photoelectric effect was discovered in 1887 by the German physicist G. Hertz and experimentally studied by A. G. Stoletov in 1888-1890. The most complete study of the phenomenon of the photoelectric effect was carried out by F. Lenard in 1900. By this time, the electron had already been discovered (1897, J. Thomson), and it became clear that the photoelectric effect (or, more precisely, the external photoelectric effect) consists in pulling electrons out of matter under the influence of light falling on it.
The layout of the experimental setup for studying the photoelectric effect is shown in fig. 5.2.1.
The experiments used a glass vacuum vessel with two metal electrodes, the surface of which was thoroughly cleaned. A voltage was applied to the electrodes U, the polarity of which could be changed using a double key. One of the electrodes (cathode K) was illuminated through a quartz window with monochromatic light of a certain wavelength λ. At a constant luminous flux, the dependence of the photocurrent strength was taken I from the applied voltage. On fig. 5.2.2 shows typical curves of such a dependence, obtained for two values of the intensity of the light flux incident on the cathode.
The curves show that at sufficiently high positive voltages at the anode A, the photocurrent reaches saturation, since all the electrons ejected by light from the cathode reach the anode. Careful measurements have shown that the saturation current I n is directly proportional to the intensity of the incident light. When the voltage across the anode is negative, the electric field between the cathode and anode slows down the electrons. The anode can only reach those electrons whose kinetic energy exceeds | EU|. If the anode voltage is less than - U h, the photocurrent stops. measuring U h, it is possible to determine the maximum kinetic energy of photoelectrons:
To the surprise of scientists, the value U h turned out to be independent of the intensity of the incident light flux. Careful measurements have shown that the blocking potential increases linearly with increasing frequency ν of the light (Fig. 5.2.3).
Numerous experimenters have established the following basic laws of the photoelectric effect:
1. The maximum kinetic energy of photoelectrons increases linearly with increasing light frequency ν and does not depend on its intensity.
2. For each substance there is a so-called red border photo effect , i.e., the lowest frequency ν min at which an external photoelectric effect is still possible.
3. The number of photoelectrons pulled out by light from the cathode in 1 s is directly proportional to the light intensity.
4. The photoelectric effect is practically inertialess, the photocurrent occurs instantly after the start of cathode illumination, provided that the light frequency ν > ν min.
All these laws of the photoelectric effect fundamentally contradicted the ideas of classical physics about the interaction of light with matter. According to wave concepts, when interacting with an electromagnetic light wave, an electron would have to gradually accumulate energy, and it would take a considerable time, depending on the intensity of light, for the electron to accumulate enough energy to fly out of the cathode. Calculations show that this time should have been calculated in minutes or hours. However, experience shows that photoelectrons appear immediately after the start of illumination of the cathode. In this model, it was also impossible to understand the existence of the red boundary of the photoelectric effect. The wave theory of light could not explain the independence of the energy of photoelectrons from the intensity of the light flux and the proportionality of the maximum kinetic energy to the frequency of light.
Thus, the electromagnetic theory of light proved unable to explain these regularities.
A way out was found by A. Einstein in 1905. A theoretical explanation of the observed laws of the photoelectric effect was given by Einstein on the basis of M. Planck's hypothesis that light is emitted and absorbed in certain portions, and the energy of each such portion is determined by the formula E = h v, where h is Planck's constant. Einstein took the next step in the development of quantum concepts. He came to the conclusion that light has a discontinuous (discrete) structure. An electromagnetic wave consists of separate portions - quanta, subsequently named photons. When interacting with matter, a photon transfers all of its energy hν to one electron. Part of this energy can be dissipated by an electron in collisions with atoms of matter. In addition, part of the electron energy is spent on overcoming the potential barrier at the metal-vacuum interface. To do this, the electron must make work function A depending on the properties of the cathode material. The maximum kinetic energy that a photoelectron emitted from the cathode can have is determined by the energy conservation law:
This formula is called Einstein's equation for the photoelectric effect .
Using the Einstein equation, one can explain all the regularities of the external photoelectric effect. From the Einstein equation, the linear dependence of the maximum kinetic energy on frequency and independence on light intensity, the existence of a red border, and the inertia of the photoelectric effect follow. Total number photoelectrons leaving the cathode surface in 1 s should be proportional to the number of photons incident on the surface in the same time. It follows from this that the saturation current must be directly proportional to the intensity of the light flux.
As follows from the Einstein equation, the slope of the straight line expressing the dependence of the blocking potential U h from the frequency ν (Fig. 5.2.3), is equal to the ratio of Planck's constant h to the charge of an electron e:
This makes it possible to experimentally determine the value of Planck's constant. Such measurements were made in 1914 by R. Millikan and gave good agreement with the value found by Planck. These measurements also made it possible to determine the work function A:
where c- speed of light, λ cr - wavelength corresponding to the red border of the photoelectric effect. For most metals, the work function A is a few electron volts (1 eV = 1.602 10 -19 J). In quantum physics, the electron volt is often used as a unit of energy. The value of Planck's constant, expressed in electron volts per second, is
Among metals, alkaline elements have the lowest work function. For example, sodium A= 1.9 eV, which corresponds to the red border of the photoelectric effect λcr ≈ 680 nm. Therefore, alkali metal compounds are used to create cathodes in photocells designed to detect visible light.
So, the laws of the photoelectric effect indicate that light, when emitted and absorbed, behaves like a stream of particles called photons or light quanta .
The photon energy is
it follows that the photon has momentum
Thus, the doctrine of light, having completed a revolution lasting two centuries, again returned to the ideas of light particles - corpuscles.
But this was not a mechanical return to Newton's corpuscular theory. At the beginning of the 20th century, it became clear that light has a dual nature. When light propagates, its wave properties appear (interference, diffraction, polarization), and when interacting with matter, corpuscular (photoelectric effect). This dual nature of light is called wave-particle duality about which Lomonosov spoke. Later, the dual nature was discovered in electrons and other elementary particles. Classical physics cannot give a visual model of the combination of wave and corpuscular properties of micro-objects. The motion of micro-objects is controlled not by the laws of classical Newtonian mechanics, but by the laws of quantum mechanics. The black body radiation theory developed by M. Planck and Einstein's quantum theory of the photoelectric effect underlie this modern science.
He expressed a hypothesis: light is emitted and absorbed by separate portions - quanta (or photons). The energy of each photon is determined by the formula E= h ν , where h- Planck's constant, equal to 6.63. 10 -34 J. s, ν is the frequency of the light. Planck's hypothesis explained many phenomena: in particular, the phenomenon of the photoelectric effect, discovered in 1887 by the German scientist Heinrich Hertz and studied experimentally by the Russian scientist A. G. Stoletov.
photoelectric effect — This is the phenomenon of the emission of electrons by a substance under the influence of light.
As a result of the research, three laws of the photoelectric effect were established:
1. The strength of the saturation current is directly proportional to the intensity of light radiation falling on the surface of the body.
2. The maximum kinetic energy of photo-electrons increases linearly with the frequency of light and does not depend on its intensity.
3. If the frequency of light is less than a certain minimum frequency defined for a given substance, then the photoelectric effect does not occur.
The dependence of photocurrent on voltage is shown in Figure 36.
The theory of the photoelectric effect was created by the German scientist A. Einstein in 1905. Einstein's theory is based on the concept of the work function of electrons from a metal and the concept of quantum light emission. According to Einstein's theory, the photoelectric effect has the following explanation: by absorbing a quantum of light, an electron acquires energy hv. When leaving a metal, the energy of each electron decreases by a certain amount, which is called work function(A out). The work function is the work required to remove an electron from a metal. The maximum energy of electrons after departure (if there are no other losses) is: mv 2 / 2 \u003d hv - A out, This equation is called the Einstein equation .
If a hν< And then the photoelectric effect does not occur. Means, red border photo effect is equal to ν min = A out / h
Devices based on the principle of operation of which is the phenomenon of the photoelectric effect are called photo elements. The simplest such device is a vacuum photocell. The disadvantages of such a photocell are: low current, low sensitivity to long-wave radiation, difficulty in manufacturing, impossibility of use in circuits alternating current. It is used in photometry to measure luminous intensity, brightness, illumination, in cinematography for sound reproduction, in phototelegraphs and phototelephones, in the management of production processes.
There are semiconductor photocells in which, under the action of light, the concentration of current carriers changes. They are used for automatic control electric circuits (for example, in subway turnstiles), in alternating current circuits, as non-renewable current sources in watches, microcalculators, the first solar cars are being tested, they are used in solar panels on artificial satellites of the Earth, interplanetary and orbital automatic stations.
The phenomenon of the photoelectric effect is associated with photochemical processes occurring under the action of light in photographic materials.
Introduction
1. The history of the discovery of the photoelectric effect
2. Laws of Stoletov
3. Einstein's equation
4. Internal photoelectric effect
5. Application of the phenomenon of photoelectric effect
Bibliography
Introduction
Numerous optical phenomena have been consistently explained on the basis of ideas about the wave nature of light. However, in late XIX- the beginning of the XX century. Phenomena such as the photoelectric effect, X-rays, the Compton effect, the radiation of atoms and molecules, thermal radiation, and others were discovered and studied, the explanation of which from the wave point of view turned out to be impossible. An explanation of the new experimental facts was obtained on the basis of corpuscular ideas about the nature of light. A paradoxical situation arose, connected with the use of completely opposite physical models of a wave and a particle to explain optical phenomena. In some phenomena, light exhibited wave properties, in others - corpuscular.
Among the various phenomena in which the effect of light on matter is manifested, an important place is occupied by photoelectric effect, that is, the emission of electrons by a substance under the influence of light. The analysis of this phenomenon led to the idea of light quanta and played an extremely important role in the development of modern theoretical concepts. At the same time, the photoelectric effect is used in photocells that have received exclusively wide application in the most diverse fields of science and technology and promising even richer prospects.
1. The history of the discovery of the photoelectric effect
The discovery of the photoelectric effect should be attributed to 1887, when Hertz discovered that illuminating electrodes with a spark gap under voltage with ultraviolet light facilitates the spark between them.
The phenomenon discovered by Hertz can be observed in the following easily feasible experiment (Fig. 1).
The value of the spark gap F is selected in such a way that in a circuit consisting of a transformer T and a capacitor C, the spark jumps with difficulty (once or twice per minute). If the electrodes F, made of pure zinc, are illuminated with the light of an Hg mercury lamp, then the discharge of the capacitor is greatly facilitated: a spark begins to jump. 1. Scheme of Hertz's experiment.
The photoelectric effect was explained in 1905 by Albert Einstein (for which he received Nobel Prize) based on Max Planck's hypothesis about the quantum nature of light. Einstein's work contained an important new hypothesis - if Planck suggested that light is emitted only in quantized portions, then Einstein already believed that light exists only in the form of quantum portions. From the concept of light as particles (photons), Einstein's formula for the photoelectric effect immediately follows:
, is the kinetic energy of the emitted electron, is the work function for the given substance, is the frequency of the incident light, is Planck's constant, which turned out to be exactly the same as in Planck's formula for black body radiation.From this formula follows the existence of the red boundary of the photoelectric effect. Thus, studies of the photoelectric effect were among the earliest quantum mechanical studies.
2. Laws of Stoletov
For the first time (1888–1890), analyzing in detail the phenomenon of the photoelectric effect, the Russian physicist A.G. Stoletov obtained fundamentally important results. Unlike previous researchers, he took a small potential difference between the electrodes. The scheme of Stoletov's experiment is shown in fig. 2.
Two electrodes (one in the form of a grid, the other flat), located in a vacuum, are attached to the battery. The ammeter included in the circuit is used to measure the resulting current strength. Irradiating the cathode with light of various wavelengths, Stoletov came to the conclusion that ultraviolet rays have the most effective effect. In addition, it was found that the strength of the current generated by the action of light is directly proportional to its intensity.
In 1898, Lenard and Thomson, using the method of charge deflection in electric and magnetic fields determined the specific charge of charged particles ejected 2. Scheme of Stoletov's experiment.
light from the cathode, and received the expression
SGSE unit s/g, coinciding with the known specific charge of the electron. From this it followed that under the action of light, electrons are ejected from the material of the cathode. By summarizing the results obtained, the following patterns photoelectric effect:
1. With a constant spectral composition of light, the strength of the saturation photocurrent is directly proportional to the light flux incident on the cathode.
2. The initial kinetic energy of the electrons ejected by the light increases linearly with the frequency of the light and does not depend on its intensity.
3. The photoelectric effect does not occur if the frequency of light is less than a certain value characteristic of each metal
called the red border.The first pattern of the photoelectric effect, as well as the occurrence of the photoelectric effect itself, can be easily explained based on the laws of classical physics. Indeed, the light field, acting on the electrons inside the metal, excites their oscillations. The amplitude of the forced oscillations can reach such a value at which the electrons leave the metal; then the photoelectric effect is observed.
In view of the fact that, according to the classical theory, the intensity of light is directly proportional to the square of the electric vector, the number of ejected electrons increases with increasing light intensity.
The second and third laws of the photoelectric effect are not explained by the laws of classical physics.
Studying the dependence of the photocurrent (Fig. 3), which occurs when a metal is irradiated with a stream of monochromatic light, on the potential difference between the electrodes (such a dependence is usually called the volt-ampere characteristic of the photocurrent), it was found that: 1) the photocurrent occurs not only at
, but also for ; 2) the photocurrent is different from zero to a negative value of the potential difference strictly defined for a given metal, the so-called retarding potential; 3) the magnitude of the blocking (delaying) potential does not depend on the intensity of the incident light; 4) the photocurrent increases with decreasing absolute value of the retarding potential; 5) the value of the photocurrent increases with growth and from a certain value the photocurrent (the so-called saturation current) becomes constant; 6) the value of the saturation current increases with increasing intensity of the incident light; 7) the value of the delay 3. Featurepotential depends on the frequency of the incident light; photocurrent.
8) the speed of electrons ejected under the action of light does not depend on the intensity of light, but depends only on its frequency.
3. Einstein's equation
The phenomenon of the photoelectric effect and all its laws are well explained using the quantum theory of light, which confirms the quantum nature of light.
As already noted, Einstein (1905), developing Planck's quantum theory, put forward the idea that not only radiation and absorption, but also the propagation of light occurs in portions (quanta), the energy and momentum of which.
Topics of the USE codifier Key words: M.Planck's hypothesis about quanta, photoelectric effect, A.G.Stoletov's experiments, Einstein's equation for photoelectric effect.
photoelectric effect is the knocking out of electrons from a substance by incident light. The photoelectric effect was discovered by Heinrich Hertz in 1887 during his famous experiments on the emission of electromagnetic waves.
Recall that Hertz used a special spark gap (Hertz vibrator) - a rod cut in half with a pair of metal balls at the ends of the cut. A high voltage was applied to the rod, and a spark jumped between the balls. So, Hertz found that when a negatively charged ball was irradiated with ultraviolet light, the spark jump was facilitated.
Hertz, however, was absorbed in the study of electromagnetic waves and did not take this fact into account. A year later, the photoelectric effect was independently discovered by the Russian physicist Alexander Grigoryevich Stoletov. Careful experimental studies carried out by Stoletov over the course of two years made it possible to formulate the basic laws of the photoelectric effect.
Stoletov's experiments
In his famous experiments, Stoletov used a photocell of his own design ( Photocell any device capable of observing the photoelectric effect is called. Its scheme is shown in Fig. one .
Rice. 1. Stoletov photocell
Two electrodes are introduced into a glass flask, from which air is pumped out (so as not to interfere with the flight of electrons): a zinc cathode and an anode. A voltage is applied to the cathode and anode, the value of which can be changed using a potentiometer and measured with a voltmeter.
Now a "minus" is applied to the cathode, and a "plus" is applied to the anode, but it can be done vice versa (and this change of sign is an essential part of Stoletov's experiments). The voltage on the electrodes is attributed to the sign that is applied to the anode (Therefore, the voltage applied to the electrodes is often called anode voltage). AT this case, for example, the voltage is positive.
The cathode is illuminated with UV rays through a special quartz window made in the flask (glass absorbs ultraviolet, and quartz transmits). Ultraviolet radiation knocks out electrons from the cathode, which are accelerated by voltage and fly to the anode. The milliammeter included in the circuit registers electricity. This current is called photocurrent, and the knocked-out electrons that create it are called photoelectrons.
In Stoletov's experiments, three quantities can be independently varied: the anode voltage, the light intensity, and its frequency.
Photocurrent versus voltage
By changing the magnitude and sign of the anode voltage, one can trace how the photocurrent changes. This dependency graph is called photocell characteristic, shown in Fig. 2.
Rice. 2. Characteristics of the photocell
Let's discuss the course of the resulting curve. First of all, we note that electrons fly out of the cathode with various speeds and in different directions; the maximum speed that photoelectrons have under the experimental conditions is denoted by .
If the voltage is negative and large in magnitude, then there is no photocurrent. This is easy to understand: the electric field acting on the electrons from the cathode and anode is retarding (on the cathode "plus", on the anode "minus") and has such a large value that the electrons are not able to reach the anode. The initial supply of kinetic energy is not enough - the electrons lose their speed on the approaches to the anode and turn back to the cathode. The maximum kinetic energy of the emitted electrons turns out to be less than the modulus of the field work when an electron moves from the cathode to the anode:
Here kg is the electron mass, C is its charge.
We will gradually increase the voltage, i.e. move from left to right along an axis of far negative values.
At first, there is still no current, but the turning point of the electrons gets closer and closer to the anode. Finally, when the voltage is reached, which is called holding voltage, the electrons turn back at the moment they reach the anode (in other words, the electrons arrive at the anode at zero speed). We have:
(1)
In this way, the value of the delay voltage allows you to determine the maximum kinetic energy of photoelectrons.
When the delay voltage is slightly exceeded, a weak photocurrent appears. It is formed by electrons that have flown out with maximum kinetic energy almost exactly along the axis of the bulb (i.e., almost perpendicular to the cathode): now this energy is enough for the electrons to reach the anode at a non-zero speed and close the circuit. The remaining electrons, which have lower speeds or flew away from the anode, do not fall on the anode.
As the voltage increases, the photocurrent increases. Anode reaches large quantity electrons emitted from the cathode at increasing angles to the axis of the bulb. Note that photocurrent is present at zero voltage!
When the voltage goes into the region of positive values, the photocurrent continues to increase. This is understandable: the electric field now accelerates the electrons, so more and more of them get a chance to end up on the anode. However, not all photoelectrons reach the anode yet. For example, an electron that has flown out with a maximum speed perpendicular to the axis of the bulb (i.e. along the cathode), although it will turn around in the field in the right direction, but not strong enough to hit the anode.
Finally, at sufficiently large positive voltage values, the current reaches its limiting value, called saturation current, and then stops increasing.
Why? The fact is that the voltage accelerating the electrons becomes so high that the anode captures all the electrons knocked out of the cathode in general - in whatever direction and at whatever speeds they start moving. Therefore, the photocurrent simply does not have further opportunities to increase - the resource, so to speak, has been exhausted.
Laws of the photoelectric effect
The saturation current value is essentially the number of electrons knocked out of the cathode in one second. We will change the intensity of light without touching the frequency. Experience shows that the saturation current varies in proportion to the light intensity.
The first law of the photoelectric effect. The number of electrons knocked out of the cathode per second is proportional to the intensity of the radiation incident on the cathode (at its constant frequency).
There is nothing unexpected in this: the more energy the radiation carries, the more tangible the observed result. The puzzles continue.
Namely, we will study the dependence of the maximum kinetic energy of photoelectrons on the frequency and intensity of the incident light. It is not difficult to do this: after all, by virtue of formula (1), finding the maximum kinetic energy of ejected electrons actually reduces to measuring the retarding voltage.
First, we change the radiation frequency at a fixed intensity. It turns out such a graph (Fig. 3):
Rice. 3. Dependence of the energy of photoelectrons on the frequency of light
As you can see, there is a certain frequency called red border photo effect, separating two fundamentally different areas of the graph. If , then there is no photoelectric effect.
If class="tex" alt="(!LANG:\nu > \nu_0"> !}, then the maximum kinetic energy of photoelectrons increases linearly with frequency.
Now, on the contrary, we fix the frequency and change the light intensity. If at the same time, then the photoelectric effect does not occur, whatever the intensity! Not less than amazing fact is also found at class="tex" alt="(!LANG:\nu > \nu_0"> !}: the maximum kinetic energy of photoelectrons does not depend on the intensity of light.
All these facts are reflected in the second and third laws of the photoelectric effect.
The second law of the photoelectric effect. The maximum kinetic energy of photoelectrons increases linearly with the frequency of light and does not depend on its intensity.
The third law of the photoelectric effect. For each substance there is a red border of the photoelectric effect - the lowest frequency of light at which the photoelectric effect is still possible. When the photoelectric effect is not observed at any light intensity.
Difficulties in the classical explanation of the photoelectric effect
How could the photoelectric effect be explained in terms of classical electrodynamics and wave concepts of light?
It is known that in order to pull out an electron from a substance, it is required to impart to it some energy, called work function electron. In the case of a free electron in a metal, this is the work of overcoming the field of positive ions of the crystal lattice, which holds the electron at the metal boundary. In the case of an electron in an atom, the work function is the work done to break the bond between the electron and the nucleus.
in variable electric field light wave, the electron begins to oscillate.
And if the vibration energy exceeds the work function, then the electron will be torn out of the substance.
However, within the framework of such ideas, it is impossible to understand the second and third laws of the photoelectric effect.. Indeed, why does the kinetic energy of ejected electrons not depend on the radiation intensity? After all, the greater the intensity, the greater the strength of the electric field in the electromagnetic wave, the greater the force acting on the electron, the greater the energy of its oscillations, and the greater the kinetic energy of the electron will fly out of the cathode. Is it logical? Logically. But experiment shows otherwise.
Next, where does the red border of the photoelectric effect come from? What is wrong with low frequencies? It would seem that as the intensity of light increases, so does the force acting on the electrons; therefore, even at a low frequency of light, the electron will sooner or later be pulled out of the substance - when the intensity reaches enough of great importance. However, the red border puts a strict prohibition on the emission of electrons at low frequencies incident radiation.
In addition, it is not clear inertialessness photoelectric effect. Namely, when the cathode is illuminated by radiation of an arbitrarily weak intensity (with a frequency above the red limit), the photoelectric effect begins instantly- at the time of switching on the lighting. Meanwhile, it would seem that electrons need some time to “loosen” the bonds that hold them in the substance, and this “buildup” time should be the longer, the weaker the incident light. The analogy is this: the weaker you push the swing, the longer it will take them to swing to a given amplitude.
It looks logical again, but experience is the only criterion of truth in physics! - contradicts these arguments.
So on turn of XIX and XX centuries in physics, an impasse arose: electrodynamics, which predicted the existence of electromagnetic waves and works perfectly in the radio wave range, refused to explain the phenomenon of the photoelectric effect.
The way out of this impasse was found by Albert Einstein in 1905. He found a simple equation describing the photoelectric effect. All three laws of the photoelectric effect turned out to be consequences of the Einstein equation.
Einstein's main merit was to abandon attempts to interpret the photoelectric effect from the standpoint of classical electrodynamics. Einstein drew on Max Planck's bold quanta hypothesis five years earlier.
Planck's quantum hypothesis
Classical electrodynamics refused to work not only in the field of the photoelectric effect. It also gave a serious failure when it was tried to be used to describe the radiation of a heated body (the so-called thermal radiation).
The essence of the problem was that a simple and natural electrodynamic model of thermal radiation led to a meaningless conclusion: any heated body, continuously radiating, must gradually lose all its energy and cool down to absolute zero. As we well know, nothing like this is observed.
In the course of solving this problem, Max Planck expressed his famous hypothesis.
The quantum hypothesis. Electromagnetic energy is not emitted and absorbed continuously, but in separate indivisible portions - quanta. The quantum energy is proportional to the radiation frequency:
(2)
Relation (2) is called Planck's formula, and the coefficient of proportionality - Planck's constant.
The acceptance of this hypothesis allowed Planck to construct a theory of thermal radiation that agrees perfectly with experiment. Having the spectra of thermal radiation known from experience, Planck calculated the value of his constant:
J s (3)
The success of Planck's hypothesis suggested that the laws of classical physics do not apply to small particles like atoms or electrons, as well as to the phenomena of the interaction of light and matter. This idea was confirmed by the phenomenon of the photoelectric effect.
Einstein's equation for the photoelectric effect
Planck's hypothesis spoke of discreteness radiation and takeovers electromagnetic waves, that is, the intermittent nature of the interaction of light with matter. At the same time, Planck believed that Spread light is a continuous process that occurs in full accordance with the laws of classical electrodynamics.
Einstein went even further: he suggested that light, in principle, has a discontinuous structure: not only emission and absorption, but also the propagation of light occurs in separate portions - quanta with energy.
Planck considered his hypothesis only as a mathematical trick and did not dare to refute electrodynamics in relation to the microcosm. Quanta became a physical reality thanks to Einstein.
Quanta electromagnetic radiation(in particular, light quanta) later became known as photons. Thus, light consists of special particles - photons moving in vacuum with a speed.
Each photon of monochromatic light that has a frequency carries energy.
Photons can exchange energy and momentum with particles of matter (the momentum of a photon will be discussed in the next sheet); in this case we are talking about collision photon and particles. In particular, there is a collision of photons with electrons of the cathode metal.
The absorption of light is the absorption of photons, that is inelastic collision of photons with particles (atoms, electrons). Absorbed upon collision with an electron, the photon transfers its energy to it. As a result, the electron receives kinetic energy instantly, and not gradually, and this is precisely what explains the inertia of the photoelectric effect.
Einstein's equation for the photoelectric effect is nothing more than the law of conservation of energy. What is the energy of the photon? in its inelastic collision with an electron? It is spent on doing the work of extracting an electron from a substance and on giving the electron kinetic energy:
(4)
The term turns out to be maximum kinetic energy of photoelectrons. Why maximum? This question requires a little clarification.
Electrons in a metal can be free or bound. Free electrons "walk" throughout the metal, bound electrons "sit" inside their atoms. In addition, an electron can be located both near the surface of the metal and in its depth.
It is clear that the maximum kinetic energy of a photoelectron will be obtained when the photon hits a free electron in the surface layer of the metal - then only the work function is sufficient to knock out the electron.
In all other cases, additional energy will have to be expended - on tearing out a bound electron from an atom or on “dragging” a deep electron to the surface.
These extra costs will lead to the fact that the kinetic energy of the emitted electron will be less.
Remarkable in its simplicity and physical clarity, equation (4) contains the entire theory of the photoelectric effect. Let's see how the laws of the photoelectric effect are explained in terms of the Einstein equation.
1. The number of ejected electrons is proportional to the number of absorbed photons. As the light intensity increases, the number of photons incident on the cathode per second increases.
Therefore, the number of absorbed photons and, accordingly, the number of electrons knocked out per second increase proportionally.
2. We express from formula (4) the kinetic energy:
Indeed, the kinetic energy of the ejected electrons increases linearly with frequency and does not depend on the light intensity.
The dependence of kinetic energy on frequency has the form of an equation of a straight line passing through the point. This fully explains the course of the graph in Fig. 3 .
3. In order for the photoelectric effect to begin, the photon energy must be sufficient at least to perform the work function: . The lowest frequency, defined by the equality
just will be the red border of the photoelectric effect. As we can see, the red boundary of the photoelectric effect is determined only by the work function, i.e. depends only on the material of the irradiated cathode surface.
If , then there will be no photoelectric effect - no matter how many photons per second fall on the cathode. Therefore, the intensity of light does not play a role; the main thing is whether a single photon has enough energy to knock out an electron.
Einstein's equation (4) makes it possible to experimentally find Planck's constant. To do this, it is necessary to first determine the radiation frequency and the work function of the cathode material, as well as measure the kinetic energy of photoelectrons.
In the course of such experiments, a value was obtained that exactly coincided with (3) . Such a coincidence of the results of two independent experiments - based on the spectra of thermal radiation and Einstein's equation for the photoelectric effect - meant that completely new "rules of the game" were discovered, according to which the interaction of light and matter occurs. In this area, classical physics, represented by Newton's mechanics and Maxwell's electrodynamics, gives way to quantum physics- the theory of the microcosm, the construction of which continues today.
Laws of the external photoelectric effect
Along with thermal radiation, a phenomenon that does not fit into the framework of classical physics, is the photoelectric effect.
The external photoelectric effect is the phenomenon of the emission of electrons by a substance when irradiated with electromagnetic waves.
The photoelectric effect was discovered by Hertz in 1887. He noticed that the spark between the zinc balls is facilitated if the gap between the sparks is irradiated with light. Experimentally, the law of the external photoelectric effect was studied by Stoletov in 1888. The scheme for studying the photoelectric effect is shown in Fig. 1.
| Fig.1. |
The cathode and anode are located in a vacuum tube, since negligible contamination of the metal surface affects the emission of electrons. The cathode is illuminated with monochromatic light through a quartz window (quartz, in contrast to ordinary glass transmits ultraviolet light). The voltage between anode and cathode is adjusted by a potentiometer and measured with a voltmeter. Two rechargeable batteries and , connected towards each other, allow using a potentiometer to change the value and sign of the voltage. The strength of the photocurrent is measured with a galvanometer.
In Fig.2. curves of the dependence of the photocurrent strength on the voltage are shown, corresponding to different illuminations of the cathode and (). The frequency of light is the same in both cases.
where and are the charge and mass of the electron.
As the voltage increases, the photocurrent increases, since all more photoelectrons reaches the anode. Maximum value photocurrent is called saturation photocurrent. It corresponds to such voltage values at which all electrons ejected from the cathode reach the anode: , where is the number of photoelectrons emitted from the cathode in 1 second.
Stoletov empirically established the following laws of the photoelectric effect:
Serious difficulties arose in explaining the second and third laws. According to the electromagnetic theory, the pulling out of free electrons from the metal should be the result of their "rocking" in the electric field of the wave. Then it is not clear why the maximum speed of the emitted electrons depends on the frequency of light, and not on the amplitude of oscillations of the electric field strength vector and the intensity of the wave associated with it. Difficulties in interpreting the second and third laws of the photoelectric effect raised doubts about the universal applicability of the wave theory of light.
Einstein's equation for the photoelectric effect
In 1905, Einstein explained the laws of the photoelectric effect using the quantum theory he proposed. Light with a frequency is not only emitted, as Planck assumed, but is also absorbed by matter in certain portions (quanta). Light is a stream of discrete light quanta (photons) moving at the speed of light. The quantum energy is . Each quantum is absorbed by only one electron. Therefore, the number of ejected electrons must be proportional to the intensity of light (1 law of the photoelectric effect).
The energy of the incident photon is spent on the electron's work of exit from the metal and on the communication of the kinetic energy to the emitted photoelectron:
 | (2) |
Equation (2) is called the Einstein equation for the external photoelectric effect. Einstein's equation makes it possible to explain the second and third laws of the photoelectric effect. Equation (2) directly implies that the maximum kinetic energy increases with increasing frequency of the incident light. With decreasing frequency, the kinetic energy decreases and at a certain frequency it becomes equal to zero and the photoelectric effect stops (). From here
where is the number of absorbed photons.
In this case, the red border of the photoelectric effect shifts towards lower frequencies:
| . | (5) |
In addition to the external photoelectric effect, the internal photoelectric effect is also known. When solid and liquid semiconductors and dielectrics are irradiated, electrons pass from the bound state to the free state, but do not fly out. The presence of free electrons leads to the appearance of photoconductivity. Photoconductivity is the increase in the electrical conductivity of a substance when exposed to light.
Photon and its properties
The phenomena of interference, diffraction, polarization can only be explained by the wave properties of light. However, the photoelectric effect and thermal radiation are only corpuscular (assuming light is a stream of photons). Wave and quantum description properties of light complement each other. Light is both a wave and a particle. The basic equations that establish the relationship between wave and particle properties are as follows:
| (7) |
And - quantities characterizing the particle, and - the wave.
Let's find the mass of a photon from relation (6): .
A photon is a particle that always moves at the speed of light and has zero rest mass. The momentum of a photon is: .
Compton effect
The most complete corpuscular properties are manifested in the Compton effect. In 1923, the American physicist Compton investigated the scattering of x-rays by paraffin, whose atoms are light.
From the wave point of view, the scattering of X-rays is due to the forced oscillations of the electrons of the substance, so that the frequency of the scattered light must coincide with the frequency of the incident light. However, a large wavelength was found in the scattered light. does not depend on the wavelength of the scattered X-rays and on the material of the scattering substance, but depends on the direction of scattering. Let be the angle between the direction of the primary beam and the direction of the scattered light, then 
, where (m).
This law is true for light atoms ( , , , ) with electrons weakly bound to the nucleus. The scattering process can be explained by the elastic collision of photons with electrons. Under the action of X-rays, electrons are easily separated from the atom. Therefore, one can consider scattering by free electrons. A photon with momentum collides with an electron at rest and gives it part of the energy, while it acquires momentum (Fig. 3).
 Fig.3. |
Using the laws of conservation of energy and momentum for an absolutely elastic impact, we obtain for the expression: 
, which coincides with the experimental one, while 
, which proves the corpuscular theory of light.
Luminescence, photoluminescence and its main regularities
Luminescence is a non-equilibrium radiation that is excess at a given temperature over thermal radiation. Luminescence occurs under the influence of external influences, not due to heating of the body. This is a cold glow. Depending on the method of excitation, there are: photoluminescence (under the action of light), chemiluminescence (under the action of chemical reactions), cathodoluminescence (under the action of fast electrons) and electroluminescence (under the influence of an electric field).
Luminescence that stops immediately (c) after the disappearance of external influences is called fluorescence. If the luminescence disappears within s after the end of exposure, then it is called phosphorescence.
Substances that luminesce are called phosphors. These include compounds of uranium, rare earths, as well as conjugated systems in which bonds alternate, aromatic compounds: fluorescein, benzene, naphthalene, anthracene.
Photoluminescence obeys Stokes' law: the frequency of the exciting light is greater than the emitted frequency 
, where is the part of the absorbed energy that turns into heat.
The main characteristic of luminescence is the quantum yield equal to the ratio of the number of absorbed photons to the number of emitted ones. There are substances whose quantum yield is close to 1 (for example, fluorescein). Anthracene has a quantum yield of 0.27.
The phenomenon of luminescence has been widely used in practice. For example, luminescent analysis is a method for determining the composition of a substance by its characteristic glow. The method is very sensitive (approximately ), allows detecting an insignificant amount of impurities and is used for the most accurate research in the field of chemistry, biology, medicine and the food industry.
Fluorescent flaw detection makes it possible to detect the finest cracks on the surface of machine parts (the surface to be examined is covered for this with a luminescent solution, which remains in the cracks after removal).
Phosphors are used in fluorescent lamps, are the active medium of optical quantum generators, are used in electron-optical converters. Used for the manufacture of luminous pointers of various devices.
Physical principles night vision devices
The basis of the device is an image intensifier tube (EOC), which converts an image of an object invisible to the eye in IR rays into a visible image (Fig. 4).
 Fig.4. |
1 - photocathode, 2 - electronic lens, 3 - luminescent screen,
Infrared radiation from the object causes photoelectron emission from the surface of the photocathode, and the amount of emission from different parts of the latter varies in accordance with the distribution of the brightness of the image projected onto it. Photoelectrons are accelerated by an electric field in the area between the photocathode and the screen, are focused by an electron lens and bombard the screen, causing its luminescence. The intensity of the glow of individual points of the screen depends on the density of the photoelectron flux, as a result of which a visible image of the object appears on the screen.
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