The photoelectric effect is the release (full or partial) of electrons from bonds with atoms and molecules of a substance under the influence of light (visible, infrared and ultraviolet). If electrons go beyond the illuminated substance ( complete liberation), then the photoelectric effect is called external (discovered in 1887 by Hertz and studied in detail in 1888 by L.G. Stoletov). If electrons lose contact only with “their” atoms and molecules, but remain inside the illuminated substance as “free electrons” (partial release), thereby increasing the electrical conductivity of the substance, then the photoelectric effect is called internal (discovered in 1873 by the American physicist W. Smith).

The external photoelectric effect is observed in metals. If, for example, a zinc plate connected to an electroscope and negatively charged is illuminated ultraviolet rays, then the electroscope will quickly discharge; in the case of a positively charged plate, no discharge occurs. It follows that light pulls negatively charged particles out of the metal; determination of the magnitude of their charge (performed in 1898 by J. J. Thomson) showed that these particles are electrons.

The basic measuring circuit with which the external photoelectric effect was studied is shown in Fig. 368.

The negative pole of the battery is connected to the metal plate K (cathode), the positive pole is connected to the auxiliary electrode A (anode). Both electrodes are placed in an evacuated vessel having a quartz window F (transparent to optical radiation). Since the electrical circuit is open, there is no current in it. When the cathode is illuminated, light pulls out electrons (photoelectrons) from it, rushing to the anode; a current (photocurrent) appears in the circuit.

The circuit makes it possible to measure the strength of the photocurrent (with a galvanometer and the speed of photoelectrons at different meanings voltage between cathode and anode and at different conditions cathode lighting.

Experimental studies carried out by Stoletov, as well as other scientists, led to the establishment of the following basic laws external photoelectric effect.

1. Saturation photocurrent I (i.e., the maximum number of electrons released by light in 1 s) is directly proportional to the luminous flux F:

where the proportionality coefficient is called the photosensitivity of the illuminated surface (measured in microamperes per lumen, abbreviated as

2. The speed of photoelectrons increases with increasing frequency of incident light and does not depend on its intensity.

3. Regardless of the light intensity, the photoelectric effect begins only at a certain (for a given metal) minimum frequency of light, called the “red limit” of the photoelectric effect.

The second and third laws of the photoelectric effect cannot be explained on the basis of the wave theory of light. Indeed, according to this theory, the intensity of light is proportional to the square of the amplitude of the electromagnetic wave “swinging” the electron in the metal. Therefore, light of any frequency, but of sufficiently high intensity, would have to pull electrons out of the metal; in other words, there should be no “red limit” of the photoelectric effect. This conclusion contradicts the third law of the photoelectric effect. Further, the greater the intensity of the light, the greater the kinetic energy the electron should receive from it. Therefore, the speed of the photoelectron would increase with increasing light intensity; this conclusion contradicts the second law of the photoelectric effect.

The laws of the external photoelectric effect receive a simple interpretation based on the quantum theory of light. According to this theory, the magnitude of the light flux is determined by the number of light quanta (photons) falling per unit time on the metal surface. Each photon can interact with only one electron. That's why

the maximum number of photoelectrons must be proportional to the luminous flux (the first law of the photoelectric effect).

The photon energy absorbed by the electron is spent on the electron performing the work of exit A from the metal (see § 87); the remainder of this energy is the kinetic energy of the photoelectron (mass of the electron, its speed). Then, according to the law of conservation of energy, we can write

This formula, proposed in 1905 by Einstein and then confirmed by numerous experiments, is called the Einstein equation.

From Einstein's equation it is directly clear that the speed of a photoelectron increases with increasing frequency of light and does not depend on its intensity (since neither nor depend on the intensity of light). This conclusion corresponds to the second law of the photoelectric effect.

According to formula (26), with decreasing light frequency kinetic energy photoelectrons decreases (the value of A is constant for a given illuminated substance). At some sufficiently low frequency (or wavelength), the kinetic energy of the photoelectron will become zero and the photoelectric effect will cease (third law of the photoelectric effect). This occurs when, i.e., in the case when all the photon energy is spent on performing the work function of the electron. Then

Formulas (27) determine the “red limit” of the photoelectric effect. From these formulas it follows that it depends on the value of the work function (on the material of the photocathode).

The table shows the values ​​of the work function A (in electron volts) and the red limit of the photoelectric effect (in micrometers) for some metals.

(see scan)

The table shows that, for example, a cesium film deposited on tungsten gives a photoelectric effect even under infrared irradiation; in sodium, the photoelectric effect can only be caused by visible and ultraviolet light, and for zinc - only ultraviolet.

An important physical and technical device called a vacuum photocell is based on the external photoelectric effect (it is a modification of the installation schematically shown in Fig. 368).

The cathode K of the vacuum photocell is a layer of metal deposited on the inner surface of the evacuated glass container B (Fig. 369; G - galvanometer); anode A is made in the form of a metal ring placed in the central part of the cylinder. When the cathode is illuminated in the photocell circuit, electric current, the strength of which is proportional to the magnitude of the luminous flux.

Most modern solar cells have antimony-cesium or oxygen-cesium cathodes, which have high photosensitivity. Cesium oxygen photocells are sensitive to infrared and visible light(sensitivity antimony-cesium photocells are sensitive to visible and ultraviolet light (sensitivity

In some cases, to increase the sensitivity of the photocell, it is filled with argon at a pressure of about 1 Pa. The photocurrent in such a photocell is enhanced due to argon ionization caused by collisions of photoelectrons with argon atoms. The photosensitivity of gas-filled photocells is approx.

The internal photoelectric effect is observed in semiconductors and, to a lesser extent, in dielectrics. The scheme for observing the internal photoelectric effect is shown in Fig. 370. A semiconductor plate is connected in series with a galvanometer to the poles of a battery. The current in this circuit is negligible because the semiconductor has high resistance. However, when the plate is illuminated, the current in the circuit increases sharply. This is due to the fact that light removes electrons from the atoms of the semiconductor, which, remaining inside the semiconductor, increase its electrical conductivity (reduce resistance).

Photovoltaic cells based on the internal photoelectric effect are called semiconductor photocells or photoresistors. Selenium, lead sulfide, cadmium sulfide and some other semiconductors are used for their manufacture. The photosensitivity of semiconductor photocells is hundreds of times higher than the photosensitivity of vacuum photocells. Some photocells have a distinct spectral sensitivity. The selenium photocell has a spectral sensitivity close to the spectral sensitivity of the human eye (see Fig. 304, § 118).

The disadvantage of semiconductor photocells is their noticeable inertia: the change in photocurrent lags behind the change in the illumination of the photocell. Therefore semiconductor

photocells are unsuitable for recording rapidly changing light fluxes.

Another type of photocell is based on the internal photoelectric effect - a semiconductor photocell with a barrier layer or a gate photocell. The diagram of this photocell is shown in Fig. 371.

A metal plate and a thin layer of semiconductor deposited on it are connected by an external electrical circuit containing a galvanometer. As was shown (see § 90), in the contact zone of the semiconductor with the metal, a blocking layer B is formed, which has gate conductivity: it passes electrons only in the direction from the semiconductor to the metal. When a semiconductor layer is illuminated, free electrons appear in it due to the internal photoelectric effect. Passing (in the process of chaotic movement) through the barrier layer into the metal and not being able to move in the opposite direction, these electrons form an excess negative charge in the metal. A semiconductor, deprived of some of its “own” electrons, acquires a positive charge. The potential difference (about 0.1 V) that arises between the semiconductor and the metal creates a current in the photocell circuit.

Thus, a valve photocell is a current generator that directly converts light energy into electrical energy.

Selenium, cuprous oxide, thallium sulfide, germanium, and silicon are used as semiconductors in a valve photocell. The photosensitivity of valve photocells is

Coefficient useful action modern silicon solar cells (illuminated sunlight) reaches according to theoretical calculations, it can be increased to 22%.

Since the photocurrent is proportional to the luminous flux, photocells are used as photometric devices. Such devices include, for example, a lux meter (light meter) and a photoelectric exposure meter.

The photocell allows you to convert fluctuations in the light flux into corresponding fluctuations in the photocurrent, which is wide application in the technology of sound cinema, television, etc.

The importance of photocells for telemechanization and automation is extremely high production processes. In combination with an electronic amplifier and a relay, the photocell is an integral part of automatic devices that, in response to light signals, control the operation of various industrial and agricultural installations and transport mechanisms.

The practical use of valve photocells as electricity generators is very promising. Batteries of silicon photocells, called solar cells, are successfully used on Soviet space satellites and ships to power radio equipment. For this total area photocells must be large enough. For example, on spaceship Soyuz-3, the surface area of ​​the solar panels was about

When the efficiency of solar panels is increased to 20-22%, they will undoubtedly become of paramount importance among the sources that generate electricity for industrial and domestic needs.

Topics Unified State Exam codifier : M. Planck's hypothesis about quanta, photoelectric effect, experiments by A.G. Stoletov, Einstein's equation for the photoelectric effect.

Photo effect- This is the knocking out of electrons from a substance by incident light. The phenomenon of the photoelectric effect was discovered by Heinrich Hertz in 1887 during his famous experiments on radiation electromagnetic waves.
Let us 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 discovered that when a negatively charged ball was irradiated with ultraviolet light, the spark was easier to spark.

Hertz, however, was absorbed in the study of electromagnetic waves and did not accept this fact into account. A year later, the photoelectric effect was independently discovered by Russian physicist Alexander Grigorievich Stoletov. Careful experimental studies carried out by Stoletov for 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 that allows one to observe the photoelectric effect is called. Its diagram is shown in Fig. 1.

Rice. 1. Stoletov photocell

Two electrodes are inserted into a glass flask, from which air has been pumped out (so as not to interfere with the flow 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 “minus” is applied to the cathode, and “plus” is applied to the anode, but it can be done the other way around (and this change of sign is an essential part of Stoletov’s experiments). The voltage on the electrodes is assigned the sign that is applied to the anode (Therefore, the voltage applied to the electrodes is often called anode voltage). In this case, for example, the voltage is positive.

The cathode is illuminated by ultraviolet rays of the UV through a special quartz window made in the flask (glass absorbs ultraviolet radiation, but quartz transmits it). Ultraviolet radiation knocks out electrons from the cathode, which are accelerated by voltage and fly to the anode. A milliammeter connected to the circuit registers electric current. 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: anode voltage, light intensity and frequency.

Dependence of photocurrent on voltage

By changing the magnitude and sign of the anode voltage, you can trace how the photocurrent changes. The graph of this relationship, called characteristics of the photocell, 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 at different speeds and in different directions; Let us denote the maximum speed that photoelectrons have under experimental conditions.

If the voltage is negative and large in absolute value, then there is no photocurrent. This is easy to understand: the electric field acting on electrons from the cathode and anode is braking (at the cathode “plus”, at the anode “minus”) and is so large 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 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 mass of the electron, C is its charge.

We will gradually increase the voltage, i.e. move from left to right along the axis of distant negative values.

At first there is still no current, but the electron reversal point is getting closer to the anode. Finally, when the voltage is reached, which is called holding voltage, the electrons turn back the moment they reach the anode (in other words, the electrons arrive at the anode with zero speed). We have:

(1)

Thus, the magnitude of the retarding voltage allows one to determine the maximum kinetic energy of photoelectrons.

When the delay voltage is slightly exceeded, a weak photocurrent appears. It is formed by electrons emitted with maximum kinetic energy almost exactly along the axis of the bulb (i.e. almost perpendicular to the cathode): now the electrons have enough of this energy to reach the anode with a non-zero speed and close the circuit. The remaining electrons, which have lower speeds or fly away from the anode, do not reach the anode.

As the voltage increases, the photocurrent increases. Anode reaches more electrons escaping from the cathode at increasingly greater angles to the axis of the bulb. Note that photocurrent is present at zero voltage!

When the voltage reaches positive values, the photocurrent continues to increase. This is understandable: the electric field now accelerates the electrons, so an increasing number of them get a chance to end up at the anode. However, not all photoelectrons reach the anode yet. For example, an electron emitted from maximum speed perpendicular to the axis of the bulb (i.e. along the cathode), although it will be turned by the field in the desired direction, but not so much as to get to the anode.

Finally, for sufficiently large positive values voltage current reaches its limit value, called saturation current, and stops increasing further.

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 whatever direction and at whatever speeds they begin to move. Consequently, the photocurrent simply has no further opportunities to increase - the resource, so to speak, has been exhausted.

Laws of the photoelectric effect

The amount of saturation current is essentially the number of electrons knocked out of the cathode in one second. We will change the light intensity without changing the frequency. Experience shows that the saturation current varies in proportion to the light intensity.

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 noticeable the observed result. The mysteries begin further.

Namely, we will study the dependence of the maximum kinetic energy of photoelectrons on the frequency and intensity of the incident light. This is not difficult to do: after all, by virtue of formula (1), finding the maximum kinetic energy of knocked out electrons actually comes down to measuring the retarding voltage.

First, we change the radiation frequency at a fixed intensity. The result is a graph like this (Fig. 3):

Rice. 3. Dependence of photoelectron energy on light frequency

As we can see, there is a certain frequency called red photo effect border, separating two fundamentally different areas of the graph. If , then there is no photoelectric effect.

If class="tex" alt="\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, no matter what the intensity! No less amazing fact is also found when class="tex" alt="\nu > \nu_0"> !}: The maximum kinetic energy of photoelectrons does not depend on light intensity.

All these facts are reflected in the second and third laws of the photoelectric effect.

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.

Third law of the photoelectric effect. For each substance there is a red limit 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 of the classical explanation of the photoelectric effect

How could the photoelectric effect be explained from the point of view of classical electrodynamics and wave concepts of light?

It is known that in order to remove an electron from a substance, it is necessary 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 crystal lattice, holding an electron at the metal boundary. In the case of an electron located in an atom, the work function is the work done to break the bond between the electron and the nucleus.

In the alternating electric field of a 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 electric field strength in the electromagnetic wave, the more more strength, acting on the electron, the greater the energy of its oscillations and the greater the kinetic energy the electron will fly out of the cathode. Logical? Logical. But the experiment shows otherwise.

Next, where does the red border of the photoelectric effect come from? What is wrong with the low frequencies? It would seem that as the intensity of light increases, the force acting on the electrons also increases; therefore, even at a low frequency of light, an electron will sooner or later be torn out of the substance - when the intensity reaches enough of great importance. However, the red boundary strictly prohibits the emission of electrons at low frequencies of incident radiation.

Moreover, it is unclear inertia photoelectric effect Namely, when the cathode is illuminated with radiation of arbitrarily low intensity (with a frequency above the red limit), the photoelectric effect begins instantly- at the moment the lighting is turned on. Meanwhile, it would seem that electrons need some time to “loose” the bonds that hold them in the substance, and this “loosening” time should be longer, the weaker the incident light. The analogy is this: the weaker you push a swing, the longer it will take to swing it to a given amplitude.

Again, it looks logical, but experience is the only criterion of truth in physics! - contradicts these arguments.

Thus, at the turn of the 19th and 20th centuries, a deadlock situation arose in physics: electrodynamics, which predicted the existence of electromagnetic waves and works excellently 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 that describes the photoelectric effect. All three laws of the photoelectric effect turned out to be consequences of Einstein's equation.

Einstein's main merit was his rejection of attempts to interpret the photoelectric effect from the standpoint of classical electrodynamics. Einstein drew on a bold hypothesis about quanta, expressed by Max Planck five years earlier.

Planck's hypothesis about quanta

Classical electrodynamics refused to work not only in the field of the photoelectric effect. It also failed seriously when they tried to use it to describe the radiation of a heated body (the so-called thermal radiation).

The essence of the problem was that the 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 know very well, nothing of the kind is observed.

While solving this problem, Max Planck expressed his famous hypothesis.

Quantum hypothesis. Electromagnetic energy is emitted and absorbed not continuously, but in separate indivisible portions - quanta. Quantum energy is proportional to the radiation frequency:

(2)

Relationship (2) is called Planck's formula, and the proportionality coefficient is Planck's constant.

The acceptance of this hypothesis allowed Planck to construct a theory of thermal radiation that was in excellent agreement 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 did not apply to small particles such as atoms or electrons, or to the phenomena of interaction between 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, about the intermittent nature of the interaction of light with matter. At the same time, Planck believed that spreading 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, which have 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 a vacuum at a speed of .

Each photon of monochromatic light having 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 particle. In particular, photons collide with electrons of the cathode metal.

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 what explains the inertia-free photoelectric effect.

Einstein's equation for the photoelectric effect is nothing more than the law of conservation of energy. Where does the photon energy go? during its inelastic collision with an electron? It is spent on performing the work function of extracting an electron from a substance and giving the electron kinetic energy:

(4)

The term turns out to be maximum kinetic energy of photoelectrons. Why maximum? This question requires a little explanation.

Electrons in a metal can be free or bound. Free electrons “walk” throughout the metal, while bound electrons “sit” inside their atoms. In addition, the 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 in the case when the photon hits a free electron in the surface layer of the metal - then the work function alone is enough to knock out the electron.

In all other cases, additional energy will have to be expended - to tear out a bound electron from an atom or to “drag” 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.

Equation (4), remarkable in its simplicity and physical clarity, contains the entire theory of the photoelectric effect. Let's see how the laws of the photoelectric effect are explained from the point of view of Einstein's equation.

1. The number of electrons knocked out is proportional to the number of absorbed photons. As 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 increases proportionally.

2. Let us express the kinetic energy from formula (4):

Indeed, the kinetic energy of 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 to at least complete the work function: . The smallest frequency determined by the equality

this will be the red border of the photoelectric effect. As we can see, the red limit of the photoelectric effect is determined only by the work function, i.e. depends only on the substance of the irradiated cathode surface.

If , then there will be no photoelectric effect - no matter how many photons fall on the cathode per second. Therefore, light intensity does not matter; the main thing is whether an individual 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 work function of the cathode material, as well as measure the kinetic energy of photoelectrons.

During such experiments, a value was obtained that exactly coincides with (3). Such a coincidence of the results of two independent experiments - based on thermal radiation spectra 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 Newtonian mechanics and Maxwellian electrodynamics, gives way to quantum physics- the theory of the microworld, the construction of which continues today.

Laws of 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 by electromagnetic waves.

The photoelectric effect was discovered by Hertz in 1887. He noticed that the spark between zinc balls was facilitated if the interspark gap was irradiated with light. The law of the external photoelectric effect was studied experimentally by Stoletov in 1888. The diagram for studying the photoelectric effect is shown in Fig. 1.

Fig.1.

The cathode and anode are located in a vacuum tube, since insignificant contamination of the metal surface affects the emission of electrons. The cathode is illuminated with monochromatic light through a quartz window (quartz, unlike ordinary glass, transmits ultraviolet light). The voltage between the anode and cathode is adjusted by a potentiometer and measured by a voltmeter. Two batteries and connected towards each other allow you to change the value and sign of the voltage using a potentiometer. The strength of the photocurrent is measured by a galvanometer.

In Fig.2. curves showing the dependence of the photocurrent strength on voltage corresponding to different cathode illumination 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 everything larger number photoelectrons reach the anode. The maximum value of the photocurrent is called saturation photocurrent. It corresponds to voltage values ​​at which all electrons knocked out of the cathode reach the anode: , where is the number of photoelectrons emitted from the cathode in 1 second.

Stoletov experimentally established the following laws of the photoelectric effect:

Serious difficulties arose in explaining the second and third laws. According to electromagnetic theory, the ejection of free electrons from the metal should be the result of their “swinging” 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 associated wave intensity. Difficulties in interpreting the second and third laws of the photoelectric effect have 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 his proposed quantum theory. Light is not only emitted by frequency, 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 equal to . Each quantum is absorbed by only one electron. Therefore, the number of ejected electrons must be proportional to the light intensity (1st law of the photoelectric effect).

The energy of the incident photon is spent on the electron performing the work of leaving the metal and on imparting kinetic energy to the emitted photoelectron:

(2)

Equation (2) is called the Einstein equation for the external photoelectric effect. Einstein's equation explains the second and third laws of the photoelectric effect. It follows directly from equation (2) that the maximum kinetic energy increases with increasing frequency of the incident light. As the frequency decreases, 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 boundary of the photoelectric effect shifts towards lower frequencies:

.

(5)

In addition to the external photoelectric effect, the internal photoeffect is also known. When solid and liquid semiconductors and dielectrics are irradiated, electrons move from a bound state to a free state, but do not fly out. The presence of free electrons gives rise to photoconductivity. Photoconductivity is an increase in the electrical conductivity of a substance under the influence of light.

Photon and its properties

The phenomena of interference, diffraction, and polarization can only be explained by the wave properties of light. However, the photoelectric effect and thermal radiation are only corpuscular (considering light a flux of photons). Wave and quantum descriptions of the properties of light complement each other. Light is both a wave and a particle. The basic equations establishing the connection between wave and corpuscular properties are as follows:

(7)

And are quantities characterizing a particle, and are a wave.

We find the photon mass from relation (6): .

A photon is a particle that always moves at the speed of light and has a rest mass of zero. The photon momentum is equal to: .

Compton effect

The most complete corpuscular properties are manifested in the Compton effect. In 1923, the American physicist Compton studied the scattering of X-rays by paraffin, whose atoms are light.

X-ray scattering from the wave point of view is related forced oscillations electrons of the substance, so that the frequency of the scattered light must coincide with the frequency of the incident light. However, in the diffused light it was revealed long length waves 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 ( , , , ) having electrons weakly bound to the nucleus. The scattering process can be explained by the elastic collision of photons with electrons. When exposed to X-rays, electrons are easily separated from the atom. Therefore, scattering by free electrons can be considered. A photon with momentum collides with a stationary electron and gives it part of the energy, and itself acquires momentum (Fig. 3).

Fig.3.

Using the laws of conservation of energy and momentum for an absolutely elastic impact, we obtain the following expression: , which coincides with the experimental one, while , which proves the corpuscular theory of light.

Luminescence, photoluminescence and its basic principles

Luminescence is nonequilibrium radiation that is excess at a given temperature over thermal radiation. Luminescence occurs under the influence of external influences not caused by heating of the body. This is a cold glow. Depending on the method of excitation, they are distinguished: photoluminescence (under the influence of light), chemiluminescence (under the influence of chemical reactions), cathodoluminescence (under the influence of fast electrons) and electroluminescence (under the influence of an electric field).

Luminescence stopping immediately (s) after disappearance external influence, is called fluorescence. If 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 quanta to the number of emitted quanta. 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 is widely used in practice. For example, luminescence analysis is a method for determining the composition of a substance by its characteristic glow. The method is very sensitive (approximately ) to detect minute amounts of impurities and is used for precise research in the fields of chemistry, biology, medicine and the food industry.

Luminescent flaw detection allows you to detect the finest cracks on the surface of machine parts (the surface being examined is covered with a luminescent solution, which, after removal, remains in the cracks).

Phosphors are used in fluorescent lamps, are the active medium of optical quantum generators and are used in electron-optical converters. Used to make luminous indicators for various devices.

Physical principles night vision devices

The basis of the device is an electron-optical converter (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 – electron 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 changes in accordance with the brightness distribution of the image projected onto it. Photoelectrons accelerate electric field in the area between the photocathode and the screen, are focused by an electron lens and bombard the screen, causing it to luminesce. The intensity of the glow of individual points of the screen depends on the flux density of photoelectrons, as a result of which a visible image of the object appears on the screen.

Planck's hypothesis, which brilliantly solved the problem of thermal radiation of a black body, was confirmed and further development when explaining the photoelectric effect, a phenomenon whose discovery and study played an important role in the development of quantum theory. In 1887, G. Hertz discovered that when the negative electrode is illuminated with ultraviolet rays, the discharge between the electrodes occurs at a lower voltage. This phenomenon, as shown by the experiments of V. Galvaks (1888) and A.G. Stoletov (1888–1890), due to the knocking out of negative charges from the electrode under the influence of light. The electron had not yet been discovered. It was not until 1898 that J.J. Thompson and F. Leonard, having measured the specific charge of particles emitted by the body, established that these were electrons.

There are external, internal, gate and multiphoton photoeffects.

External photoeffect is the emission of electrons by a substance under the influence of electromagnetic radiation. External photoeffect observed in solids(metals, semiconductors, dielectrics), as well as in gases on individual atoms and molecules (photoionization).

Internal photoelectric effect – these are transitions of electrons inside a semiconductor or dielectric caused by electromagnetic radiation from bound states to free ones without escaping outside. As a result, the concentration of current carriers inside the body increases, which leads to the appearance of photoconductivity (an increase in the electrical conductivity of a semiconductor or dielectric when illuminated) or the appearance of an electromotive force (EMF).

Valve photoeffect is a type of internal photoelectric effect - this is the occurrence of emf (photo emf) when illuminating the contact of two different semiconductors or a semiconductor and a metal (in the absence of an external electric field). The valve photoelectric effect opens the way for the direct conversion of solar energy into electrical energy.

Multiphoton photoelectric effect possible if the light intensity is very high (for example, when using laser beams). In this case, an electron emitted by a metal can simultaneously receive energy not from one, but from several photons.

First basic research photoelectric effect were performed by the Russian scientist A.G. Stoletov. A schematic diagram for studying the photoelectric effect is shown in Fig. 2.1.

	Rice. 2.1	Rice. 2.2

Two electrodes (cathode TO from the material under study and anode A, for which Stoletov used a metal mesh) in a vacuum tube are connected to the battery so that using a potentiometer R You can change not only the value, but also the sign of the voltage applied to them. The current generated when the cathode is illuminated with monochromatic light (through quartz glass) is measured by a milliammeter connected to the circuit.

In 1899, J. J. Thompson and F. Lenard proved that in the photoelectric effect, light knocks electrons out of matter.

Current-voltage characteristic (volt-ampere characteristic) of the photoelectric effect – photocurrent dependence I, formed by the flow of electrons, from the voltage, is shown in Fig. 2.2.

This dependence corresponds to two different cathode irradiances (the light frequency is the same in both cases). As you increase U The photocurrent gradually increases, i.e. an increasing number of photoelectrons reach the anode. The flat nature of the curves shows that electrons are emitted from the cathode at different speeds.

Maximum value saturation photocurrent is determined by this voltage value U, at which all electrons emitted by the cathode reach the anode:

Where n– the number of electrons emitted by the cathode in 1 s.

From the current-voltage characteristic it follows, at U= 0 photocurrent does not disappear. Consequently, electrons knocked out from the cathode have some initial speedυ, and therefore non-zero kinetic energy, so they can reach the cathode without an external field. In order for the photocurrent to become zero, it is necessary to apply holding voltage . When none of the electrons, even those with maximum speed when leaving the cathode, can overcome the retarding field and reach the anode. Hence,

In 1887, Heinrich Rudolf Hertz discovered a phenomenon later called the photoelectric effect. He defined its essence as follows:

If the light from a mercury lamp is directed onto sodium metal, then electrons will fly out from its surface.

The modern formulation of the photoelectric effect is different:

When light quanta fall on a substance and upon their subsequent absorption, charged particles will be partially or completely released in the substance.

In other words, when light photons are absorbed, the following is observed:

1. Emission of electrons from matter
2. Change in electrical conductivity of a substance
3. The appearance of photo-EMF at the interface of media with different conductivities (for example, metal-semiconductor)

Currently, there are three types of photoelectric effect:

1. Internal photoeffect. It consists of changing the conductivity of semiconductors. It is used in photoresistors, which are used in X-ray and dosimeters. ultraviolet radiation, also used in medical devices (oximeter) and fire alarms.
2. Valve photoeffect. It consists in the occurrence of photo-EMF at the interface of substances with different types conductivity, as a result of carrier separation electric charge electric field. It is used in solar powered, in selenium photocells and sensors that record light levels.
3. External photoeffect. As mentioned earlier, this is the process of electrons leaving matter into a vacuum under the influence of quanta of electromagnetic radiation.

Laws of external photoelectric effect.

They were installed by Philip Lenard and Alexander Grigorievich Stoletov at the turn of the 20th century. These scientists measured the number of ejected electrons and their speed as a function of the intensity and frequency of the applied radiation.

First law (Stoletov’s law):

The strength of the saturation photocurrent is directly proportional to the luminous flux, i.e. incident radiation on matter.

Theoretical formulation: When the voltage between the electrodes is zero, the photocurrent is not zero. This is explained by the fact that after leaving the metal, electrons have kinetic energy. If there is a voltage between the anode and the cathode, the photocurrent strength increases with increasing voltage, and at a certain voltage value the current reaches its maximum value (saturation photocurrent). This means that all the electrons emitted by the cathode every second under the influence of electromagnetic radiation take part in the creation of current. When the polarity is reversed, the current drops and soon becomes zero. Here the electron does work against the retarding field due to kinetic energy. As the radiation intensity increases (the number of photons increases), the number of energy quanta absorbed by the metal increases, and therefore the number of emitted electrons increases. This means that the greater the luminous flux, the greater the saturation photocurrent.

I f us ~ F, I f us = k F

k - proportionality coefficient. Sensitivity depends on the nature of the metal. The sensitivity of a metal to the photoelectric effect increases with increasing frequency of light (as the wavelength decreases).

This wording of the law is technical. It is valid for vacuum photovoltaic devices.

The number of emitted electrons is directly proportional to the density of the incident flux with its constant spectral composition.

Second Law (Einstein's Law):

The maximum initial kinetic energy of a photoelectron is proportional to the frequency of the incident radiant flux and does not depend on its intensity.

E kē = => ~ hυ

Third law (law of the “red border”):

For each substance there is a minimum frequency or maximum length wave beyond which there is no photoelectric effect.

This frequency (wavelength) is called the “red edge” of the photoelectric effect.

Thus, he establishes the conditions of the photoelectric effect for a given substance depending on the work function of the electron from the substance and on the energy of the incident photons.

If the photon energy is less than the work function of the electron from the substance, then there is no photoelectric effect. If the photon energy exceeds the work function, then its excess after absorption of the photon goes to the initial kinetic energy of the photoelectron.

Using it to explain the laws of the photoelectric effect.

Einstein's equation for the photoelectric effect is a special case of the law of conservation and transformation of energy. He based his theory on the laws of the still nascent quantum physics.

Einstein formulated three propositions:

1. When exposed to electrons of a substance, the incident photons are completely absorbed.
2. One photon interacts with only one electron.
3. One absorbed photon contributes to the release of only one photoelectron with a certain E kē.

The photon energy is spent on the work function (Aout) of the electron from the substance and on its initial kinetic energy, which will be maximum if the electron leaves the surface of the substance.

E kē = hυ - A output

The higher the frequency of the incident radiation, the greater the energy of the photons and the more (minus the work function) remains for the initial kinetic energy of the photoelectrons.

The more intense the incident radiation, the more photons enter the light flux and the more electrons can escape from the substance and participate in the creation of photocurrent. That is why the strength of the saturation photocurrent is proportional to the luminous flux (I f us ~ F). However, the initial kinetic energy does not depend on intensity, because One electron absorbs the energy of only one photon.