Laws of Karach. Reference sources - blackbody models

An absolutely 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

TO end of the 19th century centuries, scientists, studying the interaction of electromagnetic radiation (in particular, light) with atoms of matter, faced 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. (Absolutely black body- like many other conceptual physical phenomena- the object is purely hypothetical, 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 be completely absorbed after repeated reflections, and the hole will appear completely black from the outside. 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.

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 the ultraviolet catastrophe, since high-frequency radiation lies in the ultraviolet part of the spectrum.

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, 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.

The dual particle-wave nature of quantum particles is described by a differential equation.

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 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.

Radiation from heated metal in the visible range

Absolutely black body- physical idealization used in thermodynamics, a body that absorbs everything falling on it electromagnetic radiation in all ranges and does not reflect anything. Despite the name, a completely black body itself can emit electromagnetic radiation of any frequency and visually have color.Emission spectrum an absolutely black body is determined only by its temperature.

The importance of an absolutely black body in the question of the spectrum of thermal radiation of any (gray and colored) bodies in general, in addition to the fact that it represents the simplest non-trivial case, also lies in the fact that the question of the spectrum of equilibrium thermal radiation of bodies of any color and reflection coefficient is reduced by the methods of classical thermodynamics to the question of the radiation of an absolutely black body (and historically this was already done by the end of the 19th century, when the problem of radiation of an absolutely black body came to the fore).

The blackest real substances, for example, soot, absorb up to 99% of incident radiation (that is, they have albedo, equal to 0.01) in the visible wavelength range, but infrared radiation is absorbed much worse by them. Among the bodies solar system has the properties of an absolutely black body to the greatest extent Sun.

The term was introduced by Gustav Kirchhoff in 1862. Practical model

Black body model

Absolutely black bodies do not exist in nature, so in physics they are used for experiments. model. It is a closed cavity with a small hole. Light entering through this hole will be completely absorbed after repeated reflections, and the hole will appear completely black from the outside. 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 exits (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 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).

Laws of black body radiation Classical approach

Initially, purely classical methods were applied to solve the problem, which gave a number of important and correct results, but they did not allow the problem to be completely solved, ultimately leading not only to a sharp discrepancy with experiment, but also to an internal contradiction - the so-called ultraviolet disaster .

The study of the laws of black body radiation was one of the prerequisites for the appearance quantum mechanics.

Wien's first law of radiation

In 1893 Wilhelm Wien, using, in addition to classical thermodynamics, the electromagnetic theory of light, he derived the following formula:

uν - radiation energy density

ν - radiation frequency

T- temperature of the radiating body

f- a function that depends only on frequency and temperature. The form of this function cannot be established based only on thermodynamic considerations.

Wien's first formula is valid for all frequencies. Any more specific formula (for example, Planck's law) must satisfy Wien's first formula.

From the first formula of Wine we can deduce Wien's displacement law(maximum law) and Stefan-Boltzmann law, but it is impossible to find the values of the constants included in these laws.

Historically, it was Wien's first law that was called the displacement law, but currently the term " Wien's displacement law is called the law of maximum.

Pure black body

Radiation from a heated black body in the visible range

Absolutely black body- a physical abstraction used in thermodynamics, a body that absorbs all electromagnetic radiation incident on it in all ranges and does not reflect anything. Despite the name, a completely black body itself can emit electromagnetic radiation of any frequency and visually have a . The radiation spectrum of an absolutely black body is determined only by its temperature.

The blackest real substances, for example, soot, absorb up to 99% of incident radiation (i.e., have an albedo equal to 0.01) in the visible wavelength range, but infrared radiation is absorbed by them much worse. Among the bodies of the Solar System, the Sun has the properties of an absolutely black body to the greatest extent. The term was introduced by Gustav Kirchhoff in.

Practical model

Black body model

Absolutely black bodies do not exist in nature, so in physics a model is used for experiments. It is a closed cavity with a small hole. Light entering through this hole will be completely absorbed after repeated reflections, and the hole will appear completely black from the outside. But when this cavity is heated, it will develop its own visible radiation.

Laws of black body radiation

Classic approach

The study of the laws of black body radiation was one of the prerequisites for the emergence of quantum mechanics.

Wien's first law of radiation

Nevertheless, the Rayleigh-Jeans radiation law is valid for the long-wave region of the spectrum and adequately describes the nature of the radiation. The fact of such correspondence can be explained only by using a quantum mechanical approach, according to which radiation occurs discretely. Based on quantum laws, one can obtain Planck's formula, which will coincide with the Rayleigh-Jeans formula at .

This fact is an excellent illustration of the principle of correspondence, according to which a new physical theory must explain everything that the old one was able to explain.

Planck's law

Dependence of black body radiation power on wavelength

The radiation intensity of an absolutely black body, depending on temperature and frequency, is determined by Planck's law:

Where I(ν) dν - radiation power per unit area of the radiating surface in the frequency range from ν to ν + dν .

Equivalently,

Where u(λ) dλ - radiation power per unit area of the emitting surface in the wavelength range from λ to λ + dλ .

Stefan-Boltzmann law

The total energy of thermal radiation is determined Stefan-Boltzmann law:

Where j is the power per unit area of the radiating surface, and

W/(m²·K 4) - Stefan-Boltzmann constant.

Thus, an absolutely black body at T= 100 K emits 5.67 watts per square meter of its surface. At a temperature of 1000 K, the radiation power increases to 56.7 kilowatts per square meter.

Wien's displacement law

The wavelength at which the radiation energy of a completely black body is maximum is determined by Wien's displacement law:

So, if we assume as a first approximation that human skin is close in properties to an absolutely black body, then the maximum of the radiation spectrum at a temperature of 36°C (309 K) lies at a wavelength of 9400 nm (in the infrared region of the spectrum).

The apparent color of completely black bodies at different temperatures is shown in the diagram.

Blackbody radiation

Electromagnetic radiation that is in thermodynamic equilibrium with a blackbody at a given temperature (for example, radiation inside a cavity in a blackbody) is called blackbody (or thermal equilibrium) radiation. Equilibrium thermal radiation is homogeneous, isotropic and non-polarized, there is no energy transfer in it, all its characteristics depend only on the temperature of the absolutely blackbody emitter (and, since blackbody radiation is in thermal equilibrium with this body, this temperature can be attributed to radiation). The volumetric energy density of blackbody radiation is equal to , its

- a physical abstraction used in thermodynamics, a body that completely absorbs radiation in all ranges incident on it. Despite its name, a blackbody itself can emit electromagnetic radiation. The radiation spectrum of a completely black body is determined only by its temperature. A practical model of a blackbody would be a cavity with a small hole and blackened walls, since light entering the cavity through the hole experiences multiple reflections and is strongly absorbed. The deep black color of some materials (charcoal, black velvet) and the pupil of the human eye is explained by the same mechanism.
The term was coined by Gustav Kirchhoff in 1862.

The intensity of black body radiation depending on temperature and frequency is determined by Planck's law:

Where I (?) d ? – radiation power per unit area of the emitting surface per unit solid angle in the frequency range from? before? + d ?

The total energy of thermal radiation is determined by the Stefan-Boltzmann law:

Where F is the power per unit area of the radiating surface, and

W / (m 2 K 4) – became Stefan-Boltzmann.

The wavelength at which the radiation energy is maximum is determined by Wien's displacement law:

Where T is the temperature in Kelvin, and ? max– wavelength with maximum intensity in meters.
The apparent color of completely black bodies at different temperatures is shown in the diagram on the right.
Movement of light rays in an absolutely black body It is possible to artificially produce an almost absolutely black body by transforming the inner surface of an opaque body heated to a certain temperature with a cavity and a small hole. Any ray passing through hole A into cavity C practically does not come out back, and therefore experiences multiple reflections and absorption. So, hole A absorbs rays like a completely black body.
It should be noted that the geometric dimensions of an absolutely black body impose natural restrictions on the length of the electromagnetic wave that can propagate in it. Indeed, if the wavelength is greater than the size of the black body, then it simply cannot be seen from the walls in it. This fact is especially important in cosmology, when modeling the Universe in the form of an absolutely black body on early stages development, especially when considering cosmic microwave background radiation.
The concept of an absolute black body is widely used in astrophysics. The radiation of the Sun is close to the radiation of such a body with a temperature of 6000K. The entire Universe is permeated with so-called cosmic microwave background radiation, close to the radiation of an absolutely black body with a temperature of 3K. Comparing the total radiation of stars with the radiation of such a body allows us to approximately estimate the effective temperature of the star. The deviation of the star's radiation from that of a black body is often quite noticeable. In the depths of the Sun and stars, heated to tens of millions of degrees, the radiation corresponds to such radiation with high accuracy.
For the practical implementation of the black body model, it is necessary to ensure the possibility of uniform heating of the walls of the cavity and the emission of radiation out through a small hole. One of the first experimental samples of a black body was a device made by Lummer and Pringsheim. It was a metal container with double walls (similar to a thermostat). The space between the walls was used as a “temperature bath” to maintain a certain and uniform temperature. This was achieved by passing steam through boiling water or, for low temperatures, by filling it with ice, solid carbon dioxide, liquid air, etc.
To study radiation at high temperatures a black body of a different design was used. A cylinder made of platinum sheet, through which the electricity, is needed for uniform heating of the inner porcelain cylinder. The temperature inside the cylinder was measured by a thermocouple, and the diaphragms prevented cooling by the penetrating air.
Using similar simple devices - black body models, the laws of radiation were experimentally studied, its constants were accurately determined and the spectral distribution of brightness was studied.

To record the laws of radiation and absorption, the concept of an absolutely black body is introduced. Absolutely black body called an imaginary body that absorbs all the energy incident on it at any temperature. The emissive and absorptive abilities are interconnected, this connection is expressed Kirchhoff's law .

For all bodies at a given temperature, the ratio of emissive ability to absorptive ability is a constant value and equal to the emissive ability of an absolutely black body.

R depends on temperature, this dependence is expressed Stefan-Boltzmann law: