By the end of the 19th century, scientists, studying the interaction of electromagnetic radiation (in particular, light) with atoms of matter, encountered serious problems that could only be solved within the framework of quantum mechanics, which, in many ways, arose due to the fact that these problems arose. To understand the first and perhaps most serious of these problems, imagine a large black box with a mirrored interior surface, and in one of the walls there is a small hole made. A ray of light penetrating into a box through a microscopic hole remains inside forever, endlessly reflecting off the walls. An object that does not reflect light, but completely absorbs it, appears black, which is why it is usually called black body. (A black body, like many other conceptual physical phenomena, is a purely hypothetical object, although, for example, a hollow, uniformly heated sphere mirrored from the inside, into which light penetrates through a single tiny hole, is a good approximation.)
You, however, have probably seen quite close analogues of a black body in reality. In a fireplace, for example, it happens that several logs are stacked almost tightly together, and a rather large cavity burns out inside them. The outside of the logs remains dark and does not glow, while inside the burnt cavity heat (infrared radiation) and light accumulate, and these rays are reflected repeatedly from the walls of the cavity before escaping outside. If you look into the gap between such logs, you will see a bright yellow-orange high-temperature glow and from there you will literally be blazing with heat. The rays were simply trapped for some time between the logs, just as light is completely trapped and absorbed by the black box described above.
The model of such a black box helps us understand how the light absorbed by a black body behaves, interacting with the atoms of its substance. Here it is important to understand that light is absorbed by an atom, immediately emitted by it and absorbed by another atom, again emitted and absorbed, and this will happen until the state of equilibrium saturation is reached. When a black body is heated to an equilibrium state, the intensities of emission and absorption of rays inside the black body are equalized: when a certain amount of light of a certain frequency is absorbed by one atom, another atom somewhere inside simultaneously emits the same amount of light of the same frequency. Thus, the amount of absorbed light of each frequency within a black body remains the same, although different atoms of the body absorb and emit it.
Until this moment, the behavior of the black body remains quite understandable. Problems within the framework of classical physics (by “classical” here we mean physics before the advent of quantum mechanics) began when trying to calculate the radiation energy stored inside a black body in an equilibrium state. And two things soon became clear:
- the higher the wave frequency of the rays, the more of them accumulate inside the black body (that is, the shorter the wavelengths of the studied part of the spectrum of radiation waves, the more rays of this part of the spectrum inside the black body are predicted by the classical theory);
- The higher the frequency of the wave, the more energy it carries and, accordingly, the more of it is stored inside the black body.
Taken together, these two conclusions led to an unthinkable result: the radiation energy inside a black body should be infinite! This evil mockery of the laws of classical physics was dubbed ultraviolet disaster, since high-frequency radiation lies in the ultraviolet part of the spectrum.
Order was restored by the German physicist Max Planck ( cm. Planck's constant) - he showed that the problem is removed if we assume that atoms can absorb and emit light only in portions and only at certain frequencies. (Later Albert Einstein generalized this idea by introducing the concept photons- strictly defined portions of light radiation.) According to this scheme, many radiation frequencies predicted by classical physics simply cannot exist inside a black body, since atoms are unable to absorb or emit them; Accordingly, these frequencies are excluded from consideration when calculating the equilibrium radiation inside a black body. By leaving only permissible frequencies, Planck prevented the ultraviolet catastrophe and set science on the path to a correct understanding of the structure of the world at the subatomic level. In addition, he calculated the characteristic frequency distribution of equilibrium black body radiation.
This distribution gained worldwide fame many decades after its publication by Planck himself, when cosmologists discovered that the cosmic microwave background radiation they discovered ( cm. The Big Bang) follows exactly the Planck distribution in its spectral characteristics and corresponds to black body radiation at a temperature of about three degrees above absolute zero.
A completely black body that completely absorbs electromagnetic radiation of any frequency, when heated, emits energy in the form of waves evenly distributed over the entire frequency spectrum
By the end of the 19th century, scientists, studying the interaction of electromagnetic radiation (in particular, light) with atoms of matter, encountered serious problems that could only be solved within the framework of quantum mechanics, which, in many ways, arose due to the fact that these problems arose. To understand the first and perhaps most serious of these problems, imagine a large black box with a mirrored interior surface, and in one of the walls there is a small hole made. A ray of light penetrating into a box through a microscopic hole remains inside forever, endlessly reflecting off the walls. An object that does not reflect light, but completely absorbs it, appears black, which is why it is commonly called a black body. (A black body, like many other conceptual physical phenomena, is a purely hypothetical object, although, for example, a hollow, uniformly heated sphere mirrored from the inside, into which light penetrates through a single tiny hole, is a good approximation.)
Absolutely black bodies do not exist in nature, so in physics a model is used for experiments. It is an opaque closed cavity with a small hole, the walls of which have the same temperature. Light entering through this hole will, after repeated reflections, be completely absorbed, and the outside of the hole will appear completely black. But when this cavity is heated, it will develop its own visible radiation. Since the radiation emitted by the inner walls of the cavity, before it leaves (after all, the hole is very small), in the overwhelming majority of cases will undergo a huge amount of new absorption and radiation, we can say with confidence that the radiation inside the cavity is in thermodynamic equilibrium with the walls. (In fact, the hole is not important for this model at all, it is only needed to emphasize the fundamental observability of the radiation inside; the hole can, for example, be completely closed, and quickly opened only when equilibrium has already been established and the measurement is being carried out). |
You, however, have probably seen quite close analogues of a black body in reality. In a fireplace, for example, it happens that several logs are stacked almost tightly together, and a rather large cavity burns out inside them. The outside of the logs remains dark and does not glow, while inside the burnt cavity heat (infrared radiation) and light accumulate, and these rays are reflected repeatedly from the walls of the cavity before escaping outside. If you look into the gap between such logs, you will see a bright yellow-orange high-temperature glow and from there you will literally be blazing with heat. The rays were simply trapped for some time between the logs, just as light is completely trapped and absorbed by the black box described above.
The model of such a black box helps us understand how the light absorbed by a black body behaves, interacting with the atoms of its substance. Here it is important to understand that light is absorbed by an atom, immediately emitted by it and absorbed by another atom, again emitted and absorbed, and this will happen until the state of equilibrium saturation is reached. When a black body is heated to an equilibrium state, the intensities of emission and absorption of rays inside the black body are equalized: when a certain amount of light of a certain frequency is absorbed by one atom, another atom somewhere inside simultaneously emits the same amount of light of the same frequency. Thus, the amount of absorbed light of each frequency within a black body remains the same, although different atoms of the body absorb and emit it.
Until this moment, the behavior of the black body remains quite understandable. Problems within the framework of classical physics (by “classical” here we mean physics before the advent of quantum mechanics) began when trying to calculate the radiation energy stored inside a black body in an equilibrium state. And two things soon became clear:
- the higher the wave frequency of the rays, the more of them accumulate inside the black body (that is, the shorter the wavelengths of the studied part of the spectrum of radiation waves, the more rays of this part of the spectrum inside the black body are predicted by the classical theory);
- The higher the frequency of the wave, the more energy it carries and, accordingly, the more of it is stored inside the black body.
The German physicist Max Planck managed to restore order (see Planck's constant) - he showed that the problem is removed if we assume that atoms can absorb and emit light only in portions and only at certain frequencies. (Later, Albert Einstein generalized this idea by introducing the concept of photons - strictly defined portions of light radiation.) According to this scheme, many frequencies of radiation predicted by classical physics simply cannot exist inside a black body, since atoms are unable to absorb or emit them; Accordingly, these frequencies are excluded from consideration when calculating the equilibrium radiation inside a black body. By leaving only permissible frequencies, Planck prevented the ultraviolet catastrophe and set science on the path to a correct understanding of the structure of the world at the subatomic level. In addition, he calculated the characteristic frequency distribution of equilibrium black body radiation.
This distribution gained worldwide fame many decades after its publication by Planck himself, when cosmologists discovered that the cosmic microwave background radiation they discovered exactly obeys the Planck distribution in its spectral characteristics and corresponds to the radiation of a completely black body at a temperature of about three degrees above absolute zero.
Encyclopedia by James Trefil “The Nature of Science. 200 laws of the universe."
James Trefil is a professor of physics at George Mason University (USA), one of the most famous Western authors of popular science books.
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One of the facts of the subatomic world is that its objects - such as electrons or photons - are not at all similar to the usual objects of the macroworld. They behave neither like particles nor like waves, but like completely special formations that exhibit both wave and corpuscular properties depending on the circumstances. It is one thing to make a statement, but quite another to connect together the wave and particle aspects of the behavior of quantum particles, describing them with an exact equation. This is exactly what was done in the de Broglie relation.
In everyday life, there are two ways to transfer energy in space - through particles or waves. In everyday life, there are no visible contradictions between the two mechanisms of energy transfer. So, a basketball is a particle, and sound is a wave, and everything is clear. However, in quantum mechanics things are not so simple. Even from the simplest experiments with quantum objects, it very soon becomes clear that in the microworld the principles and laws of the macroworld that we are familiar with do not apply. Light, which we are accustomed to thinking of as a wave, sometimes behaves as if it consists of a stream of particles (photons), and elementary particles, such as an electron or even a massive proton, often exhibit the properties of a wave.
There are a number of types of electromagnetic radiation, ranging from radio waves to gamma rays. Electromagnetic rays of all types propagate in a vacuum at the speed of light and differ from each other only in wavelengths.
Max Planck, one of the founders of quantum mechanics, came to the ideas of energy quantization, trying to theoretically explain the process of interaction between recently discovered electromagnetic waves and atoms and, thereby, solve the problem of black body radiation. He realized that to explain the observed emission spectrum of atoms, it is necessary to take for granted that atoms emit and absorb energy in portions (which the scientist called quanta) and only at individual wave frequencies.
The dual particle-wave nature of quantum particles is described by a differential equation.
The word “quantum” comes from the Latin quantum (“how much, how much”) and the English quantum (“quantity, portion, quantum”). “Mechanics” has long been the name given to the science of the movement of matter. Accordingly, the term “quantum mechanics” means the science of the movement of matter in portions (or, in modern scientific language, the science of the movement of quantized matter). The term “quantum” was coined by the German physicist Max Planck to describe the interaction of light with atoms.
Most of all, Einstein protested against the need to describe the phenomena of the microworld in terms of probabilities and wave functions, and not from the usual position of coordinates and particle velocities. That's what he meant by "rolling the dice." He recognized that describing the movement of electrons in terms of their speeds and coordinates contradicts the uncertainty principle. But, Einstein argued, there must be some other variables or parameters, taking into account which the quantum mechanical picture of the microworld will return to the path of integrity and determinism. That is, he insisted, it only seems to us that God is playing dice with us, because we do not understand everything. Thus, he was the first to formulate the hidden variable hypothesis in the equations of quantum mechanics. It lies in the fact that in fact electrons have fixed coordinates and speed, like Newton’s billiard balls, and the uncertainty principle and the probabilistic approach to their determination within the framework of quantum mechanics are the result of the incompleteness of the theory itself, which is why it does not allow them for certain define.
Light is the basis of life on our planet. Answering the questions “Why is the sky blue?” and “Why is the grass green?” you can give a definite answer - “Thanks to the light.” This is an integral part of our life, but we are still trying to understand the phenomenon of light...
Waves are one of two ways of energy transfer in space (the other way is corpuscular, using particles). Waves usually propagate in some medium (for example, waves on the surface of a lake propagate in water), but the direction of movement of the medium itself does not coincide with the direction of movement of the waves. Imagine a float bobbing on the waves. Rising and falling, the float follows the movements of the water as the waves pass by it. The phenomenon of interference occurs when two or more waves of the same frequency, propagating in different directions, interact.
The basics of the phenomenon of diffraction can be understood by referring to Huygens' principle, according to which each point along the path of propagation of a light beam can be considered as a new independent source of secondary waves, and the further diffraction pattern is determined by the interference of these secondary waves. When a light wave interacts with an obstacle, some of the secondary Huygens waves are blocked.
Kirchhoff's law leads to an interesting consequence. Bodies exchanging heat through radiation receive (given the same intensity of electromagnetic waves from their neighbors, regardless of the material and properties of the body. For each wavelength (or frequency, this is the same thing) and for each temperature, experience leads to a universal value Thus, there is a universal function of radiation frequency and temperature, which characterizes the process of heat exchange by radiation.
Functions can be given visual content. Consider a body that absorbs 100% of the energy incident on it at all wavelengths. For such a completely black body and
The function is the emissivity of a completely black body. But how to create a body that absorbs light of any wavelength? Of course, black substances such as soot will allow us to get closer to such a body. However, a few percent will always separate us from the condition. Perhaps a more ingenious solution.
Imagine a box with a small hole. By reducing the size of this hole, you can make it completely black. This feature of the holes is well known from everyday observations. A deep hole, an open window in a room not lit from the inside, a well - these are examples of absolutely black “bodies”. It is quite clear what is going on here: a beam entering a cavity through a hole is able to come out only after multiple reflections (Fig. 187). But with each reflection, a share of energy is lost.
Therefore, with a small hole in a large cavity, the beam will not be able to exit, i.e., it will be completely absorbed.
To measure blackbody emissivity, a long tube of refractory material is made, placed in an oven and heated. Through the hole in the tube, the nature of the radiation is studied using a spectrograph. The results of such experiments are shown in Fig. 188. Curves represent radiation intensity as a function of wavelength, plotted for several temperatures. We see that the radiation is concentrated in a relatively narrow spectral range, lying within the limits of Only at higher temperatures, the curve covers the region of the visible spectrum and begins to move towards short waves. Waves with a length of several microns are called infrared. Since they take on the main responsibility of energy transfer at ordinary temperatures, we call them thermal.
The thermal radiation curve has a maximum, which is more pronounced the higher the temperature. As the temperature increases, the wavelength corresponding to the maximum of the spectrum shifts towards shorter waves. This shift obeys the so-called Wien's law, which is easily established experimentally:
In this formula, the wavelength must be expressed in microns, in degrees absolute scale. We observe a shift in radiation towards short waves when we monitor the heating of a metal - a change from red to yellow as the temperature rises.
The second circumstance that we pay attention to when considering radiation curves is the rapid growth of all ordinates of the curve with increasing If there is an intensity for a given wave, then the total intensity of the spectrum will be represented by the integral
This integral is nothing more than the area under the radiation curve. How fast does it grow with an increase of 7? Analysis of the curves shows that very quickly - proportional to the fourth power of temperature:
where This is the Stefan-Boltzmann law.
Both laws are important in determining the temperature of hot bodies far from us. It is in this way that the temperature of the Sun, stars, and the hot cloud of an atomic explosion is determined.
The laws of thermal radiation underlie the determination of the temperature of molten metal. The principle of optical pyrometers is to select such an incandescent filament of an electric lamp, at which the glow of this filament becomes the same as the glow of molten metal. We use the law: if the radiation is identical, then the temperatures are identical. As for the temperature of the hot filament, it is directly dependent on the electric current passing through the filament. Based on this, the optical pyrometer is easy to calibrate.
Real bodies are not absolutely black, and for each of them a factor less than unity (the absorption capacity of the given body) must be introduced into the Stefan-Boltzmann formula. These factors are determined empirically and are of interest for practical heat engineering, for which the problems of heat transfer by radiation are extremely significant. Nevertheless, the laws considered are important, since the laws of radiation (variation with temperature, variation with wavelength) are generally preserved for non-black bodies. The theoretical significance of the question of an absolutely black body will become clear in the next paragraph.
Thermal radiation is electromagnetic radiation that is emitted by heated bodies due to their internal energy. Thermal radiation reduces the internal energy of the body, and, consequently, its temperature. The spectral characteristic of thermal radiation is the spectral density of energy luminosity.
2. What body is called absolutely black? Give examples of absolutely black bodies.
A completely black body is a body that absorbs all the energy of radiation incident on it of any frequency at an arbitrary temperature (black hole).
3. What is ultraviolet catastrophe? Formulate Planck's quantum hypothesis.
An ultraviolet catastrophe is the discrepancy between experimental results and classical wave theory. Planck's quantum hypothesis: Energy and frequency of radiation are related to each other. Radiation from molecules and atoms of a substance occurs in separate portions - quanta.
4. What microparticle is called a photon? List the main physical characteristics of a photon.
Photon is a quantum of electromagnetic radiation.
1) its energy is proportional to the frequency of electromagnetic radiation.
3) its speed in all reference systems is equal to the speed of light in vacuum.
4) its rest mass is 0.
5) the photon momentum is equal to:
6) Electromagnetic radiation pressure:
5. Formulate the laws of black body radiation: Wien’s and Stefan-Boltzmann’s laws.
Stefan-Boltzmann law: the integral luminosity of a completely black body depends only on its temperature
Kikoin A.K. Absolutely black body // Quantum. - 1985. - No. 2. - P. 26-28.
By special agreement with the editorial board and editors of the journal "Kvant"
Light and color
When we look at various bodies around us in daylight (sunlight), we see them painted in different colors. So, grass and tree leaves are green, flowers are red or blue, yellow or purple. There are also black, white, gray bodies. All this cannot but cause surprise. It would seem that all bodies are illuminated by the same light - the light of the Sun. Why are their colors different? Let's try to answer this question.
We will proceed from the fact that light is an electromagnetic wave, that is, a propagating alternating electromagnetic field. Sunlight contains waves in which electric and magnetic fields oscillate at different frequencies.
Every substance consists of atoms and molecules containing charged particles that interact with each other. Since particles are charged, under the influence of an electric field they can move, and if the field is variable, then they can oscillate, and each particle in the body has a certain natural frequency of oscillation.
This simple, although not very accurate, picture will allow us to understand what happens when light interacts with matter.
When light falls on a body, the electric field “brought” by it causes the charged particles in the body to perform forced oscillations (the field of the light wave is variable!). In this case, for some particles, their natural frequency of oscillations may coincide with some frequency of oscillations of the light wave field. Then, as is known, the phenomenon of resonance will occur - a sharp increase in the amplitude of oscillations (this is discussed in § 9 and 20 of Physics 10). During resonance, the energy brought by the wave is transferred to the atoms of the body, which ultimately causes it to heat up. Light whose frequency resonates is said to be absorbed by the body.
But some waves from the incident light do not resonate. However, they also cause particles in the body to vibrate, but to vibrate with a small amplitude. These particles themselves become sources of so-called secondary electromagnetic waves of the same frequency. Secondary waves, adding to the incident wave, make up reflected or transmitted light.
If the body is opaque, then absorption and reflection are all that can happen to the light falling on the body: light that does not resonate is reflected, and light that does reach is absorbed. This is the “secret” of the color of bodies. If, for example, vibrations corresponding to the red color are included in the resonance from the composition of the incident sunlight, then they will not be present in the reflected light. And our eye is designed in such a way that sunlight, deprived of its red part, causes the sensation of green. The color of opaque bodies thus depends on which frequencies of the incident light are absent in the light reflected by the body.
There are bodies in which charged particles have so many different natural frequencies of vibration that each or almost every frequency in the incident light falls into resonance. Then all the incident light is absorbed, and there is simply nothing to be reflected. Such bodies are called black, that is, bodies of black color. In reality, black is not a color, but the absence of any color.
There are also bodies in which not a single frequency in the incident light hits resonance, then there is no absorption at all, and all the incident light is reflected. Such bodies are called white. White is also not a color, it is a mixture of all colors.
Emitting light
It is known that any body can itself become a source of light. This is understandable - after all, in every body there are oscillating charged particles that can become sources of emitted waves. But under normal conditions - at low temperatures - the frequencies of these vibrations are relatively small, and the emitted wavelengths significantly exceed the wavelengths of visible light (infrared light). At a high temperature, vibrations of higher frequencies “turn on” in the body, and it begins to emit light waves visible to the eye.
What kind of light does a body emit, what frequency vibrations can be “turned on” when heated? Obviously, only oscillations with natural frequencies can arise. At low temperatures, the number of charged particles with high natural vibration frequencies is small, and their radiation is imperceptible. As the temperature increases, the number of such particles increases, and the emission of visible light becomes possible.
Relationship between emission and absorption of light
Absorption and emission are opposite phenomena. However, there is something in common between them.
To absorb means to “take”, to emit means to “give”. What does the body “take” when it absorbs light? Obviously, what it can take is light of those frequencies that are equal to the natural frequencies of vibration of its particles. What does the body “give” when it emits light? What it has is light corresponding to its own frequencies of vibration. Therefore, there must be a close connection between the body's ability to emit light and its ability to absorb it. And this connection is simple: the more a body emits, the more it absorbs. In this case, naturally, the brightest emitter should be a black body, which absorbs vibrations of all frequencies. This connection was established mathematically in 1859 by the German physicist Gustav Kirchhoff.
Let us call the emissivity of a body the energy emitted per unit area of its surface per unit time, and denote it by Eλ,T . It is different for different wavelengths ( λ ) and different temperatures ( T), hence the indices λ And T. The absorption capacity of a body is the ratio of the light energy absorbed by the body per unit time to the incident energy. Let us denote it by Aλ,T - it is also different for different λ And T.
Kirchhoff's law states that the ratio of emissive and absorptive abilities is the same for all bodies:
\(~\frac(E_(\lambda, T))(A_(\lambda, T)) = C\) .
Magnitude WITH does not depend on the nature of the bodies, but depends on the wavelength of light and temperature: C = f(λ , T). According to Kirchhoff's law, a body that absorbs better at a given temperature should radiate more intensely.
Pure black body
Kirchhoff's law is valid for all bodies. This means that it can also be applied to a body that absorbs all wavelengths without exception. Such a body is called completely black. For it, the absorption capacity is equal to unity, so Kirchhoff’s law takes the form
\(~E_(\lambda, T) = C = f(\lambda, T)\) .
Thus, the meaning of the function becomes clear f(λ , T): it is equal to the emissivity of a completely black body. Function Finding Problem C = f(λ , T) turned into the problem of finding the dependence of the radiation energy of a completely black body on temperature and wavelength. Finally, after two decades of futile attempts, it was solved. Its solution, given by the German theoretical physicist Max Planck, became the beginning of a new physics - quantum physics.
Note that absolutely black bodies do not exist in nature. Even the blackest of all known substances - soot - absorbs not 100, but 98% of the light falling on it. Therefore, an artificial device was used to experimentally study black body radiation.
It turned out that the properties of an absolutely black body are possessed by... a closed cavity with a small hole (see figure). In fact, when a ray of light enters a hole, it experiences many successive reflections inside the cavity, so that it has very little chance of leaving the hole to the outside. (For the same reason, an open window in the house seems dark even on a bright sunny day). If such a body is heated, then the radiation emanating from the hole is practically no different from the radiation of an absolutely black body.
A pipe, one end of which is closed, can also serve as a good imitation of a completely black body. If the pipe is heated, its open end shines as a completely black body. At normal temperatures, it looks completely black, like the hole in the cavity.
