The bar constant is a numerical value. Planck constant

PLANK CONSTANT
h, one of the universal numerical constants of nature, which is included in many formulas and physical laws that describe the behavior of matter and energy on a microscopic scale. The existence of this constant was established in 1900 by Professor of Physics at the University of Berlin M. Planck in a work that laid the foundations of quantum theory. They also gave a preliminary estimate of its magnitude. The currently accepted value of Planck's constant is (6.6260755 ± 0.00023)*10 -34 J*s. Planck made this discovery while trying to find a theoretical explanation for the spectrum of radiation emitted by heated bodies. Such radiation is emitted by all bodies consisting of a large number of atoms at any temperature above absolute zero, but it becomes noticeable only at temperatures close to the boiling point of water of 100 ° C and above it. In addition, it covers the entire frequency spectrum from the radio frequency range to the infrared, visible and ultraviolet regions. In the visible light region, the radiation becomes sufficiently bright only at about 550°C. The frequency dependence of the radiation intensity per unit time is characterized by the spectral distributions shown in Fig. 1 for multiple temperatures. The radiation intensity at a given frequency value is the amount of energy radiated in a narrow frequency band in the vicinity of a given frequency. The area of ​​the curve is proportional to the total energy radiated at all frequencies. It is easy to see that this area increases rapidly with increasing temperature.

Planck wanted to theoretically derive the spectral distribution function and find an explanation for two simple experimental regularities: the frequency corresponding to the brightest glow of a heated body is proportional to the absolute temperature, and the total energy radiated for 1 with a unit area of ​​the surface of a completely black body is the fourth power of its absolute temperature . The first regularity can be expressed by the formula

Where nm is the frequency corresponding to the maximum radiation intensity, T is the absolute temperature of the body, and a is a constant depending on the properties of the emitting object. The second regularity is expressed by the formula

Where E is the total energy emitted by a single surface area in 1 s, s is a constant characterizing the radiating object, and T is the absolute temperature of the body. The first formula is called the Wien displacement law, and the second is called the Stefan-Boltzmann law. Based on these laws, Planck sought to derive an exact expression for the spectral distribution of radiated energy at any temperature. The universal nature of the phenomenon could be explained from the standpoint of the second law of thermodynamics, according to which thermal processes occurring spontaneously in a physical system always go in the direction of establishing thermal equilibrium in the system. Let us imagine that two hollow bodies A and B of different shapes, different sizes and from different materials with the same temperature face each other, as shown in Fig. 2. If we assume that more radiation comes from A to B than from B to A, then the body B would inevitably become warmer due to A and the equilibrium would be spontaneously disturbed. This possibility is excluded by the second law of thermodynamics, and therefore, both bodies must radiate the same amount of energy, and, therefore, the value of s in formula (2) does not depend on the size and material of the radiating surface, provided that the latter is a kind of cavity. If the cavities were separated by a colored screen that would filter and reflect back all radiation except radiation with any one frequency, then everything said would remain true. This means that the amount of radiation emitted by each cavity in each region of the spectrum is the same, and the spectral distribution function for the cavity has the character of a universal law of nature, and the value a in formula (1), like the value s, is a universal physical constant.

Planck, who was well versed in thermodynamics, preferred just such a solution to the problem and, acting by trial and error, found a thermodynamic formula that allowed him to calculate the spectral distribution function. The resulting formula agreed with all available experimental data and, in particular, with empirical formulas (1) and (2). To explain this, Planck used a clever trick suggested by the second law of thermodynamics. Rightly believing that the thermodynamics of matter is better studied than the thermodynamics of radiation, he concentrated his attention mainly on the matter of the walls of the cavity, and not on the radiation inside it. Since the constants included in the laws of Wien and Stefan-Boltzmann do not depend on the nature of the substance, Planck was free to make any assumptions about the material of the walls. He chose a model in which the walls are composed of a huge number of tiny electrically charged oscillators, each with its own frequency. Oscillators under the action of radiation incident on them can oscillate, while radiating energy. The whole process could be investigated based on the well-known laws of electrodynamics, i.e. the spectral distribution function could be found by calculating the average energy of oscillators with different frequencies. Reversing the sequence of reasoning, Planck, based on the correct spectral distribution function he had guessed, found a formula for the average energy U of an oscillator with a frequency n in a cavity in equilibrium at an absolute temperature T:

Where b is a quantity determined experimentally, and k is a constant (called the Boltzmann constant, although it was first introduced by Planck), which appears in thermodynamics and the kinetic theory of gases. Since this constant usually enters with a factor T, it is convenient to introduce a new constant h = bk. Then b = h/k and formula (3) can be rewritten as

The new constant h is Planck's constant; its value calculated by Planck was 6.55×10-34 JChs, which is only about 1% different from the modern value. Planck's theory made it possible to express the value of s in formula (2) in terms of h, k and the speed of light c:

This expression agreed with experiment to the extent that the constants were known; more accurate measurements later found no discrepancies. Thus, the problem of explaining the spectral distribution function has been reduced to a more "simple" problem. It was necessary to explain what is the physical meaning of the constant h, or rather the product hn. Planck's discovery was that its physical meaning can be explained only by introducing a completely new concept of "energy quantum" into mechanics. On December 14, 1900, at a meeting of the German Physical Society, Planck showed in his report that formula (4), and thus the rest of the formulas, can be explained if we assume that an oscillator with a frequency n exchanges energy with an electromagnetic field not continuously, but, as it were, in steps, gaining and losing its energy in discrete portions, quanta, each of which is equal to hn.
see also
ELECTROMAGNETIC RADIATION ;
HEAT ;
THERMODYNAMICS.
The consequences of the discovery made by Planck are set out in the articles PHOTOELECTRIC EFFECT;
COMPTON EFFECT;
ATOM;
ATOM STRUCTURE;
QUANTUM MECHANICS . Quantum mechanics is a general theory of phenomena on the scale of the microcosm. Planck's discovery now appears as an important consequence of a special nature following from the equations of this theory. In particular, it turned out that it is valid for all energy exchange processes that occur during oscillatory motion, for example, in acoustics and in electromagnetic phenomena. This explains the high penetrating power of X-rays, whose frequencies are 100-10,000 times higher than the frequencies characteristic of visible light, and whose quanta have a correspondingly higher energy. Planck's discovery serves as the basis for the entire wave theory of matter dealing with the wave properties of elementary particles and their combinations. It is known from Maxwell's theory that a beam of light with energy E carries a momentum p equal to

Where c is the speed of light. If light quanta are considered as particles, each of which has an energy hn, then it is natural to assume that each of them has a momentum p equal to hn/c. The fundamental relation relating the wavelength l to the frequency n and the speed of light c has the form

So the expression for momentum can be written as h/l. In 1923, graduate student L. de Broglie suggested that not only light, but also all forms of matter, are characterized by wave-particle duality, expressed in the relations

Between the characteristics of a wave and a particle. This hypothesis was confirmed, which made Planck's constant a universal physical constant. Her role turned out to be much more significant than one might have assumed from the very beginning.
LITERATURE
Quantum metrology and fundamental constants. M., 1973 Shepf H.-G. From Kirchhoff to Planck. M., 1981

Collier Encyclopedia. - Open Society. 2000 .

See what "PLANK CONSTANT" is in other dictionaries:

- (quantum of action) the main constant of quantum theory (see Quantum mechanics), named after M. Planck. Planck constant h ??6,626.10 34 J.s. The value is often used. \u003d h / 2???? 1.0546.10 34 J.s, which is also called Planck's constant ... Big Encyclopedic Dictionary

- (quantum of action, denoted by h), fundamental physical. a constant that defines a wide range of physical. phenomena for which the discreteness of quantities with the dimension of the action is essential (see QUANTUM MECHANICS). Introduced by him. physicist M. Planck in 1900 with ... ... Physical Encyclopedia

- (quantum of action), the main constant of quantum theory (see Quantum mechanics). Named after M. Planck. Planck constant h≈6.626 10 34 J s. The value h = h / 2π≈1.0546 10 34 J s is often used, also called the Planck constant. * * *… … encyclopedic Dictionary

Planck's constant (quantum of action) is the main constant of quantum theory, a coefficient that relates the magnitude of the energy of electromagnetic radiation to its frequency. It also has the meaning of an action quantum and an angular momentum quantum. Introduced into scientific use by M ... Wikipedia

Quantum of action (See. Action), a fundamental physical constant (See. Physical constants), which determines a wide range of physical phenomena for which the discreteness of action is essential. These phenomena are studied in quantum mechanics (See ... Great Soviet Encyclopedia

- (quantum of action), osn. constant of quantum theory (see Quantum mechanics). Named after M. Planck. P. p. h 6.626 * 10 34 J * s. The value H \u003d h / 2PI 1.0546 * 10 34 J * s is often used, also called. P. p ... Natural science. encyclopedic Dictionary

Fundamental physics. constant, quantum of action, having the dimension of the product of energy and time. Defines a physical phenomena of the microworld, for which discrete physical is characteristic. quantities with the dimension of action (see Quantum mechanics). In size... ... Chemical Encyclopedia

One of the absolute physical constants, which has the dimension of action (energy X time); in the CGS system, the P. p. h is (6.62377 + 0.00018). 10 27 erg x sec (+0.00018 possible measurement error). It was first introduced by M. Planck (M. Planck, 1900) in ... ... Mathematical Encyclopedia

Quantum of action, one of the main. constants of physics, reflects the specifics of regularities in the microworld and plays a fundamental role in quantum mechanics. P. p. h (6.626 0755 ± 0.000 0040) * 10 34 J * s. Often use the value L \u003d d / 2n \u003d (1.054 572 66 ± ... Big encyclopedic polytechnic dictionary

Plank constant (quantum of action)- one of the fundamental world constants (constants), which plays a decisive role in the microcosm, manifested in the existence of discrete properties of micro-objects and their systems, expressed in integer quantum numbers, with the exception of half-integers ... ... Beginnings of modern natural science

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Material from the free Russian encyclopedia "Tradition"

Values h	Units
6,626   070  040(81) 10 −34	J∙s
4,135   667  662(25) 10 −15	eV∙c
6,626   070  040(81) 10 −27	erg∙c

Constant Planck , denoted as h, is a physical constant used to describe the magnitude of an action quantum in quantum mechanics. This constant first appeared in the works of M. Planck on thermal radiation, and therefore is named after him. It is present as a coefficient between energy E and frequency ν photon in Planck's formula:

speed of light c related to frequency ν and wavelength λ ratio:

With this in mind, the Planck relation is written as follows:

Often used value

j c,

Erg c,

EV c,

called the reduced (or rationalized) Planck constant or.

The Dirac constant is convenient to use when the angular frequency is applied ω , measured in radians per second, instead of the usual frequency ν measured in cycles per second. Because ω = 2π ν , then the formula is valid:

According to Planck's hypothesis, later confirmed, the energy of atomic states is quantized. This leads to the fact that the heated substance emits electromagnetic quanta or photons of certain frequencies, the spectrum of which depends on the chemical composition of the substance.

In Unicode, the Planck constant takes the position U+210E (h) and the Dirac constant U+210F (ħ).

Content 1 Value 2 Origin of Planck's constant 2.1 blackbody radiation 2.2 photoelectric effect 2.3 Atom structure 2.4 The uncertainty principle 2.5 Bremsstrahlung spectrum 3 Physical constants related to Planck's constant 3.1 Rest mass of an electron 3.2 Avogadro constant 3.3 elementary charge 3.4 Bohr magneton and nuclear magneton 4 Definition from experiments 4.1 Josephson constant 4.2 Power balance 4.3 magnetic resonance 4.4 Faraday constant 4.5 5 Planck's constant in SI units 6 Planck's constant in the theory of infinite nesting of matter 7 See also 8 Links 9 Literature 10 External links

Value

Planck's constant has the dimension of energy times time, just like the dimension of action. In the international SI system of units, Planck's constant is expressed in units of J s. The product of an impulse by a distance in the form of N ms, as well as the angular momentum, has the same dimension.

The value of Planck's constant is:

J s eV s

The two digits between brackets indicate the uncertainty in the last two digits of the value of Planck's constant (data are updated approximately every 4 years).

Origin of Planck's constant

blackbody radiation

Main article: Planck formula

At the end of the 19th century, Planck investigated the problem of black body radiation, which Kirchhoff had formulated 40 years earlier. Heated bodies glow the stronger, the higher their temperature and the greater the internal thermal energy. Heat is distributed among all the atoms of the body, setting them in motion relative to each other and excitation of electrons in the atoms. During the transition of electrons to stable states, photons are emitted, which can again be absorbed by atoms. At each temperature, a state of equilibrium between radiation and matter is possible, while the share of radiation energy in the total energy of the system depends on temperature. In a state of equilibrium with radiation, an absolutely black body not only absorbs all radiation incident on it, but also emits the very same amount of energy, according to a certain law of energy distribution over frequencies. The law relating body temperature to the power of the total radiated energy per unit surface of the body is called the Stefan-Boltzmann law and was established in 1879–1884.

When heated, not only the total amount of radiated energy increases, but the composition of the radiation also changes. This can be seen from the fact that the color of the heated bodies changes. According to Wien's displacement law of 1893, based on the principle of the adiabatic invariant, for each temperature it is possible to calculate the wavelength of radiation at which the body glows most strongly. Win made a fairly accurate estimate of the shape of the blackbody energy spectrum at high frequencies, but was unable to explain either the shape of the spectrum or its behavior at low frequencies.

Planck suggested that the behavior of light is similar to the movement of a set of identical harmonic oscillators. He studied the change in the entropy of these oscillators with temperature, trying to justify Wien's law, and found a suitable mathematical function for the spectrum of a black body.

However, Planck soon realized that, in addition to his solution, other solutions are also possible, leading to other values ​​of the oscillator entropy. As a result, he was forced to use statistical physics, which he had previously rejected, instead of the phenomenological approach, which he described as "an act of desperation ... I was ready to sacrifice any of my previous convictions in physics." One of the new terms adopted by Planck was:

interpret U N( oscillation energy of N oscillators ) not as a continuous infinitely divisible quantity, but as a discrete quantity consisting of a sum of limited equal parts. Let's designate each such part in the form of an element of energy through ε;

With this new condition, Planck actually introduced the quantization of the energy of oscillators, saying that this is "a purely formal assumption ... in fact, I did not think about it deeply ...", however, this led to a real revolution in physics. Application of a new approach to Wien's displacement law showed that the "energy element" must be proportional to the frequency of the oscillator. This was the first version of what is now called "Planck's formula":

Planck managed to calculate the value h from experimental data on black body radiation: his result was 6.55 10 −34 J s, with an accuracy of 1.2% of the currently accepted value. He was also able to determine for the first time k B from the same data and his theory.

Before Planck's theory, it was assumed that the energy of the body can be any, being a continuous function. This is equivalent to the fact that the energy element ε (the difference between the allowed energy levels) is equal to zero, therefore it must be equal to zero and h. Based on this, one should understand the statements that "Planck's constant is equal to zero in classical physics" or that "classical physics is the limit of quantum mechanics when the Planck constant tends to zero." Due to the smallness of Planck's constant, it almost does not appear in ordinary human experience and was invisible before Planck's work.

The blackbody problem was revisited in 1905 when Rayleigh and Jeans on the one hand, and Einstein on the other hand, independently proved that classical electrodynamics could not justify the observed radiation spectrum. This led to the so-called "ultraviolet catastrophe", thus designated by Ehrenfest in 1911. The efforts of theorists (together with Einstein's work on the photoelectric effect) led to the recognition that Planck's postulate of quantization of energy levels is not a simple mathematical formalism, but an important element of ideas about physical reality. The first Solvay congress in 1911 was devoted to "the theory of radiation and quanta". Max Planck was awarded the Nobel Prize in Physics in 1918 "for his contribution to the development of physics and the discovery of the quantum of energy."

photoelectric effect

Main article: photoelectric effect

The photoelectric effect is the emission of electrons (called photoelectrons) from a surface when illuminated by light. It was first observed by Becquerel in 1839, although Heinrich Hertz, who published an extensive study on the subject in 1887, is usually mentioned. Stoletov in 1888–1890 made several discoveries in the field of the photoelectric effect, including the first law of the external photoelectric effect. Another important study of the photoelectric effect was published by Lenard in 1902. Although Einstein did not himself experiment on the photoelectric effect, his 1905 work considered the effect based on light quanta. This earned Einstein the Nobel Prize in 1921 when his predictions were confirmed by Millikan's experimental work. At this time, Einstein's theory of the photoelectric effect was seen as more significant than his theory of relativity.

Before Einstein's work, each electromagnetic radiation was considered as a set of waves with its own "frequency" and "wavelength". The energy carried by a wave per unit of time is called intensity. Other types of waves have similar parameters, for example, a sound wave or a wave on water. However, the energy transfer associated with the photoelectric effect does not agree with the wave pattern of light.

The kinetic energy of photoelectrons appearing in the photoelectric effect can be measured. It turns out that it does not depend on the light intensity, but depends linearly on the frequency. In this case, an increase in light intensity does not lead to an increase in the kinetic energy of photoelectrons, but to an increase in their number. If the frequency is too low and the kinetic energy of the photoelectrons is about zero, then the photoelectric effect disappears, despite the significant light intensity.

According to Einstein's explanation, the quantum nature of light is revealed in these observations; light energy is carried in small "packets" or quanta rather than as a continuous wave. The magnitude of these "packets" of energy, which were later called photons, was the same as that of Planck's "elements of energy". This led to the modern form of Planck's formula for the photon energy:

Einstein's postulate was proved experimentally: the constant of proportionality between the frequency of light ν and photon energy E turned out to be equal to Planck's constant h.

Atom structure

Main article: Bohr's postulates

Niels Bohr introduced the first quantum model of the atom in 1913 in an attempt to get rid of the difficulties of Rutherford's classical model of the atom. According to classical electrodynamics, a point charge, when rotating around a fixed center, must radiate electromagnetic energy. If such a picture is valid for an electron in an atom as it rotates around the nucleus, then over time the electron will lose energy and fall onto the nucleus. To overcome this paradox, Bohr proposed to consider, similarly to how it takes place for photons, that an electron in a hydrogen-like atom must have quantized energies E n:

Where R∞ is an experimentally determined constant (the Rydberg constant in reciprocal length units), With is the speed of light, n is an integer ( n = 1, 2, 3, …), Z- the serial number of the chemical element in the periodic table, equal to one for the hydrogen atom. An electron that has entered the lower energy level ( n= 1), is in the ground state of the atom and can no longer, due to reasons not yet determined in quantum mechanics, reduce its energy. This approach allowed Bohr to arrive at the Rydberg formula, which empirically describes the emission spectrum of the hydrogen atom, and calculate the value of the Rydberg constant R∞ in terms of other fundamental constants.

Bohr also introduced the quantity h/2π , known as the reduced Planck's constant or ħ, as the quantum of angular momentum. Bohr assumed that ħ determines the modulus of the angular momentum of each electron in the atom. But this proved to be inaccurate despite improvements in Bohr's theory by Sommerfeld and others. Quantum theory turned out to be more correct, in the form of Heisenberg's matrix mechanics in 1925 and in the form of the Schrödinger equation in 1926. At the same time, the Dirac constant remained the fundamental quantum of angular momentum. If J is the total angular momentum of the system with rotational invariance, and Jz is the angular momentum measured along the selected direction, then these quantities can only have the following values:

The uncertainty principle

Planck's constant is also contained in the expression for Werner Heisenberg's uncertainty principle. If we take a large number of particles in the same state, then the uncertainty in their position Δ x, and the uncertainty in their momentum (in the same direction), Δ p, obey the relation:

where the uncertainty is given as the standard deviation of the measured quantity from its mathematical expectation. There are other similar pairs of physical quantities for which the uncertainty relation is valid.

In quantum mechanics, Planck's constant enters the expression for the commutator between the position operator and the momentum operator:

where δ ij is the Kronecker symbol.

Bremsstrahlung spectrum

When electrons interact with the electrostatic field of atomic nuclei, bremsstrahlung occurs in the form of X-ray quanta. It is known that the frequency spectrum of X-ray bremsstrahlung has a precise upper limit, called the violet limit. Its existence follows from the quantum properties of electromagnetic radiation and the law of conservation of energy. Really,

where is the speed of light,

is the X-ray wavelength,

is the charge of an electron,

is the accelerating voltage between the electrodes of the X-ray tube.

Then Planck's constant will be equal to:

Physical constants related to Planck's constant

The list of constants below is based on 2014 data CODATA. . Approximately 90% of the inaccuracies in these constants are due to the inaccuracy in determining the Planck constant, as can be seen from the square of the Pearson correlation coefficient ( r 2 > 0,99, r> 0.995). When compared with other constants, Planck's constant is known to an accuracy of the order with measurement uncertainty 1 σ .This accuracy is significantly better than or UGC.

Rest mass of an electron

As a rule, the Rydberg constant R∞ (in reciprocal length units) is defined in terms of the mass m e and other physical constants:

The Rydberg constant can be determined very precisely ( ) from the spectrum of the hydrogen atom, while there is no direct way to measure the mass of the electron. Therefore, to determine the mass of an electron, the formula is used:

Where c is the speed of light and α There is . The speed of light is determined quite accurately in the SI system of units, as is the fine structure constant ( ). Therefore, the inaccuracy in determining the electron mass depends only on the inaccuracy of Planck's constant ( r 2 > 0,999).

Avogadro constant

Main article: Avogadro's number

Avogadro's number N A is defined as the ratio of the mass of one mole of electrons to the mass of one electron. To find it, you need to take the mass of one mole of electrons in the form of the "relative atomic mass" of the electron A r (e) measured in Penning trap () times the unit molar mass M u , which in turn is defined as 0.001 kg/mol. The result is:

The dependence of the Avogadro number on the Planck constant ( r 2 > 0.999) is repeated for other constants related to the amount of substance, for example, for the atomic mass unit. Uncertainty in the value of Planck's constant limits the values ​​of atomic masses and particles in SI units, that is, in kilograms. At the same time, the particle mass ratios are known with better accuracy.

elementary charge

Sommerfeld originally determined the fine structure constant α So:

Where e there is an elementary electric charge, ε 0 - (also called the vacuum permittivity), μ 0 - magnetic constant or magnetic permeability of vacuum. The last two constants have fixed values ​​in the SI system of units. Meaning α can be determined experimentally by measuring the electron g-factor g e and subsequent comparison with the value following from quantum electrodynamics.

Currently, the most accurate value of the elementary electric charge is obtained from the above formula:

Bohr magneton and nuclear magneton

Main articles: Bohr magneton , nuclear magneton

The Bohr magneton and the nuclear magneton are units used to describe the magnetic properties of the electron and atomic nuclei, respectively. The Bohr magneton is the magnetic moment expected of an electron if it behaved like a spinning charged particle according to classical electrodynamics. Its value is derived through the Dirac constant, the elementary electric charge and the mass of the electron. All these quantities are derived through Planck's constant, the resulting dependence on h ½ ( r 2 > 0.995) can be found using the formula:

The nuclear magneton has a similar definition, with the difference that the proton is much more massive than the electron. The ratio of the electronic relative atomic mass to the proton relative atomic mass can be determined with great accuracy ( ). For the connection between both magnetons, we can write:

Definition from experiments

Method	Meaning h, 10 –34 J∙s	Accuracy definitions
Power balance	6,626 068 89(23)	3,4∙10 –8
X-ray density of a crystal	6,626 074 5(19)	2,9∙10 –7
Josephson constant	6,626 067 8(27)	4,1∙10 –7
magnetic resonance	6,626 072 4(57)	8,6∙10 –7	[ 20 ]
Faraday constant	6,626 065 7(88)	1,3∙10 –6
CODATA 20 10 accepted value	6,626 06 9 57 (29 )	4 , 4 ∙10 –8	[ 22 ]
For five different methods, nine recent measurements of Planck's constant are listed. If there is more than one measurement, the weighted average is indicated h according to the CODATA methodology.

Planck's constant can be determined from the spectrum of a radiating blackbody or the kinetic energy of photoelectrons, as was done in the early twentieth century. However, these methods are not the most accurate. Meaning h according to CODATA based on the basis of three measurements by the power balance method of the product of quantities K J2 R K and one interlaboratory measurement of the molar volume of silicon, mainly by the power balance method until 2007 in the USA at the National Institute of Standards and Technology (NIST). Other measurements indicated in the table did not affect the result due to insufficient accuracy.

There are both practical and theoretical difficulties in determining h. Thus, the most accurate methods for balancing the power and X-ray density of a crystal do not fully agree with each other in their results. This may be due to an overestimation of the accuracy in these methods. Theoretical difficulties stem from the fact that all methods, except for the X-ray density of a crystal, are based on the theoretical basis of the Josephson effect and the quantum Hall effect. With some possible inaccuracy of these theories, there will also be an inaccuracy in the definition of Planck's constant. At the same time, the obtained value of Planck's constant can no longer be used as a test to test these theories in order to avoid a vicious logical circle. On the positive side, there are independent statistical ways to test these theories.

Josephson constant

Main article: Josephson effect

Josephson constant K J links the potential difference U, arising in the Josephson effect in "Josephson contacts", with a frequency ν microwave radiation. From the theory, the expression follows quite strictly:

The Josephson constant can be measured by comparing it to the potential difference that occurs in a battery of Josephson contacts. To measure the potential difference, the compensation of the electrostatic force by the force of gravity is used. It follows from the theory that after the replacement of the electric charge e on its value in terms of fundamental constants (see above elementary charge ), the expression for Planck's constant in terms of K J:

Power balance

This method compares two types of power, one of which is measured in SI units in watts, and the other is measured in conventional electrical units. From the definition conditional watt W 90 , he gives the measure for the product K J2 R K in SI units, where R K is the Klitzing constant that appears in the quantum Hall effect. If the theoretical treatment of the Josephson effect and the quantum Hall effect is correct, then R K= h/e 2 , and measurement K J2 R K leads to the definition of Planck's constant:

magnetic resonance

Main article: Gyromagnetic ratio

Gyromagnetic ratio γ is the proportionality factor between the frequency ν nuclear magnetic resonance (or electron paramagnetic resonance for electrons), and an applied magnetic field B: ν = γB. Although there is difficulty in determining the gyromagnetic ratio due to inaccurate measurements B, for protons in water at 25 °C it is known with a better accuracy than 10–6. The protons are partially "shielded" from the applied magnetic field by the electrons of the water molecules. The same effect leads to chemical shift in nuclear magnetic spectroscopy, and is indicated by a stroke at the gyromagnetic ratio symbol, γ′ p . The gyromagnetic ratio is related to the magnetic moment of the screened proton μ′ p , spin quantum number S (S=1/2 for protons) and the Dirac constant:

The ratio of the magnetic moment of a shielded proton μ′ p to the magnetic moment of the electron μ e can be measured independently with high accuracy, since the inaccuracy of the magnetic field has little effect on the result. Meaning μ e , expressed in Bohr magnetons, is equal to half of the electronic g-factor g e. Hence,

A further complication is due to the fact that for the measurement γ′ p you need to measure the electric current. This current is independently measured in conditional amperes, so conversion to SI amps requires a conversion factor. Symbol Γ′ p-90 denotes the measured gyromagnetic ratio in conventional electrical units (the permitted use of these units began in the beginning of 1990). This value can be measured in two ways, the "weak field" method and the "strong field" method, and the conversion factor in these cases is different. Usually, the strong field method is used to measure the Planck constant and the value Γ′ p-90 (hi):

After the replacement, the expression for Planck's constant is obtained in terms of Γ′ p-90 (hi):

Faraday constant

Main article: Faraday constant

Faraday constant F is the charge of one mole of electrons, equal to Avogadro's number N A multiplied by the elementary electric charge e. It can be determined by careful electrolysis experiments, by measuring the amount of silver transferred from one electrode to another in a given time at a given electrical current. In practice, it is measured in conventional electrical units, and is denoted F 90 . Substituting values N A and e, and moving from conventional electrical units to SI units, we get the ratio for Planck's constant:

X-ray density of a crystal

The crystal X-ray density method is the main method for measuring the Avogadro constant N A , and through it the Planck constant h. For finding N A is the ratio between the volume of a unit cell of a crystal, measured by X-ray diffraction analysis, and the molar volume of a substance. Silicon crystals are used because they are available in high quality and purity due to technology developed in semiconductor manufacturing. The unit cell volume is calculated from the space between two crystal planes, denoted d 220 . Molar volume V m (Si) is calculated in terms of the density of the crystal and the atomic weight of the silicon used. Planck's constant is given by:

Planck's constant in SI units

Main article: Kilogram

As mentioned above, the numerical value of Planck's constant depends on the system of units used. Its value in the SI system of units is known with an accuracy of 1.2∙10 -8, although in atomic (quantum) units it is determined exactly(in atomic units, by choosing the units of energy and time, one can achieve that the Dirac constant, as the reduced Planck constant, is equal to 1). The same situation takes place in conventional electrical units, where Planck's constant (written h 90, in contrast to the notation in SI) is given by the expression:

Where K J-90 and R K–90 are well-defined constants. Atomic units and conventional electrical units are convenient to use in their respective fields, since the uncertainties in the final result depend only on the measurement uncertainties, without requiring an additional and inaccurate SI conversion factor.

There are a number of proposals for modernizing the values ​​of the existing system of SI base units with the help of fundamental physical constants. This has already been done for the meter, which is defined in terms of a given value for the speed of light. A possible next unit for revision is the kilogram, whose value has been fixed since 1889 by the mass of a small cylinder of platinum-iridium alloy stored under three glass jars. There are about 80 copies of such mass standards, which are periodically compared with the international mass unit. The accuracy of secondary standards varies over time due to their use, up to values ​​of tens of micrograms. This roughly corresponds to the inaccuracy in the definition of Planck's constant.

At the 24th General Conference on Weights and Measures on October 17-21, 2011, a resolution was unanimously adopted, in which, in particular, it was proposed in a future revision of the International System of Units (SI) to redefine the SI units in such a way that the Planck constant was exactly equal to 6.62606X 10 −34 J s where X replaces one or more significant figures to be determined based on the best CODATA recommendations. . In the same resolution, it was proposed in the same way to determine the exact values ​​of the Avogadro constant, and .

Planck's constant in the theory of infinite nesting of matter

Unlike atomism, there are no material objects in the theory - particles with a minimum mass or size. Instead, it assumes an infinite divisibility of matter into increasingly smaller structures, and at the same time the existence of many objects that are much larger than our Metagalaxy. At the same time, matter is organized into separate levels according to masses and sizes, for which arises, manifests itself and is realized.

Just like the Boltzmann constant and a number of other constants, the Planck constant reflects the properties inherent in the level of elementary particles (primarily nucleons and , which make up matter). On the one hand, Planck's constant relates the energy of photons and their frequency; on the other hand, it, up to a small numerical coefficient 2π , in the form of ħ sets the unit of the orbital momentum of an electron in an atom. Such a connection is not accidental, since when emitting from an atom, an electron reduces its orbital angular momentum, transferring it to a photon during the period of existence of the excited state. For one period of revolution of the electron cloud around the nucleus, the photon receives such a fraction of energy that corresponds to the fraction of the angular momentum transferred by the electron. The average frequency of the photon is close to the frequency of rotation of the electron near the energy level where the electron passes during radiation, since the radiation power of the electron increases rapidly as it approaches the nucleus.

Mathematically, this can be described as follows. The equation of rotational motion has the form:

Where K - moment of power, L is the moment of momentum. If we multiply this ratio by the rotation angle increment and take into account that there is a change in the electron rotation energy, and there is an angular frequency of the orbital rotation, then it will be:

In this ratio, the energy dE can be interpreted as an increment in the energy of the emitted photon when it increments the angular momentum by the value dL . For the total photon energy E and the total angular momentum of the photon, the value ω should be understood as the average angular frequency of the photon.

In addition to correlating the properties of emitted photons and atomic electrons through angular momentum, atomic nuclei also have angular momentum expressed in units of ħ. It can therefore be assumed that Planck's constant describes the rotational motion of elementary particles (nucleons, nuclei and electrons, the orbital motion of electrons in an atom), and the transformation of the energy of rotation and vibrations of charged particles into radiation energy. In addition, based on the idea of ​​wave-particle duality, in quantum mechanics, all particles are attributed to the de Broglie material wave accompanying them. This wave is considered in the form of a wave of the amplitude of the probability of finding a particle at a particular point in space. As for photons, the Planck and Dirac constants in this case become coefficients of proportionality for a quantum particle, entering into the expressions for the momentum of the particle , for the energy E and for action S :

· Mixed state · Measurement · Uncertainty · Pauli principle · Dualism · Decoherence · Ehrenfest's theorem · Tunnel effect

Experiments
Davisson-Germer Experiment Popper Experiment Stern-Gerlach Experiment Young Experiment Verification of Bell's Inequalities Photoelectric Effect Compton Effect

Wording
Schrödinger representation Heisenberg representation Interaction representation Matrix quantum mechanics Path integrals Feynman diagrams

Equations
Schrödinger equation Pauli equation Klein-Gordon equation Dirac equation Schwinger-Tomonaga equation Von Neumann equation Bloch equation Lindblad equation Heisenberg equation

Interpretations
Copenhagen Hidden Variables Theory Many Worlds De Broglie-Bohm Theory

Development of the theory
Quantum field theory Quantum electrodynamics Glashow-Weinberg-Salam theory Quantum chromodynamics Standard model Quantum gravity

Notable scientists
Planck Einstein Schrödinger Heisenberg Jordan Bohr Pauli Dirac Fock Born de Broglie Landau Feynman Bohm Everett

See also: Portal:Physics

physical meaning

In quantum mechanics, momentum has the physical meaning of a wave vector, energy - frequencies, and action - wave phases, however, traditionally (historically) mechanical quantities are measured in other units (kg m / s, J, J s) than the corresponding wave (m −1, s −1, dimensionless phase units). Planck's constant plays the role of a conversion factor (always the same) connecting these two systems of units - quantum and traditional:

$\backslash mathbf\; p\; =\; \backslash hbar\; \backslash mathbf\; k$(pulse) $(|\backslash mathbf\; p|=\; 2\; \backslash pi\; \backslash hbar\; /\; \backslash lambda)$ $E\; =\; \backslash hbar\; \backslash omega$(energy) $S\; =\; \backslash hbar\; \backslash phi$(action)

If the system of physical units had already been formed after the advent of quantum mechanics and adapted to simplify the basic theoretical formulas, Planck's constant would probably simply have been made equal to one, or at least to a more round number. In theoretical physics, a system of units with $\backslash hbar\; =\; 1$, in it

$\backslash mathbf\; p\; =\; \backslash mathbf\; k$ $(|\backslash mathbf\; p|=\; 2\; \backslash pi\; /\; \backslash lambda)$ $E\; =\; \backslash omega$ $S\; =\; \backslash phi$ $(\backslash hbar\; =\; 1)$.

Planck's constant also has a simple evaluative role in delimiting the areas of applicability of classical and quantum physics: in comparison with the magnitude of the action or angular momentum values ​​characteristic of the system under consideration, or the products of the characteristic momentum by the characteristic size, or the characteristic energy by the characteristic time, it shows how applicable to a given physical system classical mechanics. Namely, if $S$ is the operation of the system, and $M$ is its angular momentum, then $\backslash frac(S)(\backslash hbar)\backslash gg1$ or $\backslash frac(M)(\backslash hbar)\backslash gg1$ the behavior of the system is described with good accuracy by classical mechanics. These estimates are quite directly related to the Heisenberg uncertainty relations.

Discovery history

Planck's formula for thermal radiation

Planck's formula is an expression for the spectral power density of radiation from a black body, which was obtained by Max Planck for the equilibrium radiation density $u(\backslash omega,\; T)$. Planck's formula was obtained after it became clear that the Rayleigh-Jeans formula satisfactorily describes radiation only in the region of long waves. In 1900, Planck proposed a formula with a constant (later called Planck's constant), which agreed well with experimental data. At the same time, Planck believed that this formula is just a successful mathematical trick, but has no physical meaning. That is, Planck did not assume that electromagnetic radiation is emitted in the form of separate portions of energy (quanta), the magnitude of which is related to the cyclic frequency of radiation by the expression:

$\backslash varepsilon\; =\; \backslash hbar\; \backslash omega.$

Proportionality factor $\backslash hbar$ subsequently called Planck's constant, $\backslash hbar$= 1.054 10 −34 J s.

photoelectric effect

The photoelectric effect is the emission of electrons by a substance under the influence of light (and, generally speaking, any electromagnetic radiation). In condensed substances (solid and liquid), external and internal photoelectric effects are distinguished.

Then the same photocell is irradiated with monochromatic light with a frequency $\backslash nu\_2$ and in the same way they lock it with the help of voltage $U\_2:$

$h\backslash nu\_2=A+eU\_2.$

Subtracting the second expression term by term from the first one, we obtain

$h(\backslash nu\_1-\backslash nu\_2)=e(U\_1-U\_2),$

whence it follows

$h=\backslash frac\; (e(U\_1-U\_2))((\backslash nu\_1-\backslash nu\_2)).$

Analysis of the bremsstrahlung spectrum

This method is considered the most accurate of the existing ones. The fact that the frequency spectrum of bremsstrahlung X-rays has a sharp upper limit, called the violet border, is used. Its existence follows from the quantum properties of electromagnetic radiation and the law of conservation of energy. Really,

$h\backslash frac(c)(\backslash lambda)=eU,$

Where $c$- the speed of light,

$\backslash lambda$- wavelength of X-ray radiation, $e$ is the charge of an electron, $U$- accelerating voltage between the electrodes of the x-ray tube.

Then Planck's constant is

$h=\backslash frac((\backslash lambda)(Ue))(c).$

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Notes

Literature

• John D. Barrow. The Constants of Nature; From Alpha to Omega - The Numbers that Encode the Deepest Secrets of the Universe. - Pantheon Books, 2002. - ISBN 0-37-542221-8.
• Steiner R.// Reports on Progress in Physics. - 2013. - Vol. 76. - P. 016101.

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An excerpt characterizing Planck's Constant

“This is my cup,” he said. - Just put your finger in, I'll drink it all.
When the samovar was all drunk, Rostov took the cards and offered to play kings with Marya Genrikhovna. A lot was cast as to who should form the party of Marya Genrikhovna. The rules of the game, at the suggestion of Rostov, were that the one who would be the king had the right to kiss the hand of Marya Genrikhovna, and that the one who remained a scoundrel would go to put a new samovar for the doctor when he wakes up.
“Well, what if Marya Genrikhovna becomes king?” Ilyin asked.
- She's a queen! And her orders are the law.
The game had just begun, when the doctor's confused head suddenly rose from behind Marya Genrikhovna. He had not slept for a long time and listened to what was said, and apparently did not find anything cheerful, funny or amusing in everything that was said and done. His face was sad and dejected. He did not greet the officers, scratched himself and asked for permission to leave, as he was blocked from the road. As soon as he left, all the officers burst into loud laughter, and Marya Genrikhovna blushed to tears, and thus became even more attractive to the eyes of all the officers. Returning from the courtyard, the doctor told his wife (who had already ceased to smile so happily and, fearfully awaiting the verdict, looked at him) that the rain had passed and that we had to go to spend the night in a wagon, otherwise they would all be dragged away.
- Yes, I'll send a messenger ... two! Rostov said. - Come on, doctor.
"I'll be on my own!" Ilyin said.
“No, gentlemen, you slept well, but I haven’t slept for two nights,” said the doctor, and sat down gloomily beside his wife, waiting for the game to be over.
Looking at the gloomy face of the doctor, looking askance at his wife, the officers became even more cheerful, and many could not help laughing, for which they hastily tried to find plausible pretexts. When the doctor left, taking his wife away, and got into the wagon with her, the officers lay down in the tavern, covering themselves with wet overcoats; but they didn’t sleep for a long time, now talking, remembering the doctor’s fright and the doctor’s merriment, now running out onto the porch and reporting what was happening in the wagon. Several times Rostov, wrapping himself up, wanted to fall asleep; but again someone's remark amused him, again the conversation began, and again there was heard the causeless, cheerful, childish laughter.

At three o'clock, no one had yet fallen asleep, when the sergeant-major appeared with the order to march to the town of Ostrovna.
All with the same accent and laughter, the officers hurriedly began to gather; again put the samovar on the dirty water. But Rostov, without waiting for tea, went to the squadron. It was already light; The rain stopped, the clouds dispersed. It was damp and cold, especially in a damp dress. Leaving the tavern, Rostov and Ilyin both looked in the twilight of dawn into the doctor's leather tent, glossy from the rain, from under the apron of which the doctor's legs stuck out and in the middle of which the doctor's bonnet was visible on the pillow and sleepy breathing was heard.
"Really, she's very nice!" Rostov said to Ilyin, who was leaving with him.
- What a lovely woman! Ilyin replied with sixteen-year-old seriousness.
Half an hour later, the lined up squadron stood on the road. The command was heard: “Sit down! The soldiers crossed themselves and began to sit down. Rostov, riding forward, commanded: “March! - and, stretching out in four people, the hussars, sounding with the slapping of hooves on the wet road, the strumming of sabers and in a low voice, set off along the large road lined with birches, following the infantry and the battery walking ahead.
Broken blue-lilac clouds, reddening at sunrise, were quickly driven by the wind. It got brighter and brighter. One could clearly see that curly grass that always sits along country roads, still wet from yesterday's rain; the hanging branches of the birch trees, also wet, swayed in the wind and dropped light drops to the side. The faces of the soldiers became clearer and clearer. Rostov rode with Ilyin, who did not lag behind him, along the side of the road, between a double row of birches.
Rostov in the campaign allowed himself the freedom to ride not on a front-line horse, but on a Cossack. Both a connoisseur and a hunter, he recently got himself a dashing Don, large and kind playful horse, on which no one jumped him. Riding this horse was a pleasure for Rostov. He thought of the horse, of the morning, of the doctor's wife, and never once thought of the impending danger.
Before, Rostov, going into business, was afraid; now he did not feel the least sense of fear. Not because he was not afraid that he was accustomed to fire (one cannot get used to danger), but because he had learned to control his soul in the face of danger. He was accustomed, going into business, to think about everything, except for what seemed to be more interesting than anything else - about the impending danger. No matter how hard he tried, or reproached himself for cowardice during the first time of his service, he could not achieve this; but over the years it has now become self-evident. He was now riding beside Ilyin between the birches, occasionally tearing leaves from the branches that came to hand, sometimes touching the horse's groin with his foot, sometimes giving, without turning, his smoked pipe to the hussar who was riding behind, with such a calm and carefree look, as if he were riding ride. It was a pity for him to look at the agitated face of Ilyin, who spoke a lot and uneasily; he knew from experience that agonizing state of expectation of fear and death in which the cornet was, and he knew that nothing but time would help him.
As soon as the sun appeared on a clear strip from under the clouds, the wind died down, as if he did not dare to spoil this charming summer morning after a thunderstorm; the drops were still falling, but already sheer, and everything was quiet. The sun came out completely, appeared on the horizon and disappeared in a narrow and long cloud that stood above it. A few minutes later the sun appeared even brighter on the upper edge of the cloud, tearing its edges. Everything lit up and sparkled. And along with this light, as if answering it, shots of guns were heard ahead.
Rostov had not yet had time to think over and determine how far these shots were, when the adjutant of Count Osterman Tolstoy galloped up from Vitebsk with orders to trot along the road.
The squadron drove around the infantry and the battery, which was also in a hurry to go faster, went downhill and, passing through some empty, without inhabitants, village, again climbed the mountain. The horses began to soar, the people blushed.
- Stop, equalize! - the command of the divisional was heard ahead.
- Left shoulder forward, step march! commanded ahead.
And the hussars along the line of troops went to the left flank of the position and stood behind our lancers, who were in the first line. On the right, our infantry stood in a dense column - these were reserves; Above it on the mountain, in the clear, clean air, in the morning, oblique and bright, illumination, on the very horizon, our cannons were visible. Enemy columns and cannons were visible ahead beyond the hollow. In the hollow we could hear our chain, already in action and merrily snapping with the enemy.
Rostov, as from the sounds of the most cheerful music, felt cheerful in his soul from these sounds, which had not been heard for a long time. Trap ta ta tap! - clapped suddenly, then quickly, one after another, several shots. Everything fell silent again, and again crackers seemed to crackle, on which someone walked.
The hussars stood for about an hour in one place. The cannonade began. Count Osterman and his retinue rode behind the squadron, stopped, spoke with the regimental commander, and rode off to the cannons on the mountain.
Following the departure of Osterman, a command was heard from the lancers:
- Into the column, line up for the attack! “The infantry ahead of them doubled up in platoons to let the cavalry through. The lancers set off, swaying with the weathercocks of their peaks, and at a trot went downhill towards the French cavalry, which appeared under the mountain to the left.
As soon as the lancers went downhill, the hussars were ordered to move uphill, to cover the battery. While the hussars took the place of the uhlans, distant, missing bullets flew from the chain, screeching and whistling.
This sound, which had not been heard for a long time, had an even more joyful and exciting effect on Rostov than the previous sounds of shooting. He, straightening up, looked at the battlefield that opened from the mountain, and wholeheartedly participated in the movement of the lancers. The lancers flew close to the French dragoons, something tangled up in the smoke there, and after five minutes the lancers rushed back not to the place where they were standing, but to the left. Between the orange lancers on red horses and behind them, in a large bunch, blue French dragoons on gray horses were visible.

Rostov, with his keen hunting eye, was one of the first to see these blue French dragoons pursuing our lancers. Closer, closer, the uhlans moved in disordered crowds, and the French dragoons pursuing them. It was already possible to see how these people, who seemed small under the mountain, collided, overtook each other and waved their arms or sabers.
Rostov looked at what was going on in front of him as if he were being persecuted. He instinctively felt that if they now attacked the French dragoons with the hussars, they would not resist; but if you strike, it was necessary now, this very minute, otherwise it would be too late. He looked around him. The captain, standing beside him, kept his eyes on the cavalry below in the same way.
“Andrey Sevastyanych,” said Rostov, “after all, we doubt them ...
“It would be a dashing thing,” said the captain, “but in fact ...
Rostov, without listening to him, pushed his horse, galloped ahead of the squadron, and before he had time to command the movement, the whole squadron, experiencing the same thing as he, set off after him. Rostov himself did not know how and why he did it. He did all this, as he did on the hunt, without thinking, without understanding. He saw that the dragoons were close, that they were jumping, upset; he knew that they would not stand it, he knew that there was only one minute that would not return if he missed it. The bullets squealed and whistled so excitedly around him, the horse begged forward so eagerly that he could not stand it. He touched the horse, commanded, and at the same instant, hearing the sound of the clatter of his deployed squadron behind him, at full trot, began to descend to the dragoons downhill. As soon as they went downhill, their gait of the lynx involuntarily turned into a gallop, becoming faster and faster as they approached their lancers and the French dragoons galloping after them. The dragoons were close. The front ones, seeing the hussars, began to turn back, the rear ones to stop. With the feeling with which he rushed across the wolf, Rostov, releasing his bottom in full swing, galloped across the frustrated ranks of the French dragoons. One lancer stopped, one on foot crouched to the ground so as not to be crushed, one horse without a rider got mixed up with the hussars. Almost all French dragoons galloped back. Rostov, choosing one of them on a gray horse, set off after him. On the way he ran into a bush; a good horse carried him over him, and, barely managing on the saddle, Nikolai saw that in a few moments he would catch up with the enemy whom he had chosen as his target. This Frenchman, probably an officer - according to his uniform, bent over, galloped on his gray horse, urging it on with a saber. A moment later, Rostov's horse struck the officer's horse with its chest, almost knocking it down, and at the same instant Rostov, without knowing why, raised his saber and hit the Frenchman with it.

PLANK CONSTANTh, one of the universal numerical constants of nature, which is included in many formulas and physical laws that describe the behavior of matter and energy on a microscopic scale. The existence of this constant was established in 1900 by Professor of Physics at the University of Berlin M. Planck in a work that laid the foundations of quantum theory. They also gave a preliminary estimate of its magnitude. The currently accepted value of Planck's constant is (6.6260755 ± 0.00023) H 10 -34 JH s.

Planck made this discovery while trying to find a theoretical explanation for the spectrum of radiation emitted by heated bodies. Such radiation is emitted by all bodies consisting of a large number of atoms at any temperature above absolute zero, but it becomes noticeable only at temperatures close to the boiling point of water of 100 ° C and above it. In addition, it covers the entire frequency spectrum from the radio frequency range to the infrared, visible and ultraviolet regions. In the visible light region, the radiation becomes sufficiently bright only at about 550°C. The frequency dependence of the radiation intensity per unit time is characterized by the spectral distributions shown in Fig. 1 for multiple temperatures. The radiation intensity at a given frequency value is the amount of energy radiated in a narrow frequency band in the vicinity of a given frequency. The area of ​​the curve is proportional to the total energy radiated at all frequencies. It is easy to see that this area increases rapidly with increasing temperature.

Planck wanted to theoretically derive the spectral distribution function and find an explanation for two simple experimental regularities: the frequency corresponding to the brightest glow of a heated body is proportional to the absolute temperature, and the total energy radiated for 1 with a unit area of ​​the surface of a completely black body is the fourth power of its absolute temperature .

The first regularity can be expressed by the formula

Where nm is the frequency corresponding to the maximum radiation intensity, T is the absolute body temperature, and a is a constant depending on the properties of the emitting object. The second regularity is expressed by the formula

Where E is the total energy emitted by a single surface area in 1 s, s is a constant characterizing the radiating object, and T is the absolute body temperature. The first formula is called the Wien displacement law, and the second is called the Stefan-Boltzmann law. Based on these laws, Planck sought to derive an exact expression for the spectral distribution of radiated energy at any temperature.

The universal nature of the phenomenon could be explained from the standpoint of the second law of thermodynamics, according to which thermal processes occurring spontaneously in a physical system always go in the direction of establishing thermal equilibrium in the system. Imagine that two hollow bodies A And IN different shapes, different sizes and from different materials with the same temperature facing each other, as shown in Fig. 2. If we assume that from A V IN more radiation comes in than IN V A, then the body IN would inevitably become warmer due to A and the balance would spontaneously break. This possibility is ruled out by the second law of thermodynamics, and consequently, both bodies must radiate the same amount of energy, and, therefore, the quantity s in formula (2) does not depend on the size and material of the radiating surface, provided that the latter is a kind of cavity. If the cavities were separated by a colored screen that would filter and reflect back all radiation except radiation with any one frequency, then everything said would remain true. This means that the amount of radiation emitted by each cavity in each section of the spectrum is the same, and the spectral distribution function for the cavity has the character of a universal law of nature, and the value a in formula (1), like the value s, is a universal physical constant.

Planck, who was well versed in thermodynamics, preferred just such a solution to the problem and, acting by trial and error, found a thermodynamic formula that allowed him to calculate the spectral distribution function. The resulting formula agreed with all available experimental data and, in particular, with empirical formulas (1) and (2). To explain this, Planck used a clever trick suggested by the second law of thermodynamics. Rightly believing that the thermodynamics of matter is better studied than the thermodynamics of radiation, he concentrated his attention mainly on the matter of the walls of the cavity, and not on the radiation inside it. Since the constants included in the laws of Wien and Stefan-Boltzmann do not depend on the nature of the substance, Planck was free to make any assumptions about the material of the walls. He chose a model in which the walls are composed of a huge number of tiny electrically charged oscillators, each with its own frequency. Oscillators under the action of radiation incident on them can oscillate, while radiating energy. The whole process could be investigated based on the well-known laws of electrodynamics, i.e. the spectral distribution function could be found by calculating the average energy of oscillators with different frequencies. Reversing the sequence of reasoning, Planck, based on the correct spectral distribution function he guessed, found a formula for the average energy U oscillator with frequency n in a cavity in equilibrium at absolute temperature T:

Where b is the value determined experimentally, and k- a constant (called the Boltzmann constant, although it was first introduced by Planck), which appears in thermodynamics and the kinetic theory of gases. Since this constant usually comes with a factor T, it is convenient to introduce a new constant h= bk. Then b = h/k and formula (3) can be rewritten as

New constant h and is Planck's constant; its value calculated by Planck was 6.55 H 10 -34 JH s, which is only about 1% different from the modern value. Planck's theory made it possible to express the quantity s in formula (2) through h, k and the speed of light With:

This expression agreed with experiment to the extent that the constants were known; more accurate measurements later found no discrepancies.

Thus, the problem of explaining the spectral distribution function has been reduced to a more "simple" problem. It was necessary to explain what is the physical meaning of the constant h or, rather, works hn. Planck's discovery was that its physical meaning can be explained only by introducing a completely new concept of "energy quantum" into mechanics. On December 14, 1900, at a meeting of the German Physical Society, Planck showed in his report that formula (4), and thus the rest of the formulas, can be explained if we assume that an oscillator with a frequency n exchanges energy with the electromagnetic field not continuously, but as if in stages, gaining and losing its energy in discrete portions, quanta, each of which is equal to hn. HEAT; THERMODYNAMICS. The consequences of the discovery made by Planck are set forth in the articles PHOTOELECTRIC EFFECT; COMPTON EFFECT; ATOM; ATOM STRUCTURE; QUANTUM MECHANICS.

Quantum mechanics is a general theory of phenomena on the scale of the microcosm. Planck's discovery now appears as an important consequence of a special nature following from the equations of this theory. In particular, it turned out that it is valid for all energy exchange processes that occur during oscillatory motion, for example, in acoustics and in electromagnetic phenomena. This explains the high penetrating power of X-rays, whose frequencies are 100–10,000 times higher than the frequencies characteristic of visible light, and whose quanta have a correspondingly higher energy. Planck's discovery serves as the basis for the entire wave theory of matter dealing with the wave properties of elementary particles and their combinations.

between the characteristics of the wave and the particle. This hypothesis was confirmed, which made Planck's constant a universal physical constant. Her role turned out to be much more significant than one might have assumed from the very beginning.

In this article, on the basis of the photon concept, the physical essence of the “fundamental constant” of Planck's constant is revealed. Arguments are given showing that Planck's constant is a typical parameter of a photon, which is a function of its wavelength.

Introduction. The end of the 19th - the beginning of the 20th centuries was marked by a crisis in theoretical physics, due to the inability of the methods of classical physics to substantiate a number of problems, one of which was the “ultraviolet catastrophe”. The essence of this problem was that when establishing the law of energy distribution in the radiation spectrum of an absolutely black body by the methods of classical physics, the spectral density of the radiation energy should have increased indefinitely as the radiation wavelength shortened. In fact, this problem showed, if not the internal inconsistency of classical physics, then, in any case, an extremely sharp discrepancy with elementary observations and experiment.

Studies of the properties of blackbody radiation, which took place for almost forty years (1860-1900), ended with the advancement of Max Planck's hypothesis that the energy of any system E when emitting or absorbing electromagnetic radiation frequency ν (\displaystyle ~\nu ) can only change by a multiple of the quantum energy:

E γ = hν (\displaystyle ~E=h\nu ) . (1)(\displaystyle~h)

Proportionality factor h in expression (1) entered science under the name "Planck constant", becoming basic constant quantum theory .

The blackbody problem was revisited in 1905 when Rayleigh and Jeans on the one hand, and Einstein on the other hand, independently proved that classical electrodynamics could not justify the observed radiation spectrum. This led to the so-called "ultraviolet catastrophe", thus designated by Ehrenfest in 1911. The efforts of theorists (together with Einstein's work on the photoelectric effect) led to the recognition that Planck's postulate of quantization of energy levels is not a simple mathematical formalism, but an important element of ideas about physical reality.

Further development of Planck's quantum ideas - substantiation of the photoelectric effect using the hypothesis of light quanta (A. Einstein, 1905), postulate in Bohr's theory of the atom quantization of the angular momentum of an electron in an atom (N. Bohr, 1913), discovery of de Broglie's relation between the mass of a particle and its length waves (L. De Broglie, 1921), and then the creation of quantum mechanics (1925 - 26) and the establishment of fundamental uncertainty relations between momentum and coordinate and between energy and time (W. Heisenberg, 1927) led to the establishment of the fundamental status of Planck's constant in physics .

Modern quantum physics also adheres to this point of view: “In the future, it will become clear to us that the formula E / ν \u003d h expresses the fundamental principle of quantum physics, namely, the relationship between energy and frequency that has a universal character: E \u003d hν. This connection is completely alien to classical physics, and the mystical constant h is a manifestation of the mysteries of nature that were not comprehended at that time.

At the same time, there was an alternative view of Planck's constant: “Textbooks on quantum mechanics say that classical physics is physics in which h equals zero. But in fact, the Planck constant h - this is nothing but a quantity that actually defines the concept well known in the classical physics of the gyroscope. An explanation to adepts studying physics that h ≠ 0 is a purely quantum phenomenon, which has no analogue in classical physics, was one of the main elements aimed at strengthening the belief about the necessity of quantum mechanics.”

Thus, the views of theoretical physicists on Planck's constant were divided. On the one hand, there is its exclusivity and mystification, and on the other hand, an attempt to give a physical interpretation that does not go beyond the framework of classical physics. This situation persists in physics at the present time, and will persist until the physical essence of this constant is established.

The physical essence of Planck's constant. Planck managed to calculate the value h from experimental data on black body radiation: its result was 6.55 10 −34 J s, with an accuracy of 1.2% of the currently accepted value , however, to substantiate the physical essence of the constant h he could not. The disclosure of the physical essence of any phenomena is not characteristic of quantum mechanics: “The reason for the crisis in specific areas of science is the general inability of modern theoretical physics to understand the physical essence of phenomena, to reveal the internal mechanism of phenomena, the structure of material formations and interaction fields, to understand the cause-and-effect relationships between elements, phenomena." Therefore, apart from mythology, she could not imagine anything else in this matter. In general, these views are reflected in the work: “Planck's constant h as a physical fact means the existence of the smallest, non-reducible and non-contractible finite amount of action in nature. As a non-zero commutator for any pair of dynamic and kinematic quantities that form the dimension of the action by their product, Planck's constant generates the non-commutativity property for these quantities, which in turn is the primary and irremovable source of the inevitably probabilistic description of physical reality in any spaces of dynamics and kinematics. Hence the universality and universality of quantum physics.”

In contrast to the ideas of the adherents of quantum physics on the nature of Planck's constant, their opponents were more pragmatic. The physical meaning of their ideas was reduced to “calculation by the methods of classical mechanics of the value of the main angular momentum of the electron P e (momentum associated with the rotation of an electron around its own axis) and obtaining the mathematical expression for Planck's constant " h » through known fundamental constants.” From which the physical entity was substantiated: “ Planck's constant « h » is equal to size classical the main angular momentum of an electron (associated with the rotation of the electron around its own axis), multiplied by 4 p. ”

The fallacy of these views lies in the misunderstanding of the nature of elementary particles and the origins of the appearance of Planck's constant. An electron is a structural element of an atom of a substance, which has its own functional purpose - the formation of the physicochemical properties of the atoms of a substance. Therefore, it cannot act as a carrier of electromagnetic radiation, i.e. Planck's hypothesis about the transfer of energy by a quantum to an electron is not applicable.

To substantiate the physical essence of Planck's constant, let's consider this problem in a historical aspect. It follows from the above that the solution to the problem of the “ultraviolet catastrophe” was Planck's hypothesis that the radiation of a completely black body occurs in portions, i.e., energy quanta. Many physicists of that time initially assumed that the quantization of energy is the result of some unknown property of matter that absorbs and emits electromagnetic waves. However, already in 1905, Einstein developed Planck's idea, assuming that energy quantization is a property of electromagnetic radiation itself. Based on the hypothesis of light quanta, he explained a number of patterns of the photoelectric effect, luminescence, and photochemical reactions.

The validity of Einstein's hypothesis was experimentally confirmed by the study of the photoelectric effect by R. Millikan (1914-1916) and by the study of X-ray scattering by electrons by A. Compton (1922-1923). Thus, it became possible to consider the light quantum as an elementary particle, subject to the same kinematic laws as the particles of matter.

In 1926, Lewis proposed the term “photon” for this particle, which was adopted by the scientific community. According to modern concepts, a photon is an elementary particle, a quantum of electromagnetic radiation. Photon rest mass m g is zero (experimental limitation m g<5 . 10 -60 г), и поэтому его скорость равна скорости света . Электрический заряд фотона также равен нулю .

If a photon is a quantum (carrier) of electromagnetic radiation, then its electric charge cannot be equal to zero in any way. The inconsistency of this representation of the photon has become one of the reasons for the misunderstanding of the physical essence of Planck's constant.

The irresolvable substantiation of the physical essence of Planck's constant within the framework of existing physical theories makes it possible to overcome the etherodynamic concept developed by V.A. Atsukovsky.

In etherodynamic models, elementary particles are interpreted as closed vortex formations(rings), in the walls of which the ether is significantly compacted, and elementary particles, atoms and molecules are structures that unite such vortices. The existence of ring and helical motions corresponds to the presence of a mechanical moment (spin) in particles directed along the axis of its free motion.

According to this concept, structurally, a photon is a closed toroidal vortex with an annular motion of the torus (like wheels) and a helical motion inside it. The source of photon generation is the proton-electron pair of atoms of matter. As a result of excitation, due to the symmetry of its structure, each proton-electron pair generates two photons. Experimental confirmation of this is the process of annihilation of an electron and a positron.

A photon is the only elementary particle that is characterized by three types of motion: rotational motion around its own axis of rotation, rectilinear motion in a given direction, and rotational motion with a certain radius R relative to the axis of linear motion. The last movement is interpreted as movement along the cycloid. A cycloid is a periodic function along the abscissa, with a period 2π R (\displaystyle 2\pi r)/…. For a photon, the cycloid period is interpreted as a wavelength λ , which is the argument of all other photon parameters.

On the other hand, the wavelength is also one of the parameters of electromagnetic radiation: a perturbation (change of state) of the electromagnetic field propagating in space. For which the wavelength is the distance between two points in space closest to each other, in which oscillations occur in the same phase.

From which follows a significant difference in the concepts of wavelength for a photon and electromagnetic radiation in general.

For a photon, the wavelength and frequency are related by the relation

ν = u γ / λ, (2)

Where u γ is the speed of the rectilinear motion of the photon.

A photon is a concept referring to a family (set) of elementary particles united by common signs of existence. Each photon is characterized by its specific set of characteristics, one of which is the wavelength. At the same time, taking into account the interdependence of these characteristics from each other, in practice it has become convenient to represent the characteristics (parameters) of a photon as functions of one variable. The photon wavelength was determined as an independent variable.

Known value u λ = 299 792 458 ± 1.2 / defined as the speed of light. This value was obtained by K. Ivenson and his co-workers in 1972 using the cesium frequency standard of the CH 4 laser, and using the krypton frequency standard, its wavelength (about 3.39 μm). Thus, formally, the speed of light is defined as the rectilinear speed of photons with a wavelength λ = 3,39 10 -6 m. Theoretically (\displaystyle 2\pi r)/… it is established that the speed of (rectilinear) photons is variable and non-linear, i.e. u λ = f( λ). Experimental confirmation of this is the work related to the research and development of laser frequency standards (\displaystyle 2\pi r)/…. It follows from the results of these studies that all photons for which λ < 3,39 10 -6 m moving faster than the speed of light. The limiting speed of photons (gamma range) is the second sound speed of the ether 3 10 8 m/s (\displaystyle 2\pi r)/….

These studies allow us to draw one more significant conclusion that the change in the speed of photons in the region of their existence does not exceed ≈ 0.1%. Such a relatively small change in the speed of photons in the region of their existence allows us to speak of the speed of photons as a quasi-constant value.

A photon is an elementary particle whose inalienable properties are mass and electric charge. Erengaft's experiments proved that the electric charge of a photon (subelectron) has a continuous spectrum, and from Millikan's experiments it follows that for an X-ray photon, with a wavelength of approximately 10 -9 m, the electric charge is 0.80108831 C (\displaystyle 2\pi r )/….

According to the first materialized definition of the physical essence of electric charge: “ the elementary electric charge is proportional to the mass distributed over the section of the elementary vortex“ follows the inverse statement that the mass distributed over the cross section of the vortex is proportional to the electric charge. Based on the physical nature of the electric charge, it follows that the mass of the photon also has a continuous spectrum. Based on the structural similarity of the elementary particles of the proton, electron and photon, the values ​​of the mass and radius of the proton (respectively, m p = 1.672621637(83) 10 -27 kg, rp = 0.8751 10 -15 m (\displaystyle 2\pi r)/…), and also, assuming the equality of the ether density in these particles, the photon mass is estimated at 10 -40 kg, and its circular orbit radius is 0.179◦10 −16 m, the radius of the photon body (the outer radius of the torus) is presumably in the range of 0.01 - 0.001 of the radius of the circular orbit, i.e., about 10 -19 - 10 -20 m.

Based on the concepts of the multiplicity of photons and the dependence of photon parameters on the wavelength, as well as the experimentally confirmed facts of the continuity of the spectrum of electric charge and mass, we can assume that e λ , m λ = f ( λ ) , which have the character of quasi-constant.

Based on the foregoing, we can say that expression (1) establishing the relationship of the energy of any system during the emission or absorption of electromagnetic radiation with a frequency ν (\displaystyle ~\nu ) is nothing more than the relationship between the energy of photons emitted or absorbed by the body and the frequency (wavelength) of these photons. And Planck's constant is the correlation coefficient. Such a representation of the relationship between the energy of a photon and its frequency removes from Planck's constant the significance of its universality and fundamentality. In this context, Planck's constant becomes one of the parameters of the photon, dependent on the wavelength of the photon.

For a complete and sufficient proof of this statement, let us consider the energy aspect of the photon. It is known from experimental data that a photon is characterized by an energy spectrum that has a non-linear dependence: for infrared photons Е λ = 0.62 eV for λ = 2 10 -6 m, x-ray Е λ = 124 eV for λ = 10 -8 m, gamma Е λ = 124000 eV for λ = 10 -11 m. From the nature of the motion of a photon, it follows that the total energy of a photon consists of the kinetic energy of rotation around its own axis, the kinetic energy of rotation along a circular path (cycloid) and the energy of rectilinear motion:

E λ = E 0 λ + E 1 λ+E 2 λ , (3)

where E 0 λ = m λ r 2 γ λ ω 2 γ λ is the kinetic energy of rotation around its own axis,

E 1 λ = m λ u λ 2 is the energy of rectilinear motion, E 2 λ = m λ R 2 λ ω 2 λ is the kinetic energy of rotation along a circular path, where r γ λ is the radius of the photon body, R γ λ is the radius of the circular trajectory , ω γ λ is the natural frequency of rotation of the photon around the axis, ω λ = ν is the circular frequency of rotation of the photon, m λ is the mass of the photon.

Kinetic energy of a photon in a circular orbit

E 2 λ = m λ r 2 λ ω 2 λ = m λ r 2 λ (2π u λ / λ) 2 = m λ u λ 2 ◦ (2π r λ / λ) 2 = E 1 λ ◦ (2π r λ /λ) 2 .

E 2 λ = E 1 λ ◦ (2π r λ / λ) 2 . (4)

Expression (4) shows that the kinetic energy of rotation along a circular trajectory is part of the energy of rectilinear motion, which depends on the radius of the circular trajectory and the wavelength of the photon

(2π r λ / λ) 2 . (5)

Let's estimate this value. For infrared photons

(2π r λ / λ) 2 \u003d (2π 10 -19 m / 2 10 -6 m) 2 \u003d π 10 -13.

For gamma-range photons

(2π r λ / λ) 2 \u003d (2π 10 -19 m / 2 10 -11 m) 2 \u003d π 10 -8.

Thus, in the entire region of existence of a photon, its kinetic energy of rotation along a circular trajectory is much less than the energy of rectilinear motion and can be neglected.

Let us estimate the energy of rectilinear motion.

E 1 λ \u003d m λ u λ 2 \u003d 10 -40 kg (3 10 8 m / s) 2 \u003d 0.9 10 -23 kg m 2 / s 2 \u003d 5.61 10 -5 eV.

The energy of the rectilinear motion of a photon in the energy balance (3) is much less than the total photon energy, for example, in the infrared range (5.61 10 -5 eV< 0,62 эВ), что указывает на то, что полная энергия фотона фактически определяется собственной кинетической энергией вращения вокруг оси фотона.

Thus, in view of the smallness of the energies of rectilinear motion and motion along a circular trajectory, we can say that the energy spectrum of a photon consists of the spectrum of its own kinetic energies of rotation around the photon axis.

Therefore, expression (1) can be represented as

E 0 λ = hν ,

i.e.(\displaystyle ~E=h\nu )

m λ r 2 γ λ ω 2 γ λ = h ν . (6)

h = m λ r 2 γ λ ω 2 γ λ / ν = m λ r 2 γ λ ω 2 γ λ / ω λ . (7)

Expression (7) can be represented in the following form

h = m λ r 2 γ λ ω 2 γ λ / ω λ = (m λ r 2 γ λ) ω 2 γ λ / ω λ = k λ (λ) ω 2 γ λ / ω λ .

h = k λ (λ) ω 2 γ λ / ω λ . (8)

Where k λ (λ) = m λ r 2 γ λ is some quasi-constant.

Let us estimate the values ​​of the natural frequencies of rotation of photons around the axis: for example,

For λ = 2 10 -6 m (infrared range)

ω 2 γ i = E 0i / m i r 2 γ i \u003d 0.62 1.602 10 −19 J / (10 -40 kg 10 -38 m 2) \u003d 0.99 1059 s -2,

ω γ i = 3.14 10 29 rpm.

For λ = 10 -11 m (gamma)

ω γ i = 1.4 10 32 rpm.

Let us estimate the ratio ω 2 γ λ / ω λ for infrared and gamma photons. After substituting the above data, we get:

For λ = 2 10 -6 m (infrared range) - ω 2 γ λ / ω λ \u003d 6.607 10 44,

For λ = 10 -11 m (gamma range) - ω 2 γ λ / ω λ \u003d 6.653 10 44.

That is, expression (8) shows that the ratio of the square of the photon's own rotation frequency to rotation along a circular path is a quasi-constant value for the entire region of photon existence. In this case, the value of the frequency of the photon's own rotation in the region of existence of the photon changes by three orders of magnitude. From which it follows that Planck's constant has the character of a quasi-constant.

We transform expression (6) as follows

m λ r 2 γ λ ω γ λ ω γ λ = h ω λ .

M =h ω λ / ω γ λ , (9)

where M = m λ r 2 γ λ ω γ λ is the intrinsic gyroscopic moment of the photon.

From expression (9) follows the physical essence of Planck's constant: Planck's constant is a proportionality coefficient that establishes the relationship between the photon's own gyroscopic moment and the ratio of rotational frequencies (along the circular trajectory and its own), which has the character of a quasi-constant in the entire region of the photon's existence.

We transform expression (7) as follows

h = m λ r 2 γ λ ω 2 γ λ / ω λ = m λ r 2 γ λ m λ r 2 γ λ R 2 λ ω 2 γ λ / (m λ r 2 γ λ R 2 λ ω λ) =

= (m λ r 2 γ λ ω γ λ) 2 R 2 λ / (m λ R 2 λ ω λ r 2 γ λ) =M 2 γ λ R 2 λ / M λ r 2 γ λ ,

h = (M 2 γ λ / M λ) (R 2 λ / r 2 γ λ),

h ( r 2 γ λ /R 2 λ), = (M 2 γ λ / M λ) (10)

Expression (10) also shows that the ratio of the square of the intrinsic gyroscopic moment of a photon to the gyroscopic moment of motion along a circular trajectory (cycloid) is a quasi-constant value in the entire region of existence of a photon and is determined by the expression h ( r 2 γ λ /R 2 λ).