Max Planck

Quantum properties of light

In 1900, the German physicist Max Planck put forward a hypothesis: light is emitted and absorbed not continuously, but in separate portions - quanta(or photons). Energy E each photon is determined by the formula E = hv , Where h - proportionality coefficient - Planck’s constant, v - frequency of light. We calculated experimentally h= 6.63·10 -34 J·s. M. Planck's hypothesis explained many phenomena, namely, the phenomenon photoelectric effect, discovered in 1887 by the German scientist G. Hertz. Next photoeffect studied experimentally by the Russian scientist Stoletov.

Photoelectric effect and its laws

Scheme of Stoletov's experiment

The photoelectric effect is the ejection of electrons from a substance under the influence of light.
As a result of the research it was established 3 laws of photoelectric effect:
1. The saturation photocurrent is directly proportional to the incident light flux.
2. Maximum kinetic energy photoelectrons increases linearly with the frequency of light and depends on its intensity.
3. For each substance there is maximum length wave at which the photoelectric effect is still observed. At long lengths there is no photoelectric effect.

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 radiation of light. According to Einstein's theory, the photoelectric effect has the following explanation: by absorbing a quantum of light, an electron acquires energy. When leaving the metal, the energy of each electron decreases by a certain amount, which is called the work function ( Avakh) . The work function is the minimum energy that must be imparted to an electron in order for it to leave the metal. It depends on the type of metal and the condition of its surface. The maximum energy of electrons after departure (if there are no other losses) has the form :

— This is Einstein's equation.

If h v< Avakh , then the photoelectric effect does not occur. Limit frequency v min and limiting wavelength λ max called red photo effect border. It is expressed like this: v min =A/h , λ max = λ cr = hc/A, where λ max (λ cr) is the maximum wavelength at which the photoelectric effect is still observed. Red photo effect border for different substances different, because A depends on the type of substance.

Application of the photoelectric effect in technology.
Devices based on the photoelectric effect are called photocells. 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 alternating current circuits. It is used in photometry to measure luminous intensity, brightness, illumination, in cinema for sound reproduction, in phototelegraphs and photophones, in the control of production processes.

There are semiconductor photocells in which the concentration of current carriers changes under the influence of light. The design of photoresistors is based on this phenomenon (internal photoelectric effect). They are used in the automatic control of electrical circuits (for example, in subway turnstiles), in alternating current circuits, in watches, and in microcalculators. Semiconductor photocells are used in solar panels on spaceships and in early cars.

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 with a potentiometer and measured with 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 illumination 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 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 ejected from 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's not clear why maximum speed 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.

From a wave point of view, the scattering of X-rays is due to the forced vibrations of the 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 has received wide application 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 distribution of brightness 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.

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 with ultraviolet rays, 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.

Schematic measuring circuit with which the study was carried out external photoelectric effect, 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 of the 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 intensity of light, 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 electromagnetic wave, “rocking” 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) incident 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), as the frequency of light decreases, the kinetic energy of 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 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 light flux into corresponding fluctuations in photocurrent, which is widely used in sound film technology, 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. Silicon photocell batteries, called solar panels, 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 the Soyuz-3 spacecraft, 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.

1. History of the discovery of the photoelectric effect

2. Stoletov’s laws

3. Einstein's equation

4. Internal photoelectric effect

5. Application of the photoelectric effect phenomenon

Introduction

Numerous optical phenomena were consistently explained based on ideas about the wave nature of light. However, at the end of the 19th – beginning of the 20th centuries. Such phenomena as the photoelectric effect, X-ray radiation, the Compton effect, radiation of atoms and molecules, thermal radiation and others were discovered and studied, the explanation of which from a 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 has arisen involving the use of completely opposite physical models waves and particles to explain optical phenomena. In some phenomena, light exhibited wave properties, in others – corpuscular properties.

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, which have received extremely wide application in a wide variety of fields of science and technology and promise even richer prospects.

History of the discovery of the photoelectric effect

The discovery of the photoelectric effect should be attributed to 1887, when Hertz discovered that illuminating the electrodes of an energized spark gap with ultraviolet light facilitates the passage of a spark between them.

The phenomenon discovered by Hertz can be observed in the following easily feasible experiment (Fig. 1).

The size of the spark gap F is selected in such a way that in a circuit consisting of a transformer T and a capacitor C, a spark slips through with difficulty (once or twice a minute). If the electrodes F, made of pure zinc, are illuminated with the light of a mercury lamp Hg, then the discharge of the capacitor is greatly facilitated: a spark begins to jump Fig. 1. Scheme of Hertz's experiment.

The photoelectric effect was explained in 1905 by Albert Einstein (for which he received a 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 idea of ​​light as particles (photons), Einstein’s formula for the photoelectric effect immediately follows:

where is the kinetic energy of the emitted electron, is the work function for a 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.

This formula implies the existence of the red boundary of the photoelectric effect. Thus, research into the photoelectric effect was one of the very first quantum mechanical studies.

Stoletov's laws

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. An ammeter connected to the circuit is used to measure the resulting current. By irradiating the cathode with light of various wavelengths, Stoletov came to the conclusion that the most effective effect is exerted by ultraviolet rays. In addition, it was found that the strength of the current generated by light is directly proportional to its intensity.

In 1898, Lenard and Thomson used the method of deflecting charges in electric and magnetic fields determined the specific charge of charged particles ejected from Fig. 2. Scheme of Stoletov’s experiment.

light from the cathode, and received the expression

SGSE units s/g, coinciding with the known specific charge of the electron. It followed that under the influence of light, electrons were ejected from the cathode substance.

By summarizing the results obtained, the following were established patterns photoeffect:

1. With constant spectral composition light, the strength of the saturation photocurrent is directly proportional to the light flux incident on the cathode.

2. The initial kinetic energy of electrons ejected by light increases linearly with increasing frequency of 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 boundary.

The first regularity 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 vibrations. Amplitude forced oscillations can reach a value at which electrons leave the metal; then the photoelectric effect is observed.

Due to the fact that, according to 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.

By 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 (this dependence is usually called the volt-ampere characteristic of the photocurrent), it was established that: 1) the photocurrent occurs not only at, but also at; 2) the photocurrent is different from zero to strictly defined for a given metal negative value potential difference, 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 magnitude of the photocurrent increases with increasing and from a certain value the photocurrent (the so-called saturation current) becomes constant; 6) the magnitude of the saturation current increases with increasing intensity of the incident light; 7) delay value Fig. 3. Characteristics

potential depends on the frequency of the incident light; photocurrent

8) the speed of electrons ejected under the influence of light does not depend on the intensity of the light, but depends only on its frequency.

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:

where is the unit vector directed along the wave vector. Applying the law of conservation of energy to the phenomenon of the photoelectric effect in metals, Einstein proposed the following formula:

, (1)

where is the work function of an electron from the metal, and is the speed of the photoelectron. According to Einstein, each quantum is absorbed by only one electron, and part of the energy of the incident photon is spent on performing the work function of the metal electron, while the remaining part imparts kinetic energy to the electron.

As follows from (1), the photoelectric effect in metals can only occur at , otherwise the photon energy will be insufficient to tear an electron out of the metal. The lowest frequency of light under the influence of which the photoelectric effect occurs is determined, obviously, from the condition

The frequency of light determined by condition (2) is called the “red limit” of the photoelectric effect. The word "red" has nothing to do with the color of light at which the photoelectric effect occurs. Depending on the type of metal, the “red edge” of the photoelectric effect can correspond to red, yellow, violet, ultraviolet light, etc.

Using Einstein's formula, other regularities of the photoelectric effect can be explained.

Let us assume that, i.e., there is a braking potential between the anode and cathode. If the kinetic energy of electrons is sufficient, then they, having overcome the braking field, create a photocurrent. Those electrons for which the condition is satisfied participate in the photocurrent . The magnitude of the retarding potential is determined from the condition

, (3)

where is the maximum speed of ejected electrons. Rice. 4.

Substituting (3) into (1), we get

Thus, the magnitude of the retarding potential does not depend on the intensity, but depends only on the frequency of the incident light.

The work function of electrons from a metal and Planck’s constant can be determined by plotting a graph as a function of the frequency of incident light (Fig. 4). As you can see, the segment cut off from the potential axis gives .

Due to the fact that the light intensity is directly proportional to the number of photons, an increase in the intensity of the incident light leads to an increase in the number of ejected electrons, i.e., to an increase in the photocurrent.

Einstein's formula for the photoelectric effect in nonmetals has the form

.

The presence of the work of removing a bound electron from an atom inside nonmetals is explained by the fact that, unlike metals, where there are free electrons, in nonmetals electrons are in a state bound to atoms. Obviously, when light falls on non-metals, part of the light energy is spent on the photoelectric effect in the atom - on the separation of an electron from the atom, and the remaining part is spent on the work function of the electron and imparting kinetic energy to the electron.

Conduction electrons do not spontaneously leave the metal in appreciable quantities. This is explained by the fact that metal represents a potential hole for them. Only those electrons whose energy is sufficient to overcome the potential barrier present on the surface are able to leave the metal. The forces causing this barrier have the following origin. The random removal of an electron from the outer layer of positive ions of the lattice results in the appearance of an excess positive charge in the place where the electron left. The Coulomb interaction with this charge forces the electron, whose speed is not very high, to return back. Thus, individual electrons constantly leave the surface of the metal, move away from it several interatomic distances and then turn back. As a result, the metal is surrounded by a thin cloud of electrons. This cloud, together with the outer layer of ions, forms an electric double layer (Fig. 5; circles are ions, black dots are electrons). The forces acting on the electron in such a layer are directed into the metal. The work done against these forces when transferring an electron from the metal outward goes to increase the potential energy of the electron (Fig. 5).

Thus, potential energy There are fewer valence electrons inside the metal than outside the metal by an amount equal to the depth of the potential well (Fig. 6). The energy change occurs over a length of the order of several interatomic distances, so the walls of the well can be considered vertical.

Electron potential energy Fig. 6.

and the potential of the point at which the electron is located have opposite signs. It follows that the potential inside the metal is greater than the potential in the immediate vicinity of its surface by an amount.

Giving the metal an excess positive charge increases the potential both on the surface and inside the metal. The potential energy of the electron decreases accordingly (Fig. 7, a).

The values ​​of potential and potential energy at infinity are taken as the reference point. The message of negative charge lowers the potential inside and outside the metal. Accordingly, the potential energy of the electron increases (Fig. 7, b).

The total energy of an electron in a metal consists of potential and kinetic energies. At absolute zero, the values ​​of the kinetic energy of conduction electrons range from zero to the energy level coinciding with the Fermi level. In Fig. 8, the energy levels of the conduction band are inscribed in the potential well (the dotted line shows the levels unoccupied at 0K). To be removed from the metal, different electrons must be given different energies. Thus, an electron located at the lowest level of the conduction band must be given energy; for an electron located at the Fermi level, there is sufficient energy .

The minimum energy that must be imparted to an electron in order to remove it from a solid or liquid body into a vacuum is called work function. The work function of an electron from a metal is determined by the expression

We obtained this expression under the assumption that the temperature of the metal is 0K. At other temperatures, the work function is also defined as the difference between the depth of the potential well and the Fermi level, i.e., definition (4) is extended to any temperature. The same definition applies to semiconductors.

The Fermi level depends on temperature. In addition, due to the change in average distances between atoms due to thermal expansion, the depth of the potential well changes slightly. This results in the work function being slightly temperature dependent.

The work function is very sensitive to the state of the metal surface, in particular to its cleanliness. Having properly selected Fig. 8.

surface coating, the work function can be greatly reduced. For example, applying a layer of alkaline earth metal oxide (Ca, Sr, Ba) to the surface of tungsten reduces the work function from 4.5 eV (for pure W) to 1.5 – 2 eV.

Internal photoelectric effect

Above we talked about the release of electrons from the illuminated surface of a substance and their transition to another medium, in particular to a vacuum. This emission of electrons is called photoelectron emission, and the phenomenon itself external photoeffect. Along with it, the so-called internal photoelectric effect, in which, in contrast to the external one, optically excited electrons remain inside the illuminated body without violating the neutrality of the latter. In this case, the concentration of charge carriers or their mobility in the substance changes, which leads to a change in the electrical properties of the substance under the influence of light incident on it. The internal photoelectric effect is inherent only in semiconductors and dielectrics. It can be detected, in particular, by changes in the conductivity of homogeneous semiconductors when illuminated. Based on this phenomenon - photoconductivity created and constantly improved large group light receivers – photoresistors. They mainly use cadmium selenide and sulfide.

In inhomogeneous semiconductors, along with a change in conductivity, the formation of a potential difference is also observed (photo - emf). This phenomenon (photogalvanic effect) is due to the fact that, due to the homogeneity of the conductivity of semiconductors, there is a spatial separation within the volume of the conductor of optically excited electrons carrying a negative charge and microzones (holes) that arise in the immediate vicinity of the atoms from which the electrons have come off, and like particles carrying positive elementary charge. Electrons and holes are concentrated at different ends of the semiconductor, as a result of which an electromotive force arises, due to which it is generated without the application of an external emf. electric current in a load connected in parallel with an illuminated semiconductor. In this way, direct conversion of light energy into electrical energy is achieved. It is for this reason that photovoltaic light receivers are used not only for recording light signals, but also in electrical circuits as sources of electrical energy.

The main industrially produced types of such receivers are based on selenium and silver sulfide. Silicon, germanium and a number of compounds are also very common - GaAs, InSb, CdTe and others. Photovoltaic cells, used to convert solar energy into electrical energy, have become particularly widespread in space research as sources of on-board power. They have a relatively high efficiency (up to 20%) and are very convenient in autonomous flight conditions. spaceship. In modern solar cells, depending on the semiconductor material, photo - emf. reaches 1 - 2 V, current pickup from several tens of milliamps, and per 1 kg of mass the output power reaches hundreds of watts.

YAGMA

Medical physics

Faculty of Medicine

1 Course

2nd semester

Lecture No. 9

"Photo effect"

Compiled by: Babenko N.I..

2011

Photo effect. Laws of external photoelectric effect.

Photo effect– a group of phenomena associated with the emission of electrons by excited atoms of a substance due to the energy of absorbed photons. Discovered by the German scientist Hertz in 1887. Experimentally studied by Russian scientist A.G. Stoletov (1888 - 1890). Theoretically explained by A. Einstein (1905).

Types of photoelectric effect.

Internal photo effect:

A. Change in the conductivity of the medium under the influence of light, photoresist effect, typical for semiconductors.

b. Change in dielectric constant of a medium under the influence of light, photodielectric effect, typical for dielectrics.

V. The appearance of photo EMF, photovoltaic effect, typical for inhomogeneous semiconductors p And n-type.

External photoeffect :

This is the phenomenon of the release (emission) of electrons from a substance into a vacuum due to the energy of absorbed photons.

Photoelectrons- These are electrons torn from the atoms of a substance due to the photoelectric effect.

Photocurrent is an electric current formed by the ordered movement of photoelectrons in an external electric field.

Light (F)“K” and “A” - electrodes,

placed in vacuum

“V” - fixes voltage

between electrodes

“G” - records photocurrent

K(-) A(+) “P” - potentiometer for

voltage changes

"F" - luminous flux

Rice. 1. Installation for studying the laws of the external photoelectric effect.

I Law of external photoelectric effect (Stoletov’s law).

WITH
The amount of saturation photocurrent (i.e., the number of electrons emitted from the cathode per unit time) is proportional to the light flux incident on the metal (Fig. 2).

where k is the coefficient of proportionality, or the sensitivity of the metal to the photoelectric effect

Rice. 2. Dependence of saturation photocurrents (I 1, I 2, I 3) on the intensity of light fluxes: Ф 1 > Ф 2 > Ф 3. The frequency of incident light fluxes is constant.

II law of the photoelectric effect (Einstein-Lenard law).

If you swap the poles of the source battery ((K(+), A(-)), then an electric field arises between the cathode (K) and anode (A), which inhibits the movement of electrons. At a certain blocking value of the reverse voltage U3, the photocurrent is 0 ( Fig. 3).

Rice. 3. Dependence of saturation photocurrents for different frequencies of incident light at a constant intensity of incident light.

In this case, electrons escaping from the cathode, even at the maximum speed Vmax, will not be able to pass through the blocking field.

By measuring the value of the blocking voltage Uз, it is possible to determine the maximum kinetic energy E k max of electrons knocked out by radiation. When the intensity of the light flux Ф changes, the maximum kinetic energy E k max does not change, but if the frequency increases electromagnetic radiation(change visible light to ultraviolet), then the maximum kinetic energy E k max of photoelectrons will increase.

N
The initial kinetic energy of the photoelectron is proportional to the frequency of the incident radiation and does not depend on its intensity.

where h is Planck's constant, v is the frequency of the incident light.

III law of external photoelectric effect (Law of the red border).

If the cathode is sequentially irradiated with various monochromatic radiations, one can find that with increasing wavelength λ, the energy of photoelectrons decreases and at a certain value of wavelength λ, the external photoelectric effect stops.

Longest wavelengthλ (or lowest frequency valuev) in which the external photoelectric effect still takes place is calledred photo effect border for a given substance.

For silver λcr = 260 nm

For cesium λcr =>620 nm

2. Einstein's equation and its application to the three laws of the photoelectric effect.

IN
In 1905, Einstein supplemented Planck's theory by suggesting that light, interacting with matter, is absorbed by the same elementary portions (quanta, photons) as it is emitted according to Planck's theory.

Photon is a particle that does not have rest mass (m 0 =0), and moves at a speed equal to the speed of light in vacuum (c = 3·10 8 m/s).

Quantum– a portion of photon energy.

Einstein's equation for the photoelectric effect is based on three postulates:

1. Photons interact with the electrons of the atom of the substance and are completely absorbed by them.

2. One photon interacts with only one electron.

3. Each absorbed photon releases one electron. In this case, the energy of the photon “ħλ” is spent on the work function “ē” from the surface of the substance A out and on the kinetic energy imparted to it

ћ·ν = ћ· =
- Einstein's equation

This energy “ħν” will be maximum if electrons are detached from the surface.

Application of the equation to explain the three laws of the photoelectric effect.

To the first law:

As the intensity of monochromatic radiation increases, the number of quanta absorbed by the metal increases, therefore the number of electrons escaping from it also increases and the strength of the photocurrent increases:

To the second law:

AND
from Einstein's equations:

Those. E k max of the photoelectron depends only on the type of metal (A out) and on the frequency ν(λ) of the incident radiation and does not depend on the intensity of the radiation (F).

To the III law:

ħν<А вых – то при любой интенсивности излученя фотоэффекта не будет, т.к. этой энергии фотона не хватит, чтобы вырвать ē из вещества.

ħν>A out - the photoelectric effect is observed, since the photon energy is enough both for the work of the output A out and for the communication ē of kinetic energy E to max.

ħν=A out – the limit of the photoelectric effect at which

and the photon energy is only enough to exit ē from the metal surface.

In this case, Einstein's equation looks like:

red photo effect border