Constant plank j s. The bar constant and the geometry of the quantum nature of light

PLANK CONSTANTh, one of the universal numerical constants of nature, included in many formulas and physical laws describing the behavior of matter and energy on the scale of the microworld. The existence of this constant was established in 1900 by a professor of physics Berlin University M.Plankom in the 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 atoms, at any temperature above absolute zero, however, 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 approximately 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 n m 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 V different shapes, of different sizes and from different materials with the same temperature, face each other, as shown in fig. 2. If we assume that from A v V more radiation comes in than V v A, then the body V 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 for 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 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- constant (called Boltzmann constant, although it was first introduced by Planck), which appears in thermodynamics and kinetic theory 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 take place during oscillatory motion, for example in acoustics and 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 wave properties 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.

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

Experiments
Davisson-Germer experiment Popper's experiment Stern-Gerlach experiment Young's 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 physical units 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 rounder 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: it, 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, 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 - an expression for the spectral power density of radiation of 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 yard, the doctor told his wife (who had already stopped smiling 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 taken 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 in the twilight of dawn looked 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 to four people, the hussars, sounding with the slap of hooves on the wet road, the strumming of sabers and 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 were visible on a clean clean air, in the morning, oblique and bright, lighting, on the very horizon, our guns. 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.

Light is a form of radiant energy that propagates through space as electromagnetic waves. In 1900, the scientist Max Planck, one of the founders of quantum mechanics, proposed a theory according to which radiant energy is emitted and absorbed not by a continuous wave stream, but by separate portions, which are called quanta (photons).

The energy carried by one quantum is equal to: E = hv where v is the radiation frequency, and h – elementary quantum of action, which is a new universal constant, which soon received the name Planck's constant(according to modern data h = 6.626 × 10 -34 J s).

In 1913, Niels Bohr created a coherent, albeit simplified, model of the atom, consistent with the Planck distribution. Bohr proposed a theory of radiation based on the following postulates:

1. There are stationary states in the atom, in which the atom does not radiate energy. Stationary states of an atom correspond to stationary orbits along which electrons move;

2. When an electron moves from one stationary orbit to another (from one stationary state to another), an energy quantum is emitted or absorbed hν = ‌‌‌‌‌‌‌‌‌|E i – E n| , where ν is the frequency of the emitted quantum, E i – the energy of the state from which it passes, and E n is the energy of the state into which the electron passes.

If an electron, under any influence, moves from an orbit close to the nucleus to some other more distant one, then the energy of the atom increases, but what is required is the expenditure of external energy. But such an excited state of the atom is unstable and the electron falls back towards the nucleus to the nearest possible orbit.

And when an electron jumps (falls) to an orbit lying closer to the nucleus of an atom, then the energy lost by the atom turns into one quantum of radiant energy emitted by the atom.

Accordingly, any atom can emit a wide range of interconnected discrete frequencies, which depends on the orbits of electrons in the atom.

A hydrogen atom consists of a proton and an electron moving around it. If an electron absorbs a portion of energy, then the atom goes into an excited state. If the electron gives off energy, then the atom passes from a higher to a lower energy state. Normally, transitions from a higher energy state to a lower energy state are accompanied by the emission of energy in the form of light. However, nonradiative transitions are also possible. In this case, the atom passes into a lower energy state without emitting light, and gives off excess energy, for example, to another atom when they collide.

If an atom, passing from one energy state to another, radiates a spectral line with a wavelength λ, then, in accordance with Bohr's second postulate, the energy is radiated E equal to: , where h- Planck's constant; c is the speed of light.

The totality of all spectral lines that an atom can emit is called its emission spectrum.

As quantum mechanics shows, the spectrum of a hydrogen atom is expressed by the formula:

, where R is a constant called the Rydberg constant; n 1 and n 2 numbers, and n 1 < n 2 .

Each spectral line is characterized by a pair of quantum numbers n 2 and n one . They indicate the energy levels of the atom, respectively, before and after radiation.

During the transition of electrons from excited energy levels to the first ( n 1 = one; respectively n 2 = 2, 3, 4, 5…) is formed Lyman series.All Lyman series lines are in ultraviolet range.

Transitions of electrons from excited energy levels to the second level ( n 1 = 2; respectively n 2 = 3,4,5,6,7…) form Balmer series. The first four lines (that is, at n 2 = 3, 4, 5, 6) are in the visible spectrum, the rest (that is, at n 2 = 7, 8, 9) in ultraviolet.

That is, the visible spectral lines of this series are obtained if the electron jumps to the second level (second orbit): red - from the 3rd orbit, green - from the 4th orbit, blue - from the 5th orbit, violet - from the 6th orbit. oh orbit.

Transitions of electrons from excited energy levels to the third ( n 1 = 3; respectively n 2 = 4, 5, 6, 7…) form Paschen series. All lines of the Paschen series are located in infrared range.

Transitions of electrons from excited energy levels to the fourth ( n 1 = 4; respectively n 2 = 6, 7, 8…) form Brackett series. All lines of the series are in the far infrared range.

Also in the spectral series of hydrogen, the Pfund and Humphrey series are distinguished.

By observing the line spectrum of a hydrogen atom in the visible region (the Balmer series) and by measuring the wavelength λ of the spectral lines of this series, one can determine Planck's constant.

In the SI system, the calculation formula for finding Planck's constant when performing laboratory work will take the form:

,

where n 1 = 2 (Balmer series); n 2 = 3, 4, 5, 6.

= 3.2 × 10 -93

λ is the wavelength ( nm)

Planck's constant appears in all equations and formulas of quantum mechanics. In particular, it determines the scale from which the heisenberg uncertainty principle. Roughly speaking, Planck's constant indicates to us the lower limit of spatial quantities, after which one cannot disregard quantum effects. For grains of sand, say, the uncertainty of their product linear dimension speed is so small that it can be neglected. In other words, Planck's constant draws the line between the macrocosm, where the laws of Newton's mechanics apply, and the microcosm, where the laws of quantum mechanics come into force. Being obtained only for the theoretical description of a single physical phenomenon, Planck's constant soon became one of the fundamental constants of theoretical physics, determined by the very nature of the universe.

The work can be performed both on a laboratory setup and on a computer.

Planck's constant defines the boundary between the macrocosm, where the laws of Newton's mechanics apply, and the microcosm, where the laws of quantum mechanics apply.

Max Planck - one of the founders of quantum mechanics - came to the idea of ​​energy quantization, trying to theoretically explain the process of interaction between recently discovered electromagnetic waves(see Maxwell's equations) and atoms, and thereby solve the problem of black body radiation. He realized that in order 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 energy carried by one quantum is equal to:

where v is the frequency of radiation, and h is the elementary quantum of action, which is a new universal constant, which soon received the name Planck's constant. Planck was the first to calculate its value on the basis of experimental data h = 6.548 x 10–34 J s (in the SI system); according to modern data h = 6.626 x 10–34 J s. Accordingly, any atom can emit a wide range of interconnected discrete frequencies, which depends on the orbits of electrons in the atom. Soon, Niels Bohr will create a coherent, albeit simplified, model of the Bohr atom, consistent with the Planck distribution.

Having published his results at the end of 1900, Planck himself - and this is evident from his publications - at first did not believe that quanta were a physical reality, and not a convenient mathematical model. However, when Albert Einstein published an article five years later explaining the photoelectric effect based on the quantization of radiation energy, in scientific circles, Planck's formula was no longer perceived as a theoretical game, but as a description of a real physical phenomenon at the subatomic level, proving the quantum nature of energy.

Planck's constant appears in all equations and formulas of quantum mechanics. In particular, it determines the scales from which the Heisenberg uncertainty principle comes into force. Roughly speaking, Planck's constant indicates to us the lower limit of spatial quantities, after which one cannot disregard quantum effects. For grains of sand, say, the uncertainty of the product of their linear size and velocity is so small that it can be neglected. In other words, Planck's constant draws the line between the macrocosm, where the laws of Newton's mechanics apply, and the microcosm, where the laws of quantum mechanics come into force. Being obtained only for the theoretical description of a single physical phenomenon, Planck's constant soon became one of the fundamental constants of theoretical physics, determined by the very nature of the universe.

Max Karl Ernst Ludwig PLANK

Max Karl Ernst Ludwig Plank, 1858–1947

German physicist. Born in Kiel in the family of a professor of jurisprudence. As a virtuoso pianist, Planck in his youth was forced to make a difficult choice between science and music. Planck defended the law of thermodynamics in 1889 at the University of Munich - and in the same year became a teacher, and since 1892 - a professor at the University of Berlin, where he worked until his retirement in 1928. Planck is rightfully considered one of the fathers of quantum mechanics. Today, a whole network of German research institutes bears his name.

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 approximately 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 patterns: 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. 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 for 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 of an oscillator with a frequency n in a cavity that is 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 in his report showed 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), defining a wide range of physical phenomena, for which the discreteness of the 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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