its own angular momentum, called spin .

L f= h /2 p= h

An object that has energy, mass, momentum, or angular momentum is most likely associated with a particle. Therefore, the energy quantum of electromagnetic radiation - a photon - is like a particle of electromagnetic radiation, in particular light.

From the fact that electromagnetic radiation is a collection of photons, it follows that the electromagnetic field of a particle is a collection of photons emitted and absorbed by the particle itself.

Within the framework of classical physics, the emission of an interaction carrier by a free particle is prohibited by the laws of conservation of energy and momentum. Quantum physics removes this prohibition using the relationship between the uncertainties of energy and time. Moreover, this establishes a connection between the mass of the interaction carrier and the range of action.

Such processes that proceed as if in violation of the law of conservation of energy are usually called virtual processes, and particles that undergo interaction and cannot have energy and momentum associated in the same way as in free particles are called virtual particles. The virtual exchange particles involved in the interaction cannot be detected. But by increasing the energy of the emitting particle, for example, by accelerating electrons, virtual photons can be turned into real, free ones that can be registered. This is the process of emission of real photons.

This representation of the electromagnetic field leads to a revision of the concept of the interaction of electrically charged particles through an electromagnetic field. If there is another charged particle from a particle, then a photon emitted by one particle can be absorbed by another, and vice versa, resulting in an exchange of photons, i.e. the particles will begin to interact. Thus, the electromagnetic interaction of particles occurs through the exchange of photons. This interaction mechanism is called exchange and applies to all interactions. Any field is a set of quanta - carriers of interactions emitted by an interacting particle, and any interaction is an exchange of carriers of interaction.

In conclusion, we note that the photon is one of the particles from the group of fundamental particles.

The impossibility of explaining the laws of the photoelectric effect on the basis of wave concepts of light.

Attempts have been made to explain the laws of the external photoelectric effect on the basis of wave concepts of light. According to these ideas, the photoelectric effect mechanism looks like this. A light wave falls on the metal. The electrons located in its surface layer absorb the energy of this wave, and their energy gradually increases. When it becomes greater than the work function, electrons begin to fly out of the metal. Thus, the wave theory of light is supposedly capable of qualitatively explaining the phenomenon of the photoelectric effect.

However, calculations showed that with this explanation, the time between the start of illumination of the metal and the start of the emission of electrons should be on the order of ten seconds. Meanwhile, it follows from experience that t<10 -9 c. Следовательно, волновая теория света не объясняет безынерционности фотоэффекта. Не может она объяснить и остальные законы фотоэффекта.

According to the wave theory, the kinetic energy of photoelectrons should increase with increasing intensity of light incident on the metal. And the intensity of the wave is determined by the amplitude of the voltage fluctuations E, and not by the frequency of the light. (Only the number of electrons knocked out and the strength of the saturation current depend on the intensity of the incident light.)

From the wave theory it follows that the energy necessary to tear electrons out of a metal can be provided by radiation of any wavelength if its intensity is high enough, i.e. that the photoelectric effect can be caused by any light radiation. However, there is a red limit to the photoelectric effect, i.e. The energy received by electrons depends not on the amplitude of the wave, but on its frequency.

Thus, attempts to explain the laws of the photoelectric effect on the basis of wave concepts of light turned out to be untenable.

Explanation of the laws of the photoelectric effect based on quantum concepts of light. Einstein's equation for the photoelectric effect.

To explain the laws of the photoelectric effect, A. Einstein used quantum concepts of light, introduced by Planck to describe the thermal radiation of bodies.

Einstein, analyzing fluctuations in the energy of radiation from an absolutely black body, came to the conclusion that the radiation behaves as if it consisted of N=W/(hv) independent energy quanta of magnitude hv each. According to Einstein, during the propagation of light emerging from any point, the energy is not distributed continuously over an ever-increasing space. Energy consists of a finite number of energy quanta localized in space. These quanta move without dividing into parts; they can only be absorbed and emitted as a whole.

Thus, Einstein came to the conclusion that light is not only emitted, but also propagates in space and is absorbed by matter in the form of quanta. Portions of light radiation - light quanta - having corpuscular properties, i.e. properties of particles that are carriers of the properties of the electromagnetic field. These particles are called photons.

From the point of view of quantum concepts of light, the energy of monochromatic radiation incident on a metal consists of photons with energy

W f = h v

W St. = NW f = Nh v

and the light energy flux is equal to

Ф= W St. / t = Nh v / t = n f h v

where N is the number of photons incident on the metal during time t; n f – the number of photons incident on the metal per unit time.

The interaction of radiation with matter consists of a huge number of elementary acts, in each of which one electron completely absorbs the energy of one photon. If the photon energy is greater than or equal to the work function, then the electrons fly out of the metal. In this case, part of the energy of the absorbed photon is spent on performing the work function A in, and the rest constitutes the kinetic energy of the photoelectron. That's why

W f =A in + W To ; h v =A in + mv 2 /2.

This expression is called Einstein's equation for the photoelectric effect.

It shows that the kinetic energy of photoelectrons depends on the frequency of the incident light (the second law of the photoelectric effect).

If the energy of the quanta is less than the work function, then no electrons are emitted at any light intensity. This explains the existence of the red boundary of the photoelectric effect (third law of the photoelectric effect).

Let us now show how the first law of the photoelectric effect is explained on the basis of quantum concepts of light.

The number of electrons released due to the photoelectric effect n e should be proportional to the number of light quanta n f incident on the surface;

n e ~ n f ; n e = kn f ,

where k is a coefficient showing what part of the incident photons knocks electrons out of the metal. (Note that only a small part of the quanta transfers their energy to photoelectrons. The energy of the remaining quanta is spent on heating the substance that absorbs light). The number of photons n f determines the energy flux of the incident light.

Thus, the quantum theory of light completely explains all the laws of the external photoelectric effect. Thus, it is indisputably experimentally confirmed that light, in addition to wave properties, has corpuscular properties.

Corpuscular-wave nature of light

The phenomena of interference, diffraction, and 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. But in these phenomena, light also has wave properties; they are simply not significant for these phenomena.

The question arises: is light a continuous electromagnetic wave emitted by a source, or a stream of discrete photons emitted by a source? The need to attribute to light, on the one hand, quantum, corpuscular properties, and on the other hand, wave properties, can create the impression of imperfection of our knowledge about the properties of light. The need to use different and seemingly mutually exclusive concepts when explaining experimental facts seems artificial. I would like to think that the entire variety of optical phenomena can be explained on the basis of one of two points of view on the properties of light.

One of the most significant achievements of physics of our century is the gradual conviction of the fallacy of attempts to contrast the wave and quantum properties of light with each other. The properties of continuity characteristic of the electromagnetic field of a light wave do not exclude the properties of discreteness characteristic of light quanta - photons. Light simultaneously has the properties of continuous electromagnetic waves and the properties of discrete photons. It represents the dialectical unity of these opposing properties. Electromagnetic radiation (light) is a stream of photons, the propagation and distribution of which in space is described by the equations of electromagnetic waves. Thus, light has a corpuscular-wave nature.

The corpuscular-wave nature of light is reflected in the formula

p f = h v / c = h / l

connecting the corpuscular characteristic of a photon - impulse with the wave characteristic of light - with frequency (or wavelength).

However, the corpuscular-wave nature of light does not mean that light is both a particle and a wave in their usual classical representation.

The relationship between the corpuscular and wave properties of light finds a simple interpretation using a statistical (probable) approach to considering the distribution and propagation of photons in space.

1) Consider the diffraction of light, for example, by a round hole.

If a single photon is passed through the hole, there will not be alternating light and dark stripes on the screen, as would be expected from a wave point of view; the photon hits one point or another on the screen, and does not spread out across it, as it should be according to wave concepts. But at the same time, it is impossible to consider a photon as a particle and calculate exactly what point it hits, which could be done if the photon were a classical particle.

If N photons are passed through a hole one after another, different photons can hit different points on the screen. But in those places where, according to wave concepts, there should be light stripes, photons will fall more often.

If all N photons are passed through the hole at once, then at each point in space and the screen there are as many photons as there were when passing them one at a time. But in this case, the corresponding number of photons hits each point of the screen simultaneously and, if N is large, the diffraction pattern expected from the point of view of wave concepts will be observed on the screen.

For example, for dark interference fringes the squared amplitude of the oscillation and the probability density of photons hitting are minimal, and for light fringes the squared amplitude and the probability density are maximum.

Thus, if light contains a very large number of photons, then under diffraction it can be considered as a continuous wave, although it consists of discrete, unblurred photons.

2) In the phenomenon of the external photoelectric effect, it is important that each photon collides with only one electron (like a particle with a particle) and is absorbed by it, without dividing into parts, as a whole, and not which particular photon hits which particular free electron (this determined by wave properties) and knocks it out. Therefore, with the photoelectric effect, light can be considered as a stream of particles.

The corpuscular-wave nature of electromagnetic radiation was established specifically for light because ordinary sunlight, with which we deal in everyday life, on the one hand, represents a flow of a large number of photons and clearly exhibits wave properties, and on the other hand, photons of light have energy sufficient to carry out such effects as photoionization, photoluminescence, photosynthesis, photoelectric effect, in which corpuscular properties play a decisive role. Photons, corresponding, for example, to radio waves, have low energy, and individual photons do not have noticeable effects, and the recorded radio waves must contain many photons and behave more like waves. g- rays arising from radioactive decays of nuclei and nuclear reactions have high energy, their action is easily recorded, but the flow of a large number of photons is obtained under special conditions in nuclear reactors. Therefore, g-rays often manifest themselves as particles rather than as waves.

So, light is corpuscular in the sense that its energy, momentum, mass and spin are localized in photons, and not diffused in space, but not in the sense that a photon can be located in a given precisely defined location in space. Light behaves like a wave in the sense that the propagation and distribution of photons in space are probabilistic: the probability that a photon is at a given point is determined by the square of the amplitude at that point. But the probabilistic (wave) nature of the distribution of photons in space does not mean that the photon is located at any one point at each moment of time.

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 be considered either as a wave or as particles (corpuscles).

Practical application of light interference

Application of holography in non-destructive testing of materials.

A typical optical diagram of a holographic installation is shown in (Fig. 4). Laser 1 emits a monochromatic beam of light, which is divided into two using a beam splitter plate 2, the beam A and the object wave are directed through a system of mirrors 3 and 7 and lenses 4 and 8 to object 5, is reflected from it and hits photographic plate 6, where it interferes with reference wave B. All elements of the installation are mounted on one rigid surface to avoid even very small movements during the shooting of the hologram. The holographic interferometry method consists of sequentially recording two holograms from one object on one photographic plate, but in the interval between recordings the object is subjected to some kind of influence (mechanical deformation, heating, etc.). As a result, the optical path length of the object waves reflected before and after the impact turns out to be different, an additional path difference arises and, accordingly, a certain phase shift of both waves.

When reading such a hologram, both object waves are reproduced and interfere. If the deformation of the object is small (comparable to the wavelength l), then the image of the object will be clear, but covered with interference fringes, the width and shape of which make it possible to quantitatively describe the deformation of the object, since the appearance of the fringes at each point on the surface is proportional to the change in the optical path length.

Holographic interferometry is also used to detect defects if they (cracks, voids, inhomogeneity of material properties, etc.) lead to abnormal deformation of the surface of an object under loading. Deformations are detected by changes in the interference pattern compared to the pattern that appears without a defective sample.

Holographic interference non-destructive testing uses various loading methods. For example, under mechanical loading, microcracks several millimeters long are detected and localized, both on the surface of the material and in its vicinity. Such studies are carried out, in particular, to detect cracks in concrete and monitor their growth.

Holographic interferometry is used to study the quality of joints in hollow structures, then pressure loading and vacuum loading are used. The deformation in defective areas and, therefore, the interference patterns are different from the deformation of other areas of the structure.

Thermal loading is often used. This method is based on the study of surface deformations that occur when the surface temperature changes. In the defect zone, the temperature field is distorted, which leads to a local change in deformation and, consequently, to a distortion of the interference pattern. Due to the high sensitivity of holographic interferometry, recorded deformations appear when the temperature of the object changes by only a few degrees compared to the ambient temperature.

Application of photoelectric effect

The simplest device that operates using the photoelectric effect is a vacuum photocell. A vacuum photocell consists of a glass bulb equipped with two electrical leads. The inner surface of the flask is partially covered with a thin layer of metal. This coating serves as the cathode of the photocell. The anode is located in the center of the cylinder. The cathode and anode terminals are connected to a constant voltage source. When the cathode is illuminated, electrons are released from its surface. This process is called the external photoelectric effect. Electrons move under the influence of an electric field towards the anode. An electric current arises in the photocell circuit; the current strength is proportional to the power of light radiation. Thus, the photocell converts the energy of light radiation into the energy of electric current.

Semiconductor photocells are also used to convert the energy of light radiation into the energy of electric current.

The semiconductor element has the following structure. A thin layer of electronically conducting semiconductor is created in a flat crystal of silicon or other hole-conducting semiconductor. A p–n junction occurs at the interface between these layers. When a semiconductor crystal is illuminated, as a result of light absorption, the energy distribution of electrons and holes changes. This process is called the internal photoelectric effect. As a result of the internal photoelectric effect, the number of free electrons and holes in the semiconductor increases, and they are separated at the p–n junction boundary.

When opposite layers of a semiconductor photocell are connected by a conductor, an electric current arises in the circuit; The current strength in the circuit is proportional to the power of the luminous flux incident on the photocell.

Switching on the photocell in series with the winding of the electromagnetic relay allows you to automatically turn on or off the actuators when light hits the photocell. Photocells are used in cinema to reproduce sound recorded on film as a soundtrack.

Semiconductor photocells are widely used on artificial Earth satellites, interplanetary automatic stations and orbital stations as power plants, with the help of which solar radiation energy is converted into electrical energy. The efficiency of modern semiconductor photovoltaic generators exceeds 20%.

Semiconductor photocells are increasingly used in everyday life. They are used as non-renewable current sources in watches and microcalculators.

Introduction 3

Interference 4

Diffraction 5

Polarization 6

Variance 8

Planck's conjecture 9

Discovery of Photo Effect 10

Laws of the photoelectric effect 11

Photons 14

The impossibility of explaining the photoelectric effect on the basis of wave concepts of light 15

Explanation of the laws of the photoelectric effect based on quantum concepts of light. Einstein's equation for the photoelectric effect 16

Corpuscular – wave nature of light 18

Practical application of light interference 21

Application of photoelectric effect 23

References 25

Moscow State Academy of Water Transport

Department of Physics and Chemistry

Abstract on the concept of modern natural science (in physics)

on the topic of:

“Wave-particle duality, its significance in theory and experimental confirmation”

Completed:

2nd year student

MVT-4 groups

Teacher:

Kobranov.M.E

Moscow 2001

Bibliography:

Gribov L.A. Prokofieva N.I., “Fundamentals of Physics”, ed. Science 1995

Zhibrov A.E., Mikhailov V.K., Galtsev V.V., “Elements of quantum mechanics and atomic physics”, MISI im. V.V Kuibysheva, 1984

Shpolsky I.V., “Atomic Physics”, ed. Science, 1974

Gursky I.P., “Elementary physics”, Edited by Savelyev I.V., 1984.

"Elementary textbook of physics", Ed. Landsberg G.S., 1986

Kabardin O.F., “Physics”, ed. Education.

Savelyev I.V., “Course of General Physics”, ed. Science, 1988

Content.

Introduction.
Wave properties of light.

a) Dispersion.

b) Diffraction.

c) Polarization

Quantum properties of light.

a) Photoelectric effect.

b) Compton effect.

5. Conclusion.

6. List of used literature.

Introduction.

Already in ancient times, three main approaches to solving the question of the nature of light were outlined. These three approaches subsequently took shape in two competing theories - the corpuscular and wave theories of light.

The vast majority of ancient philosophers and scientists viewed light as certain rays connecting a luminous body and the human eye. At the same time, some of them believed that the rays emanate from the eyes of a person, they seem to feel the object in question. This point of view had a large number of followers, among whom was Euclid. Formulating the first law of geometric optics, the law of rectilinear propagation of light,Euclid wrote: “The rays emitted by the eyes travel along a straight path.” Ptolemy and many other scientists and philosophers held the same view.

However, later, already in the Middle Ages, this idea of the nature of light loses its meaning. There are fewer and fewer scientists who follow these views. And by the beginning of the 17th century. this point of view can be considered already forgotten. 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 the atomists Democritus, Epicurus, and Lucretius.

The latter point of view on the nature of light later, in the 17th century, took shape in the corpuscular theory of light, according to which light is a stream of some particles emitted by a luminous body.

The third point of view on the nature of light was expressed by Aristotle. He considered light as an action or movement propagating in space (in a medium). Few people shared Aristotle's opinion in his time. But later, again in the 17th century, his point of view was developed and laid the foundation for the wave theory of light.

By the middle of the 17th century, facts had accumulated that pushed scientific thought beyond the boundaries of geometric optics. One of the first scientists who pushed scientific thought towards the theory of the wave nature of light was the Czech scientist Marzi. His work is known not only in the field of optics, but also in the field of mechanics and even medicine. In 1648 he discovered the phenomenon of light dispersion.

In the 17th century In connection with the development of optics, the question of the nature of light began to attract more and more interest. In this case, the formation of two opposing theories of light gradually occurs: corpuscular and wave. There was more favorable soil for the development of the corpuscular theory of light. Indeed, for geometric optics the idea that light is a stream of special particles was quite natural. The rectilinear propagation of light, as well as the laws of reflection and refraction, were well explained from the point of view of this theory.

The general idea of the structure of matter also did not conflict with the corpuscular theory of light. At that time, views on the structure of matter were based on atomism. All bodies are made of atoms. There is empty space between atoms. In particular, it was then believed that interplanetary space was empty. Light from celestial bodies propagates in it in the form of streams of light particles. Therefore, it is quite natural that in the 17th century. there were many physicists who adhered to the corpuscular theory of light. At the same time, the idea of the wave nature of light began to develop. Descartes can be considered the founder of the wave theory of light.

Unity of corpuscular and wave properties of electromagnetic radiation.

The phenomena discussed in this section - black body radiation, photoelectric effect, Compton effect - serve as evidence of quantum (corpuscular) concepts of light as a stream of photons. On the other hand, phenomena such as interference, diffraction and polarization of light convincingly confirm the wave (electromagnetic) nature of light. Finally, pressure and refraction of light are explained by both wave and quantum theories. Thus, electromagnetic radiation reveals an amazing unity of seemingly mutually exclusive properties - continuous (waves) and discrete (photons), which complement each other.

A more detailed examination of optical phenomena leads to the conclusion that the properties of continuity characteristic of the electromagnetic field of a light wave should not be opposed to the properties of discreteness characteristic of a photon. Light, possessing both corpuscular and wave properties, reveals certain patterns in their manifestation. Thus, the wave properties of light are manifested in the laws of its propagation, interference, diffraction, polarization, and the corpuscular properties - in the processes of interaction of light with matter. The longer the wavelength, the lower the energy and momentum of the photon and the more difficult it is to detect the quantum properties of light (for example, the existence of the red boundary of the photoelectric effect is connected with this). On the contrary, the shorter the wavelength, the greater the energy and momentum of the photon and the more difficult it is to detect the wave properties (for example, the wave properties (diffraction) of X-ray radiation were discovered only after using crystals as a diffraction grating).

The relationship between the dual particle-wave properties of light can be explained if we use, as quantum optics does, a statistical approach to considering the laws of viewing light. For example, diffraction of light by a slit consists in the fact that when light passes through the slit, photons are redistributed in space. Since the probability of photons hitting different points on the screen is not the same, a diffraction pattern arises. The illumination of the screen is proportional to the probability of photons hitting per unit area of the screen. On the other hand, according to the wave theory, illumination is proportional to the square of the amplitude of the light wave at the same point on the screen. Hence, The square of the amplitude of a light wave at a given point in space is a measure of the probability of photons hitting a given point.

Wave properties of light.

1.1 Dispersion.

The essence of Newton's discoveries is illustrated by the following experiments (Fig. 1) the light from a lantern illuminates a narrow hole S (slot). Using a lens L the image of the slit is obtained on the screen MN in the form of a short white rectangle S `. By placing a prism in the way P , the edge of which is parallel to the slit, we will find that the image of the slit will shift and turn into a colored stripe, the color transitions in which from red to violet are similar to those observed in a rainbow. Newton called this rainbow image a spectrum.

If you cover the gap with colored glass, i.e. if you direct colored light instead of white light to the prism, 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 at different angles from the original image S `. The described observations show that rays of different colors are refracted differently by a prism.

Newton verified this important conclusion through many experiments. The most important of them was to determine the refractive index of rays of different colors isolated from the spectrum. For this purpose in the screen MN , on which the spectrum is obtained, a hole was cut; 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 isolating uniform rays is more advanced than isolating using colored glass. Experiments have discovered that such a separated beam, refracted in a 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 color is a collection of simple colors.

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 a substance depends on the wavelength of light.

It usually increases as the wavelength decreases.

1.2 Diffraction.

A light wave does not change the geometric shape of the front when propagating in a homogeneous medium. However, if light propagates in an inhomogeneous medium, in which, for example, there are opaque screens, areas of space with a relatively sharp change in the refractive index, etc., then a distortion of the wave front is observed. In this case, a redistribution of the intensity of the light wave occurs in space. When illuminating, for example, opaque screens with a point source of light at the boundary of the shadow, where, according to the laws of geometric optics, an abrupt transition from shadow to light should take place, a number of dark and light stripes are observed; part of the light penetrates into the region of the geometric shadow. These phenomena relate to the diffraction of light.

Sommerfeld's definition: diffraction of light is understood as any deviation from linear propagation if it cannot be explained as a result of reflection, refraction or bending of light rays in media with a continuously changing refractive index.

The theory of diffraction considers wave processes in cases where there are any obstacles in the path of wave propagation.

1.3 Polarization

Let's take two identical rectangular tourmaline plates, cut so that one of the sides of the rectangle coincides with a certain direction inside the crystal, called the optical axis. Let's put one plate on top of the other so that their axes coincide in direction, and pass a narrow beam of light from a lantern or the sun through the folded pair of plates. Since tourmaline is a brown-green crystal, the trace of the transmitted beam on the screen will appear in the form of a dark green speck. Let's start rotating one of the plates around the beam, leaving the second one motionless. We will find that the trace of the beam becomes weaker, and when the plate is rotated 90 0, it will completely disappear. With further rotation of the plate, the passing beam will again begin to intensify and reach its previous intensity when the plate rotates 180 0, i.e. when the optical axes of the plates are again parallel. With further rotation of the tourmaline, the beam weakens again.

All observed phenomena can be explained if the following conclusions are drawn.

Light vibrations in the beam are directed perpendicular to the line of propagation of light (light waves are transverse).

Tourmaline is capable of transmitting light vibrations only when they are directed in a certain way relative to its axis.

In the light of a lantern (the sun), transverse vibrations of any direction are presented and, moreover, in the same proportion, so that no one direction is predominant.

Quantum properties of light.

2.1 Photoelectric effect.

Planck's quanta hypothesis served as the basis for explaining the phenomenon of the photoelectric effect, discovered in 1887. German physicist Heinrich Hertz.

There are several types of photoeffects: external and internal photoeffects, valve photoeffects and a number of other effects.

The external photoelectric effect is the phenomenon of electrons being ejected from a substance under the influence of light incident on it.

2.2 Compton effect.

The corpuscular properties of light are most fully manifested in the Compton effect. American physicist A. Compton (1892-1962), studying in 1923 the scattering of monochromatic X-ray radiation by substances with light atoms (paraffin, boron), discovered that in the composition of the scattered radiation, along with radiation of the original wavelength, longer wavelength radiation was also observed.

The Compton effect is the elastic scattering of short-wave electromagnetic radiation (X-rays and gamma radiation) on free (or weakly bound) electrons of a substance, accompanied by an increase in wavelength. This effect does not fit into the framework of the wave theory, according to which the wavelength should not change during scattering: under the influence of the periodic field of a light wave, the electron oscillates with the frequency of the field and therefore emits scattered waves of the same frequency.

An explanation of the Compton effect is given on the basis of quantum concepts about the nature of light. If we assume, as quantum theory does, that radiation is of a corpuscular nature.

The Compton effect is observed not only on electrons, but also on other charged particles, such as protons, however, due to the large mass of the proton, its recoil is “visible” only when very high-energy photons are scattered.

Both the Compton effect and the photoelectric effect based on quantum concepts are caused by the interaction of photons with electrons. In the first case, the photon is scattered, in the second, it is absorbed. Scattering occurs when a photon interacts with free electrons, and the photoelectric effect occurs with bound electrons. It can be shown that when a photon collides with free electrons, absorption of the photon cannot occur, since this is in conflict with the laws of conservation of momentum and energy. Therefore, when photons interact with free electrons, only their scattering can be observed, i.e. Compton effect.

Conclusion.

List of used literature.

1) A.A. Detlaf B.M. Yavorsky "Course of Physics" ed. "Higher School" 2000

2) T.I. Trofimov "Course of Physics" ed. "Higher School" 2001

3) H. Kuhling “Handbook of Physics” ed. "Peace" 1982

4) Gursky I.P. "Elementary Physics" ed. I.V. Savelyeva 1984

5) Tarasov L.V., Tarasova A.N. “Conversations on the refraction of light” / ed. V.A.

Fabrikanta, ed. "Science", 1982.

The discovery of the corpuscular properties of light in experiments on the photoelectric effect, in the Compton experiment and in a number of other experiments cannot cancel the firmly established facts of the presence of wave properties in light, discovered when observing the phenomena of interference, diffraction, and polarization. The fact that light has both wave and particle properties is called wave-particle duality.

The contrasting properties of waves and particles in classical physics makes it unjustified to assert that light is both a wave and a stream of particles. Light is neither a wave nor a stream of particles. The nature of light is more complex and cannot be described without internal contradictions using visual images of classical physics. The meaning of wave-particle dualism of the properties of light is that, depending on the experimental conditions, the nature of light can be approximately described using either wave or corpuscular concepts.

One of the options for reducing the complex nature of light to a simpler one is an attempt to represent a photon in the form of a train of electromagnetic waves limited in space and time, resulting from the addition of a large number of harmonic electromagnetic waves. If this idea of a photon were true, then when a beam of light passed through a plate with a translucent mirror coating, half of each train would be transmitted and half would be reflected. The division of each photon into two could be detected by the simultaneous operation of devices placed in the path of the transmitted and reflected beams of light. However, experience shows that the devices do not operate simultaneously. Either the first of them works, or the second separately. This means that each photon is not divided into two by a plate with a translucent coating, but with equal probability either

is reflected or passes through the plate as a single whole.

The limited applicability of the images of classical physics for describing the properties of light is expressed not only in the fact that wave concepts are suitable for describing the results of some experiments, and corpuscular ones for others, but also in the conventions of using these images in each case. When using corpuscular concepts when describing the photoelectric effect and Compton scattering, we must not forget about the significant differences between the properties of a photon and the properties of particles in classical physics. The rest mass of a photon is zero, the speed of its movement in any inertial frame of reference is the same, and there is no frame of reference in which its speed would be equal to zero. Considering light as a stream of particles - photons, we must use a purely wave characteristic of light - frequency - to determine the mass of a photon. When studying wave phenomena such as interference and diffraction of light, it is necessary to use a photocell or photographic plate to record the interference or diffraction pattern, i.e., use the quantum properties of light to detect its wave properties.

1. What regularities of the photoelectric effect cannot be explained on the basis of the wave theory of light?

2. Explain why the delay of the photoelectric effect follows from the wave theory.

3. Is the kinetic energy of electrons released from a metal under the influence of photons of the same frequency the same?

4. Is it possible to observe the phenomenon of Compton scattering of visible light photons?

5. Is it possible to perform Bothe's experiment using a flashlight bulb and visible light photon counters as a photon source?

If you thought that we had sunk into oblivion with our mind-blowing topics, then we hasten to disappoint you and make you happy: you were mistaken! In fact, all this time we have been trying to find an acceptable method of presenting crazy topics related to quantum paradoxes. We wrote several drafts, but they were all thrown out into the cold. Because when it comes to explaining quantum jokes, we ourselves get confused and admit that we don’t understand a lot (and in general, few people understand this matter, including the world’s cool scientists). Alas, the quantum world is so alien to the philistine worldview that it is not at all a shame to admit your misunderstanding and try a little together to understand at least the basics.

And although, as usual, we will try to talk as clearly as possible with images from Google, the inexperienced reader will need some initial preparation, so we recommend that you look through our previous topics, especially about quanta and matter.
Especially for humanists and other interested people - quantum paradoxes. Part 1.

In this topic we will talk about the most common mystery of the quantum world - wave-particle duality. When we say “the most ordinary,” we mean that physicists have become so tired of it that it doesn’t even seem like a mystery. But this is all because other quantum paradoxes are even more difficult for the average mind to accept.

And it was like this. In the good old days, somewhere in the middle of the 17th century, Newton and Huygens disagreed about the existence of light: Newton shamelessly declared that light is a stream of particles, and old Huygens tried to prove that light is a wave. But Newton was more authoritative, so his statement about the nature of light was accepted as true, and Huygens was laughed at. And for two hundred years light was considered a stream of some unknown particles, the nature of which they hoped to one day discover.

At the beginning of the 19th century, an orientalist named Thomas Young dabbled with optical instruments - as a result, he took and carried out an experiment that is now called Young's experiment, and every physicist considers this experiment sacred.

Thomas Young just directed a beam (of the same color, so that the frequency was approximately the same) of light through two slits in the plate, and placed another screen plate behind it. And showed the result to his colleagues. If light were a stream of particles, then we would see two light stripes in the background.
But, unfortunately for the entire scientific world, a series of dark and light stripes appeared on the plate screen. A common phenomenon called interference is the superposition of two (or more waves) on top of each other.

By the way, it is thanks to interference that we observe rainbow tints on an oil stain or on a soap bubble.

In other words, Thomas Young experimentally proved that light is waves. The scientific world did not want to believe Jung for a long time, and at one time he was so criticized that he even abandoned his ideas of the wave theory. But confidence in their rightness still won, and scientists began to consider light as a wave. True, a wave of what - it was a mystery.
Here, in the picture, is the good old Jung experiment.

It must be said that the wave nature of light did not greatly influence classical physics. Scientists rewrote the formulas and began to believe that soon the whole world would fall at their feet under a single universal formula for everything.
But you already guessed that Einstein, as always, ruined everything. The trouble crept up from the other side - at first scientists got confused in calculating the energy of thermal waves and discovered the concept of quanta (be sure to read about this in our corresponding topic ""). And then, with the help of these same quanta, Einstein struck a blow at physics, explaining the phenomenon of the photoelectric effect.

Briefly: the photoelectric effect (one of the consequences of which is film exposure) is the knocking out of electrons from the surface of certain materials by light. Technically, this knocking out occurs as if light were a particle. Einstein called a particle of light a quantum of light, and later it was given a name - photon.

In 1920, the amazing Compton effect was added to the anti-wave theory of light: when an electron is bombarded with photons, the photon bounces off the electron with a loss of energy (we “shoot” in blue, but the red one flies off), like a billiard ball from another. Compton won the Nobel Prize for this.

This time, physicists were wary of simply abandoning the wave nature of light, but instead thought hard. Science is faced with a terrifying mystery: is light a wave or a particle?

Light, like any wave, has a frequency - and this is easy to check. We see different colors because each color is simply a different frequency of an electromagnetic (light) wave: red is a low frequency, purple is a high frequency.
But it’s amazing: the wavelength of visible light is five thousand times the size of an atom - how does such a “thing” fit into an atom when the atom absorbs this wave? If only the photon is a particle comparable in size to an atom. Is a photon both big and small at the same time?

In addition, the photoelectric effect and the Compton effect clearly prove that light is still a stream of particles: it cannot be explained how a wave transfers energy to electrons localized in space - if light were a wave, then some electrons would be knocked out later than others, and the phenomenon We would not observe the photoelectric effect. But in the case of a flow, a single photon collides with a single electron and, under certain conditions, knocks it out of the atom.

As a result, it was decided: light is both a wave and a particle. Or rather, neither one nor the other, but a new previously unknown form of existence of matter: the phenomena we observe are just projections or shadows of the real state of affairs, depending on how you look at what is happening. When we look at the shadow of a cylinder illuminated from one side, we see a circle, and when illuminated from the other side, we see a rectangular shadow. So it is with the particle-wave representation of light.

But even here everything is not easy. We cannot say that we consider light to be either a wave or a stream of particles. Look out the window. Suddenly, even in cleanly washed glass, we see our own reflection, albeit blurry. What's the catch? If light is a wave, then it is easy to explain reflection in a window - we see similar effects on water when a wave is reflected from an obstacle. But if light is a stream of particles, then reflection cannot be explained so easily. After all, all photons are the same. However, if they are all the same, then the barrier in the form of window glass should have the same effect on them. Either they all pass through the glass, or they are all reflected. But in the harsh reality, some of the photons fly through the glass, and we see the neighboring house and immediately see our reflection.

And the only explanation that comes to mind: photons are on their own. It is impossible to predict with one hundred percent probability how a particular photon will behave - whether it will collide with glass as a particle or as a wave. This is the basis of quantum physics - completely, absolutely random behavior of matter at the micro level without any reason (and in our world of large quantities, we know from experience that everything has a reason). This is a perfect random number generator, unlike a coin toss.

The brilliant Einstein, who discovered the photon, was convinced until the end of his life that quantum physics was wrong, and assured everyone that “God does not play dice.” But modern science increasingly confirms that it does play.

One way or another, one day scientists decided to put an end to the “wave or particle” debate and reproduce Jung’s experience taking into account the technologies of the 20th century. By this time, they had learned to shoot photons one at a time (quantum generators, known among the population as “lasers”), and therefore it was decided to check what would happen on the screen if one shot one particle at two slits: it will finally become clear , what is matter under controlled experimental conditions.

And suddenly - a single quantum of light (photon) showed an interference pattern, that is, the particle flew through both slits at the same time, the photon interfered with itself (in scientific terms). Let's clarify the technical point - in fact, the interference picture was shown not by one photon, but by a series of shots at one particle at intervals of 10 seconds - over time, Young's fringes, familiar to any C student since 1801, appeared on the screen.

From the point of view of the wave, this is logical - the wave passes through the cracks, and now two new waves diverge in concentric circles, overlapping each other.
But from a corpuscular point of view, it turns out that the photon is in two places at the same time when it passes through the slits, and after passing through it mixes with itself. This is generally normal, huh?
It turned out that it was normal. Moreover, since the photon is in two slits at once, it means that it is simultaneously everywhere both before the slits and after flying through them. And in general, from the point of view of quantum physics, the released photon between the start and finish is simultaneously “everywhere and at once.” Physicists call such a finding of a particle “everywhere at once” superposition - a terrible word, which used to be a mathematical pampering, has now become a physical reality.

A certain E. Schrödinger, a well-known opponent of quantum physics, had by this time dug up a formula somewhere that described the wave properties of matter, such as water. And after tinkering with it a little, to my horror, I deduced the so-called wave function. This function showed the probability of finding a photon in a certain location. Note that this is a probability, not an exact location. And this probability depended on the square of the height of the quantum wave crest at a given location (if anyone is interested in the details).

We will devote a separate chapter to the issues of measuring the location of particles.

Further discoveries showed that things with dualism are even worse and more mysterious.
In 1924, a certain Louis de Broglie said that the wave-corpuscular properties of light are the tip of the iceberg. And all elementary particles have this incomprehensible property.
That is, a particle and a wave at the same time are not only particles of the electromagnetic field (photons), but also real particles such as electrons, protons, etc. All matter around us at the microscopic level is waves(and particles at the same time).

And a couple of years later, this was even confirmed experimentally - the Americans drove electrons in cathode ray tubes (which are known to today's old farts under the name "kinescope") - and so observations related to the reflection of electrons confirmed that an electron is also a wave (for ease of understanding, you can say that they placed a plate with two slits in the path of the electron and saw the interference of the electron as it is).

To date, experiments have discovered that atoms also have wave properties, and even some special types of molecules (the so-called “fullerenes”) manifest themselves as waves.

The inquisitive mind of the reader, who has not yet been stunned by our story, will ask: if matter is a wave, then why, for example, is a flying ball not smeared in space in the form of a wave? Why does a jet plane not at all resemble a wave, but is very similar to a jet plane?

De Broglie, the devil, explained everything here: yes, a flying ball or a Boeing is also a wave, but the length of this wave is shorter, the greater the impulse. Momentum is mass times velocity. That is, the greater the mass of matter, the shorter its wavelength. The wavelength of a ball flying at a speed of 150 km/h will be approximately 0.00 meters. Therefore, we are not able to notice how the ball is spread across space as a wave. To us it is solid matter.
An electron is a very light particle and, flying at a speed of 6000 km/sec, it will have a noticeable wavelength of 0.0000000001 meters.

By the way, let’s immediately answer the question why the atomic nucleus is not so “wavelike”. Although it is located in the center of the atom, around which the electron flies crazily and at the same time is smeared, it has a decent momentum associated with the mass of protons and neutrons, as well as high-frequency oscillation (speed) due to the existence of a constant exchange of particles inside the nucleus strong interaction (read the topic). Therefore, the core is more like the solid matter we are familiar with. The electron, apparently, is the only particle with mass that has clearly expressed wave properties, so everyone studies it with delight.

Let's return to our particles. So it turns out: an electron rotating around an atom is both a particle and a wave. That is, the particle rotates, and at the same time, the electron as a wave represents a shell of a certain shape around the nucleus - how can this even be understood by the human brain?

We have already calculated above that a flying electron has a rather huge (for a microcosm) wavelength, and in order to fit around the nucleus of an atom, such a wave needs an indecently large amount of space. This is precisely what explains such large sizes of atoms compared to the nucleus. The wavelengths of the electron determine the size of the atom. The empty space between the nucleus and the surface of the atom is filled by the “accommodation” of the wavelength (and at the same time particle) of the electron. This is a very crude and incorrect explanation - please forgive us - in reality everything is much more complicated, but our goal is to at least allow people who are interested in all this to gnaw off a piece of the granite of science.

Let's be clear again! After some comments on the article [in YP], we realized what an important point this article was missing. Attention! The form of matter we describe is neither a wave nor a particle. It only (simultaneously) has the properties of a wave and the properties of particles. It cannot be said that an electromagnetic wave or an electron wave is like sea waves or sound waves. The waves we are familiar with represent the propagation of disturbances in space filled with some substance.
Photons, electrons and other instances of the microcosm, when moving in space, can be described by wave equations; their behavior is only SIMILAR to a wave, but in no case are they a wave. It’s similar with the corpuscular structure of matter: the behavior of a particle is similar to the flight of small point balls, but these are never balls.
This must be understood and accepted, otherwise all our thoughts will ultimately lead to a search for analogues in the macrocosm and thus the understanding of quantum physics will come to an end, and friarism or charlatan philosophy will begin, such as quantum magic and the materiality of thoughts.

We will consider the remaining terrifying conclusions and consequences of Jung's modernized experiment later in the next part - Heisenberg's uncertainty, Schrödinger's cat, the Pauli exclusion principle and quantum entanglement await the patient and thoughtful reader who will re-read our articles more than once and rummage through the Internet in search of additional information.

Thank you all for your attention. Happy insomnia or cognitive nightmares to everyone!

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