Page 1
§ 36. PRESSURE OF LIGHT. PHOTONS.

Basic formulas

The pressure produced by light at normal incidence is

p=(E e /c)*(1+ρ), or p=(1+ρ),

where Ee - surface irradiance; With - speed of electromagnetic radiation in vacuum;  - volume density of radiation energy; ρ is the reflection coefficient.

Photon energy

ε = hυ=hc/λ , or ε = ħ ,

Where h- Planck's constant; ħ=h/(2π); υ - light frequency;  - circular frequency; λ is the wavelength.

The mass and momentum of a photon are expressed, respectively, by the formulas

m=ε/c 2 = h/(cλ); p=mc=h/λ .
Examples of problem solving

Example 1 A beam of monochromatic light with a wavelength of λ = 663 nm falls normally on a mirror flat surface Energy flux Ф e = 0.6 W. Determine strength F pressure experienced by this surface, as well as the number N photons falling on it in time t=5 s

Solution The force of light pressure on the surface is equal to the product of light pressure R to the area S of the surface:

F= PS. (1)

The light pressure can be found from the formula

P=E e (ρ+l)/c (2)

Substituting expression (2) for light pressure into formula (1), we obtain

F= [(E e S)/c]*(ρ+1). (3)

Since the product of the irradiance E e and the area S of the surface is equal to the flux Ф of the radiation energy incident on the surface, relation (3) can be written as

F \u003d (Ф e / s) * (ρ + 1).

After substituting the values ​​of Ф e and With taking into account that ρ=1 (mirror surface), we obtain

Number N photons incident on the surface during the time ∆t is determined by the formula

N=∆W/ε = Ф e ∆t/ε ,

where ∆W is the radiation energy received by the surface during the time ∆ t

Expressing the photon energy in this formula in terms of the wavelength (ε = hc/λ), we obtain

N= Ф e λ∆t/(hc).

Substituting in this formula the numerical values ​​of the quantities, we find

N= 10 19 photons.

Example 2 A parallel beam of light with a wavelength of λ=500 nm falls normally on a blackened surface, producing a pressure of p=10 µPa. Define: 1) concentration P photons in the beam, 2) the number n 1 of photons incident on a surface of 1 m 2 in a time of 1 s.

Solution. 1. Concentration P photons in the beam can be found as a quotient of the volumetric energy density  divided by the energy ε of one photon:

n=/ε (1)

From the formula p \u003d  (1 + ρ), which determines the pressure of light, where ρ is the reflection coefficient, we find

 = p/(ρ+1). (2)

Substituting the expression for  from equation (2) to formula (1), we obtain

n = ρ/[(ρ+1)*ε]. (3)

The photon energy depends on the frequency υ, and therefore on the light wavelength λ:

ε = hυ = hc/λ (4)

Substituting the expression for the photon energy into formula (3), we determine the required photon concentration:

n = (ρλ)/[(ρ+1)*ε]. (5)

The reflection coefficient ρ for the blackened surface is taken equal to zero.

Substituting numerical values ​​into formula (5), we obtain

n \u003d 2.52 * 10 13 m -3.

2. The number n 1 of photons incident on a surface of 1 m 2 in a time of 1 s can be found from the relation n 1 = N/(St), Where N- number of photons falling in time t onto a surface of area S. But N= ncSt, hence,

n 1 =(ncSt)/(St)=nc

Substituting here the values P And With, we get

n 1 \u003d 7.56 * 10 21 m -2 * s -1.

Example3 . Monochromatic (λ = 0.582 μm) the light beam is incident normally on the surface with a reflection coefficient ρ = 0.7. Determine the number of photons falling every second on 1 cm 2 of this surface if the light pressure on this surface is p = 1.2 μPa. Find the concentration of photons in 1 cm 3 of the incident light beam.

Solution. The pressure exerted by light on a surface at normal incidence is given by:

where E is the energy incident on a unit surface per unit time (energy illumination), c is the speed of light, ρ is the reflection coefficient of the surface.

On the other hand, irradiance can be expressed in terms of the number of incident photons N:

(2)

Where
is the energy of the incident photon. Then based on (1) and (2) we get:

(3)

Substituting numerical data, we get the number of photons falling on 1 m 2 of the surface for 1 s. Accordingly, the number of photons N" falls on the area S \u003d 1 cm 2:

(4)

Substituting numerical data in the SI system (S \u003d 10 -4 m 2), we get
photons.

The photon concentration near the surface in the incident beam is given by:

where n 0 is the number of photons in 1 m 3. Then the number of photons in 1 cm 3 is

(5)

Substituting numerical data into (5) taking into account the fact that V = 10 -6 m 3, we get

4. Monochromatic light with a wavelength is normally incident on a blackened surface λ = 0.65 µm, producing pressure p=510 -6 Pa. Determine the concentration of photons near the surface and the number of photons incident on the area S \u003d 1 m 2 in t = 1 s.

or
, (1)

Where E e– energy illumination of the surface;

With is the speed of light in vacuum; ω is the volumetric energy density.

The volumetric energy density is equal to the product of the photon concentration (the number of photons per unit volume) and the energy of one photon:

, i.e.
, where
. (2)

From expression (1) we determine the volumetric energy density
.

Then
, Where ρ = 0 (blackened surface).

The number of photons incident on the area S\u003d 1 m 2 in 1 second, numerically equal to the ratio of energy illumination to the energy of one photon:

.

From expression (1) energy illumination

The luminescence intensity can be calculated by the formula:

I l \u003d 2.3 I 0  D, whence the quantum yield of luminescence

The formula under consideration is the definition of the quantum yield of luminescence, we substitute the numbers and perform the calculations:

= .

Answer: the quantum yield of the luminescence of the substance is 0.6.

Page 1

The hypothesis of the existence of light pressure was first put forward by I. Kepler in the 17th century to explain the behavior of comet tails during their flight near the Sun. In 1873 Maxwell gave a theory of the pressure of light within the framework of his classical electrodynamics. Light pressure was first studied experimentally by P. N. Lebedev in 1899. In his experiments, a rotary balance was suspended on a thin silver thread in an evacuated vessel, to the beams of which thin disks of mica and various metals were attached. The main difficulty was to distinguish light pressure against the background of radiometric and convective forces (forces due to the difference in temperature of the surrounding gas from the illuminated and unlit sides). By alternately irradiating different sides of the wings, Lebedev leveled the radiometric forces and obtained a satisfactory (±20%) agreement with Maxwell's theory. Later, in 1907-1910. Lebedev carried out more precise experiments on the pressure of light in gases and also obtained an acceptable agreement with the theory.

physical meaning

According to today's ideas, light has corpuscular-wave dualism, that is, it exhibits the properties of particles (photons) and the properties of waves (electromagnetic radiation).

If we consider light as a stream of photons, then, according to the principles of classical mechanics, when particles hit a body, they must transfer momentum to it, in other words, exert pressure. This pressure is sometimes called radiation pressure.

To calculate the light pressure, you can use the following formula:

where is the amount of radiant energy incident normally on 1 m² of surface in 1 s; - speed of light, - reflection coefficient.

If the light falls at an angle to the normal, then the pressure can be expressed by the formula:

where is the volumetric radiation energy density, is the reflection coefficient, is the unit vector of the direction of the incident beam, is the unit vector of the direction of the reflected beam.

For example, the tangential component of the light pressure force on a unit area will be equal to:

The normal component of the light pressure force on a unit area will be equal to:

The ratio of the normal and tangential components is:

Application

Possible applications are solar sail and gas separation.

Notes

• Air
• Chronometer

See what "Light pressure" is in other dictionaries:

light pressure- Light pressure. Scheme of gas separation using resonant light pressure (the frequency of laser light is equal to the frequency of the atomic transition). Resonant atoms under the action of light, having received a directed impulse from light quanta, will go into the far ... ... Illustrated Encyclopedic Dictionary

light pressure- the pressure produced by light on reflecting or absorbing bodies. D. s. was first experimentally discovered and measured by P. N. Lebedev (1899). The value of D. s. even for the strongest light sources (the Sun, an electric arc) is negligible ... ... Great Soviet Encyclopedia

PRESSURE LIGHT- The pressure exerted by light on bodies that reflect or absorb light. The pressure of light is the result of the transfer of momentum to the body of the photons absorbed or reflected by it. Under the action of solar radiation on macroscopic bodies, it is extremely small ... ... Big Encyclopedic Dictionary

PRESSURE LIGHT- (see LIGHT PRESSURE). Physical Encyclopedic Dictionary. Moscow: Soviet Encyclopedia. Editor-in-Chief A. M. Prokhorov. 1983... Physical Encyclopedia

light pressure- the pressure produced by light on bodies that reflect or absorb light, particles, as well as individual molecules and atoms. The hypothesis of light pressure was first proposed (1619) by I. Kepler to explain the deviation of the tails of comets flying near the Sun. ... ... encyclopedic Dictionary

light pressure- šviesos slėgis statusas T sritis Standartizacija ir metrologija apibrėžtis Slėgis, kurį kuria šviesa veikdama tam tikrą paviršių. atitikmenys: engl. light pressure vok. Lichtdruck, m rus. light pressure, n; light pressure, n pranc. pression de… Penkiakalbis aiskinamasis metrologijos terminų žodynas

light pressure- šviesos slėgis statusas T sritis fizika atitikmenys: engl. light pressure vok. Lichtdruck, m rus. light pressure, n; light pressure, n pranc. pression de la lumière, f … Fizikos terminų žodynas

PRESSURE LIGHT- pressure produced by light on bodies that reflect or absorb light, particles, as well as otd. molecules and atoms. Hypothesis about D. with. for the first time (1619) I. Kepler stated to explain the deviation of the tails of comets flying near the Sun. In earthly ... ... Natural science. encyclopedic Dictionary

light pressure is the pressure exerted by the light on the illuminated surface. Plays an important role in cosmic processes (formation of comet tails, equilibrium big stars). D.S. was predicted in 1619 by him. astronomer I. Kepler. (1571 1630) and experimentally ... ... Astronomical dictionary

48. Elements of quantum optics. Energy, mass and momentum of a photon. Derivation of the light pressure formula based on quantum concepts of the nature of light.

Thus, the propagation of light should not be considered as a continuous wave

process, but as a stream of discrete particles localized in space, moving at a speed c of light propagation in vacuum. Subsequently (in 1926) these particles were called photons. Photons have all the properties of a particle (corpuscle).

The development of Planck's hypothesis led to the creation of ideas about the quantum properties of light. Light quanta are called photons. According to the law of proportionality of mass and energy and Planck's hypothesis, the energy of a photon is determined by the formulas

.

Equating the right-hand sides of these equations, we obtain an expression for the photon mass

or taking into account that ,

The momentum of a photon is determined by the formulas:

The rest mass of a photon is zero. A quantum of electromagnetic radiation exists only by propagating at the speed of light, while having finite values ​​of energy and momentum. In monochromatic light with frequency v, all photons have the same energy, momentum, and mass.

light pressure

Light radiation can transfer its energy to the body in the form of mechanical pressure.

He proved that light, completely absorbed by a blackened plate, exerts a force on it. Light pressure manifests itself in the fact that a distributed force acts on the illuminated body surface in the direction of light propagation, which is proportional to the density of light energy and depends on the optical properties of the surface.

As a result of applying the laws of mechanics to Lebedev's optical measurements, an extremely important relationship was obtained, which showed that energy is always equivalent to mass. For the first time, Einstein pointed out that the equation mc 2 = E is universal and should be valid for any kind of energy.

This phenomenon can be explained from the standpoint of both wave and corpuscular ideas about the nature of light. In the first case, this is the result of the interaction electric current induced in the body electric field light wave, with its magnetic field according to Ampère's law. Periodically changing in space and time, the electric and magnetic fields of a light wave, when interacting with the surface of a substance, exert a force effect on the electrons of the atoms of the substance. The electric field of the wave causes the electrons to oscillate. Lorentz force from the side magnetic field wave is directed along the direction of wave propagation and represents force of light pressure. Quantum theory explains the pressure of light by the fact that photons have a certain momentum and, when interacting with matter, they transfer part of the momentum to the particles of matter, thereby exerting pressure on its surface (an analogy can be drawn with the impact of molecules on the wall of a vessel, in which the momentum transferred to the wall determines pressure of the gas in the container).

When absorbed, photons transfer their momentum to the body with which they interact. This is the reason for the light pressure.

Let us determine the pressure of light on the surface using the quantum theory of radiation.

Let radiation with frequency ν fall perpendicularly to some surface (Fig. 5). Let this radiation, consisting of N photons, fall on the surface of a flat

spare ∆ S during the time ∆ t. The surface absorbs N 1 photons, and reflects

Xia N 2, i.e. N \u003d N 1 + N 2.

	Continuation 48
Each absorbed photon (inelastic impact) transfers momentum to the surface				And each of
the struck photon (elastic impact) transfers to it a momentum			Then all incident photons are transmitted
blow an impulse equal to
In this case, the light will act on the surface with a force
those. exert pressure

Multiplying and dividing the right side of this equality by N, we get

Finally

where is the energy of all N photons incident on a unit area per unit time, the size is

ness; - reflection coefficient.

For a black surface ρ = 0 and the pressure will be equal to .

Represents the volumetric energy density, its dimension .

Then the concentration n of photons in the beam incident on the surface will be

.

Substituting into the equation for light pressure (2.2), we obtain

The pressure produced by light when it falls on a flat surface can be calculated by the formula

where Her is the intensity of surface irradiation (or illumination), c is the propagation speed of electromagnetic waves in vacuum, α, is the proportion of incident energy absorbed by the body (absorption coefficient

ion), ρ is the fraction of the incident energy reflected by the body (reflection coefficient), θ is the angle between the direction of radiation and the normal to the irradiated surface. If the body is not transparent, that is, everything

incident radiation is reflected and absorbed, then α + ρ =1.

49 Elements of quantum optics. Compton effect. Corpuscular-wave dualism of light (radiation).

3) Corpuscular-wave dualism of electromagnetic radiation

So, the study of thermal radiation, the photoelectric effect, the Compton effect showed that electromagnetic radiation (in particular, light) has all the properties of a particle (corpuscle). However, a large group of optical phenomena - interference, diffraction, polarization testifies to the wave properties of electromagnetic radiation, in particular, light.

What is light - continuous electromagnetic waves emitted by a source or a stream of discrete photons, randomly for an electromagnetic wave, do not exclude the properties of discreteness characteristic of photons.

Light (electromagnetic radiation) simultaneously has the properties of continuous electromagnetic waves and the properties of discrete photons. This is the corpuscular-wave dualism (duality) of electromagnetic radiation.

2) Compton effect It consists in increasing the wavelength of X-ray radiation when it is scattered by a substance. Wavelength change

K(1-cos)=2 to sin2(/2),(9)"

where k \u003d h / (mc) is the Compton wavelength, m is the rest mass of the electric

throne. k \u003d 2.43 * 10 -12 m \u003d 0.0243 A (1 A \u003d 10-10 m).

All features of the Compton effect were explained by considering scattering as a process of elastic collision of X-ray photons with free electrons, in which the energy conservation law and the momentum conservation law are observed.

According to (9), the change in the wavelength depends only on the scattering angle and does not depend on either the X-ray wavelength or the type of substance.

1) Elements of quantum optics. Photons, energy, mass and momentum of a photon

To explain the distribution of energy in the spectrum of thermal radiation, Planck assumed that electromagnetic waves are emitted in portions (quanta). Einstein in 1905 came to the conclusion that radiation is not only emitted, but also propagated and absorbed in the form of quanta. This conclusion made it possible to explain all the experimental facts (photoelectric effect, Compton effect, etc.) that could not be explained by classical electrodynamics, which proceeded from wave ideas about the properties of radiation. Thus, the propagation of light should be considered not as a continuous wave process, but as a stream of discrete particles localized in space, moving at a speed c of light propagation in vacuum. Subsequently (in 1926) these particles were called photons. Photons have all the properties of a particle (corpuscle).

1. Photon energy

Therefore, Planck's constant is sometimes called the quantum of action. The dimension , coincides, for example, with the dimension of the angular momentum (L=r mv).

As follows from (1), the photon energy increases with increasing frequency (or with decreasing wavelength),

2. The mass of a photon is determined based on the law of the relationship between mass and energy (E=mc 2 )

3. Momentum of a photon. For any relativistic particle, its energy Since the photon has m 0 =0, then the momentum of the photon

those. wavelength is inversely proportional to momentum

50. Rutherford's nuclear model of the atom. The spectrum of the hydrogen atom. Generalized Balmer formula. Spectral series of the hydrogen atom. The term concept.

1) Rutherford proposed a nuclear model of the atom. According to this model, an atom consists of a positive nucleus with a charge Ze (Z is the element's serial number in the periodic table, e is the elementary charge), size 10 -5 -10 -4 A (1A = 10 -10 m) and a mass almost equal to the mass of an atom. Electrons move around the nucleus in closed orbits, forming the electron shell of the atom. Since the atoms are neutral, Z electrons must rotate around the nucleus, the total charge of which is Zе. The dimensions of an atom are determined by the dimensions of the outer orbits of electrons and are on the order of units of A.

The mass of electrons is a very small fraction of the mass of the nucleus (0.054% for hydrogen, less than 0.03% for other elements). The concept of "electron size" cannot be formulated consistently, although ro 10-3 A is called the classical radius of the electron. So, the nucleus of an atom occupies an insignificant part of the volume of the atom and practically the entire (99.95%) mass of the atom is concentrated in it. If the nuclei of atoms were located close to each other, then the globe would have a radius of 200 m and not 6400 km (the density of matter

atomic nuclei 1.8

2) The line spectrum of the hydrogen atom

The emission spectrum of atomic hydrogen consists of separate spectral lines, which are arranged in a certain order. In 1885, Balmer established that the wavelengths (or frequencies) of these lines can be represented by a formula.

, (9)

where R \u003d 1.0974 7 m -1 - is also called the Rydberg constant.

On fig. 1 shows a diagram of the energy levels of the hydrogen atom, calculated according to (6) at z=1.

When an electron passes from higher energy levels to the level n = 1, ultraviolet radiation or radiation of the Lyman series (SL) occurs.

When electrons pass to the level n = 2, visible radiation or radiation of the Balmer series (SB) occurs.

During the transition of electrons from higher levels to the level n =

3, infrared radiation, or radiation of the Paschen series (SP), etc., occurs.

The frequencies or wavelengths of the resulting radiation are determined by formulas (8) or (9) at m=1 - for the Lyman series, at m=2 - for the Balmer series and at m = 3 - for the Paschen series. The photon energy is determined by formula (7), which, taking into account (6), can be reduced for hydrogen-like atoms to the form:

eV (10)

50 continued

4) Spectral series of hydrogen- a set of spectral series that make up the spectrum of the hydrogen atom. Since hydrogen is the simplest atom, its spectral series are the most studied. They obey the Rydberg formula well:

,

where R = 109677 cm–1 is the Rydberg constant for hydrogen, n' is the ground level of the series. Spectral lines arising during transitions to the main energy level,

called resonant, all the rest - subordinate.

Lyman series

Discovered by T. Lyman in 1906. All lines of the series are in the ultraviolet range. The series corresponds to the Rydberg formula for n = 1 and n = 2, 3, 4,

Balmer series

Discovered by I. Ya. Balmer in 1885. The first four lines of the series are in the visible range. The series corresponds to the Rydberg formula for n′ = 2 and n = 3, 4, 5

5) Spectral term or electronic termatom, molecule or ion - config-

walkie-talkie (state) of the electronic subsystem, which determines the energy level. Sometimes the term is understood as the actual energy of a given level. The transitions between the terms determine the emission and absorption spectra of electromagnetic radiation.

The terms of an atom are usually denoted by capital letters S, P, D, F, etc., corresponding to the value of the quantum number orbital angular momentum L = 0, 1, 2, 3, etc. The quantum number of the total angular momentum J is given by the index at the bottom right. The small number at the top left indicates the multiplicity ( multiplicity) term. For example, ²P 3/2 is a doublet R. Sometimes (as a rule, for one-electron atoms and ions), the term symbol is preceded by principal quantum number(for example, 2²S 1/2 ).

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A stream of photons (light) that exerts pressure when it hits a surface.

Flux of photons incident on an absorbing surface:

Flux of photons incident on a mirror surface:

Flux of photons incident on the surface:

Physical meaning of Light pressure:

Light is a stream of photons, then, according to the principles of classical mechanics, when particles hit a body, they must transfer momentum to it, in other words, exert pressure

Instrument, measurement light pressure, was a very sensitive torsion dynamometer (torsional balance). This device was created by Lebedev. Its movable part was a light frame suspended on a thin kvarne thread with wings fixed on it - light and black discs up to 0.01 mm thick. The wings were made from metal foil. The frame was suspended inside a vessel from which the air was evacuated. The light, falling on the wings, exerted different pressure on the light and black discs. As a result, a torque acted on the frame, which twisted the suspension thread. The light pressure was determined from the twisting angle of the thread.

In the formula we used:

The force with which the photon pushes

Surface area affected by light pressure

Momentum of one photon

48. Elements of quantum optics. Energy, mass and momentum of a photon. Derivation of the light pressure formula based on quantum concepts of the nature of light.

Thus, the propagation of light should not be considered as a continuous wave

process, but as a stream of discrete particles localized in space, moving at a speed c of light propagation in vacuum. Subsequently (in 1926) these particles were called photons. Photons have all the properties of a particle (corpuscle).

The development of Planck's hypothesis led to the creation of ideas about the quantum properties of light. Light quanta are called photons. According to the law of proportionality of mass and energy and Planck's hypothesis, the energy of a photon is determined by the formulas

.

Equating the right-hand sides of these equations, we obtain an expression for the photon mass

or taking into account that ,

The momentum of a photon is determined by the formulas:

The rest mass of a photon is zero. A quantum of electromagnetic radiation exists only by propagating at the speed of light, while having finite values ​​of energy and momentum. In monochromatic light with frequency v, all photons have the same energy, momentum, and mass.

light pressure

Light radiation can transfer its energy to the body in the form of mechanical pressure.

He proved that light, completely absorbed by a blackened plate, exerts a force on it. Light pressure manifests itself in the fact that a distributed force acts on the illuminated body surface in the direction of light propagation, which is proportional to the density of light energy and depends on the optical properties of the surface.

As a result of applying the laws of mechanics to Lebedev's optical measurements, an extremely important relationship was obtained, which showed that energy is always equivalent to mass. For the first time, Einstein pointed out that the equation mc 2 = E is universal and should be valid for any kind of energy.

This phenomenon can be explained from the standpoint of both wave and corpuscular ideas about the nature of light. In the first case, this is the result of the interaction of the electric current induced in the body by the electric field of the light wave with its magnetic field according to Ampère's law. Periodically changing in space and time, the electric and magnetic fields of a light wave, when interacting with the surface of a substance, exert a force effect on the electrons of the atoms of the substance. The electric field of the wave causes the electrons to oscillate. The Lorentz force from the side of the magnetic field of the wave is directed along the direction of wave propagation and is force of light pressure. Quantum theory explains the pressure of light by the fact that photons have a certain momentum and, when interacting with matter, they transfer part of the momentum to the particles of matter, thereby exerting pressure on its surface (an analogy can be drawn with the impact of molecules on the wall of a vessel, in which the momentum transferred to the wall determines pressure of the gas in the container).

When absorbed, photons transfer their momentum to the body with which they interact. This is the reason for the light pressure.

Let us determine the pressure of light on the surface using the quantum theory of radiation.

Let radiation with frequency ν fall perpendicularly to some surface (Fig. 5). Let this radiation, consisting of N photons, fall on the surface of a flat

spare ∆ S during the time ∆ t. The surface absorbs N 1 photons, and reflects

Xia N 2, i.e. N \u003d N 1 + N 2.

	Continuation 48
Each absorbed photon (inelastic impact) transfers momentum to the surface				And each of
the struck photon (elastic impact) transfers to it a momentum			Then all incident photons are transmitted
blow an impulse equal to
In this case, the light will act on the surface with a force
those. exert pressure

Multiplying and dividing the right side of this equality by N, we get

Finally

where is the energy of all N photons incident on a unit area per unit time, the size is

ness; - reflection coefficient.

For a black surface ρ = 0 and the pressure will be equal to .

Represents the volumetric energy density, its dimension .

Then the concentration n of photons in the beam incident on the surface will be

.

Substituting into the equation for light pressure (2.2), we obtain

The pressure produced by light when it falls on a flat surface can be calculated by the formula

where Her is the intensity of surface irradiation (or illumination), c is the propagation speed of electromagnetic waves in vacuum, α, is the proportion of incident energy absorbed by the body (absorption coefficient

ion), ρ is the fraction of the incident energy reflected by the body (reflection coefficient), θ is the angle between the direction of radiation and the normal to the irradiated surface. If the body is not transparent, that is, everything

incident radiation is reflected and absorbed, then α + ρ =1.

49 Elements of quantum optics. Compton effect. Corpuscular-wave dualism of light (radiation).

3) Corpuscular-wave dualism of electromagnetic radiation

So, the study of thermal radiation, the photoelectric effect, the Compton effect showed that electromagnetic radiation (in particular, light) has all the properties of a particle (corpuscle). However, a large group of optical phenomena - interference, diffraction, polarization testifies to the wave properties of electromagnetic radiation, in particular, light.

What is light - continuous electromagnetic waves emitted by a source or a stream of discrete photons, randomly for an electromagnetic wave, do not exclude the properties of discreteness characteristic of photons.

Light (electromagnetic radiation) simultaneously has the properties of continuous electromagnetic waves and the properties of discrete photons. This is the corpuscular-wave dualism (duality) of electromagnetic radiation.

2) Compton effect It consists in increasing the wavelength of X-ray radiation when it is scattered by a substance. Wavelength change

K(1-cos)=2 to sin2(/2),(9)"

where k \u003d h / (mc) is the Compton wavelength, m is the rest mass of the electric

throne. k \u003d 2.43 * 10 -12 m \u003d 0.0243 A (1 A \u003d 10-10 m).

All features of the Compton effect were explained by considering scattering as a process of elastic collision of X-ray photons with free electrons, in which the energy conservation law and the momentum conservation law are observed.

According to (9), the change in the wavelength depends only on the scattering angle and does not depend on either the X-ray wavelength or the type of substance.

1) Elements of quantum optics. Photons, energy, mass and momentum of a photon

To explain the distribution of energy in the spectrum of thermal radiation, Planck assumed that electromagnetic waves are emitted in portions (quanta). Einstein in 1905 came to the conclusion that radiation is not only emitted, but also propagated and absorbed in the form of quanta. This conclusion made it possible to explain all the experimental facts (photoelectric effect, Compton effect, etc.) that could not be explained by classical electrodynamics, which proceeded from wave ideas about the properties of radiation. Thus, the propagation of light should be considered not as a continuous wave process, but as a stream of discrete particles localized in space, moving at a speed c of light propagation in vacuum. Subsequently (in 1926) these particles were called photons. Photons have all the properties of a particle (corpuscle).

1. Photon energy

Therefore, Planck's constant is sometimes called the quantum of action. The dimension , coincides, for example, with the dimension of the angular momentum (L=r mv).

As follows from (1), the photon energy increases with increasing frequency (or with decreasing wavelength),

2. The mass of a photon is determined based on the law of the relationship between mass and energy (E=mc 2 )

3. Momentum of a photon. For any relativistic particle, its energy Since the photon has m 0 =0, then the momentum of the photon

those. wavelength is inversely proportional to momentum

50. Rutherford's nuclear model of the atom. The spectrum of the hydrogen atom. Generalized Balmer formula. Spectral series of the hydrogen atom. The term concept.

1) Rutherford proposed a nuclear model of the atom. According to this model, an atom consists of a positive nucleus with a charge Ze (Z is the element's serial number in the periodic table, e is the elementary charge), size 10 -5 -10 -4 A (1A = 10 -10 m) and a mass almost equal to the mass of an atom. Electrons move around the nucleus in closed orbits, forming the electron shell of the atom. Since the atoms are neutral, Z electrons must rotate around the nucleus, the total charge of which is Zе. The dimensions of an atom are determined by the dimensions of the outer orbits of electrons and are on the order of units of A.

The mass of electrons is a very small fraction of the mass of the nucleus (0.054% for hydrogen, less than 0.03% for other elements). The concept of "electron size" cannot be formulated consistently, although ro 10-3 A is called the classical radius of the electron. So, the nucleus of an atom occupies an insignificant part of the volume of the atom and practically the entire (99.95%) mass of the atom is concentrated in it. If the nuclei of atoms were located close to each other, then the globe would have a radius of 200 m and not 6400 km (the density of matter

atomic nuclei 1.8

2) The line spectrum of the hydrogen atom

The emission spectrum of atomic hydrogen consists of separate spectral lines, which are arranged in a certain order. In 1885, Balmer established that the wavelengths (or frequencies) of these lines can be represented by a formula.

, (9)

where R \u003d 1.0974 7 m -1 - is also called the Rydberg constant.

On fig. 1 shows a diagram of the energy levels of the hydrogen atom, calculated according to (6) at z=1.

When an electron passes from higher energy levels to the level n = 1, ultraviolet radiation or radiation of the Lyman series (SL) occurs.

When electrons pass to the level n = 2, visible radiation or radiation of the Balmer series (SB) occurs.

During the transition of electrons from higher levels to the level n =

3, infrared radiation, or radiation of the Paschen series (SP), etc., occurs.

The frequencies or wavelengths of the resulting radiation are determined by formulas (8) or (9) at m=1 - for the Lyman series, at m=2 - for the Balmer series and at m = 3 - for the Paschen series. The photon energy is determined by formula (7), which, taking into account (6), can be reduced for hydrogen-like atoms to the form:

eV (10)

50 continued

4) Spectral series of hydrogen- a set of spectral series that make up the spectrum of the hydrogen atom. Since hydrogen is the simplest atom, its spectral series are the most studied. They obey the Rydberg formula well:

,

where R = 109677 cm–1 is the Rydberg constant for hydrogen, n' is the ground level of the series. Spectral lines arising during transitions to the main energy level,

called resonant, all the rest - subordinate.

Lyman series

Discovered by T. Lyman in 1906. All lines of the series are in the ultraviolet range. The series corresponds to the Rydberg formula for n = 1 and n = 2, 3, 4,

Balmer series

Discovered by I. Ya. Balmer in 1885. The first four lines of the series are in the visible range. The series corresponds to the Rydberg formula for n′ = 2 and n = 3, 4, 5

5) Spectral term or electronic termatom, molecule or ion - config-

walkie-talkie (state) of the electronic subsystem, which determines the energy level. Sometimes the term is understood as the actual energy of a given level. The transitions between the terms determine the emission and absorption spectra of electromagnetic radiation.

The terms of an atom are usually denoted by capital letters S, P, D, F, etc., corresponding to the value of the quantum number orbital angular momentum L = 0, 1, 2, 3, etc. The quantum number of the total angular momentum J is given by the index at the bottom right. The small number at the top left indicates the multiplicity ( multiplicity) term. For example, ²P 3/2 is a doublet R. Sometimes (as a rule, for one-electron atoms and ions), the term symbol is preceded by principal quantum number(for example, 2²S 1/2 ).