- pressure exerted by light on reflecting and absorbing bodies, particles, as well as individual molecules and atoms; one of ponderomotive action light transmission related impulse electro magnetic fieldsubstance. The hypothesis of the existence of light pressure was first put forward I. Kepler (J.Kepler) in the 17th century. to explain the deviation comet tails from the sun. The theory of light pressure within the framework of classical electrodynamics is given J. Maxwell (J.Maxwell) in 1873. In it, the pressure of light is closely related to scattering and absorption electromagnetic wave particles of matter. As part of quantum theory light pressure is the result of momentum transfer body photons.

In 1873, Maxwell, based on the electromagnetic nature of light, predicted that light should exert pressure on obstacles. This pressure is due to the forces acting from the electric and magnetic components of the electromagnetic field of the wave on the charges in the illuminated body.

Let light fall on a conductive (metal) plate. The electric component of the wave field acts on free electrons with a force

F el \u003d q E,

where q is the electron charge. E is the electric field strength of the wave.

The electrons start moving at a speed V(fig.1) Since the direction E in a wave periodically changes to the opposite, then the electrons periodically change the direction of their movement to the opposite, i.e. perform forced oscillations along the direction of the electric field of the wave.

Figure 1 - The movement of electrons

Magnetic component IN electromagnetic field of a light wave acts with the Lorentz force

F l \u003d q V B,

The direction of which, in accordance with the rule of the left hand, coincides with the direction of propagation of light. When directions E And B change to the opposite, then the direction of the electron velocity also changes, and the direction of the Lorentz force remains unchanged. The resultant of the Lorentz forces acting on free electrons in the surface layer of a substance is the force with which light presses on the surface.

Figure 2

1- mirror wing; 2 - blackened winglet; 3-mirror; 4-scale for measuring the angle of rotation; 5-glass thread

The pressure of light can also be explained on the basis of quantum ideas about light. As stated above, photons have momentum. When photons collide with matter, some of the photons are reflected and some are absorbed. Both processes are accompanied by momentum transfer from photons to the illuminated surface. According to Newton's second law, a change in the momentum of a body means that a force of light pressure acts on the body F. The ratio of the modulus of this force to the surface area of ​​the body is equal to the pressure of light on the surface: P = F giving /S.

The existence of light pressure was experimentally confirmed by Lebedev. The device created by Lebedev was a very sensitive torsion balance. The moving part of the balance was a light frame suspended on a thin quartz thread with light and dark wings 0.01 mm thick. Light exerted different pressure on light (reflecting) and dark (absorbing) wings. 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.

With normal incidence of light on the surface of a solid body, the light pressure is determined by the formula p = S(1 — R)/c, Where S — energy flux density (light intensity), R- reflection coefficient light from the surface.

Experimentally, the pressure of light on solids was first investigated P.N. Lebedev in 1899. The main difficulties in the experimental detection of the pressure of light consisted in isolating it against the background radiometric and convective forces , the value of which depends on the pressure of the gas surrounding the body and with insufficient vacuum can exceed the pressure of light by several orders of magnitude. IN Lebedev's experiments in an evacuated (mm Hg) glass vessel, rocker arms were hung on a thin silver thread torsion balances with thin disk-wings attached to them, which were irradiated. Wings were made from various metals and mica with identical opposite surfaces. By successively irradiating the anterior and posterior surfaces of wings of different thicknesses, Lebedev succeeded in leveling the residual effect of radiometric forces and obtaining satisfactory agreement (with an error of %) with Maxwell's theory. In 1907-10 Lebedev carried out even more subtle experiments to study light pressure on gases and also obtained good agreement with the theory.

Light pressure plays a large role in astronomical and atomic phenomena. In astrophysics, light pressure, along with gas pressure, keeps stars stable by counteracting the forces of gravity . The action of light pressure explains some forms of comet tails. Atomic effects include the so-called. the light output that an excited atom experiences when a photon is emitted.

In condensed media light pressure can cause carrier current (see Light-electric effect).

Specific features of light pressure are found in rarefied atomic systems at resonant scattering intense light when the frequency laser radiation equal to the frequency atomic transition . By absorbing a photon, the atom receives a momentum in the direction of the laser beam and passes into excited state . Further, by spontaneously emitting a photon, the atom acquires momentum ( light output) in an arbitrary direction. On subsequent takeovers and spontaneous emissions photons, arbitrarily directed pulses of light output are mutually canceled, and, ultimately, the resonant atom receives a momentum directed along the light beam resonant pressure of light . Force F resonant pressure of light on an atom is defined as the momentum transferred by a stream of photons with a density N per unit of time: , where — the momentum of one photon, is the absorption cross section resonant photon, wavelength of light . At relatively low radiation densities, the resonant light pressure is directly proportional to the light intensity. At high densities N due to end() lifetime of the excited level, absorption saturates and saturation of the resonant pressure of light (see Saturation effect ). In this case, the pressure of light is created by photons, which are spontaneously emitted by atoms with an average frequency (the reciprocal of the lifetime of an excited atom) in a random direction determined by atom emission diagram . The force of light pressure ceases to depend on the intensity, but is determined by the speed of spontaneous emission acts: . For typical values ​​of c -1 and µm, the light pressure force is eV/cm; when saturated, the resonant pressure of light can create an acceleration of atoms up to 10 5
g (g — acceleration free fall). Such large forces allow selective control atomic beams , varying the frequency of light and differently affecting groups of atoms that differ little in resonant absorption frequencies. In particular, it is possible to compress Maxwellian distribution in velocities, removing high-speed atoms from the beam. The laser light is directed towards the atomic beam, while selecting the frequency and shape of the radiation spectrum so that the fastest atoms experience the strongest retarding effect of the light pressure due to their greater Doppler shift resonant frequency. Another possible application of the resonant pressure of light is the separation of gases: when a two-chamber vessel filled with a mixture of two gases, one of which is in resonance with radiation, is irradiated, resonant atoms under the action of light pressure will pass into the far chamber.

The resonant pressure of light on atoms placed in an intense field has peculiar features. standing wave . WITH quantum dot of vision, a standing wave formed by counter-flows of photons causes jolts of the atom due to the absorption of photons and their stimulated emission. The average force acting on the atom is not equal to zero due to the inhomogeneity of the field at the wavelength. From the classical point of view, the pressure force of light is due to the action of a spatially inhomogeneous field on the field induced by it. atomic dipole . This force is minimum at the nodes where dipole moment is not induced, and at antinodes, where the field gradient vanishes. The maximum light pressure force is equal in order of magnitude (the signs refer to the in-phase and anti-phase motion of the dipoles with the moment d with respect to the field with intensity E). This force can reach gigantic values: for debyes, µm and V/cm, the force is eV/cm.

The field of a standing wave stratifies a beam of atoms passing through a beam of light, since dipoles oscillating in antiphase move along different trajectories, like atoms in the Stern-Gerlach experiment. In laser beams, atoms moving along the beam are affected by the radial force of light pressure, which is due to the radial inhomogeneity of the light field density.

Both standing and traveling wave there is not only a deterministic movement of atoms, but also their diffusion in phase space due to the fact that the acts of absorption and emission of photons are purely quantum random processes. Coefficient of spatial diffusion for an atom with mass M in a traveling wave is equal to .

Similar to the considered resonant pressure of light can also be experienced by quasiparticles V solids: electrons, excitons, etc.

Bibliography

Mustafaev R.A., Krivtsov V.G. Physics. M., 2006.


This video tutorial is dedicated to the topic “The pressure of light. Lebedev's experiments. Lebedev's experiments made a huge impression on the scientific world, because thanks to them, the pressure of light was measured for the first time and the validity of Maxwell's theory was proved. How did he do it? The answer to this and many others interesting questions related to the quantum theory of light, you can learn from this fascinating physics lesson.

Theme: Light pressure

Lesson: Light pressure. Lebedev's experiments

For the first time, the hypothesis of the existence of light pressure was put forward by Johannes Kepler in the 17th century to explain the phenomenon of comet tails when they fly near the Sun.

Maxwell, based on the electromagnetic theory of light, predicted that light should exert pressure on an obstacle.

Under the influence of the electric field of the wave, the electrons in the bodies oscillate - an electric current is formed. This current is directed along the electric field strength. Orderly moving electrons are affected by the Lorentz force from the side of the magnetic field, directed towards the propagation of the wave - this is light pressure force(Fig. 1).

Rice. 1. Maxwell's experiment

To prove Maxwell's theory, it was necessary to measure the pressure of light. For the first time, light pressure was measured by the Russian physicist Pyotr Nikolaevich Lebedev in 1900 (Fig. 2).



Rice. 2. Petr Nikolaevich Lebedev



Rice. 3. Lebedev device

Lebedev's device (Fig. 3) consists of a light rod on a thin glass thread, along the edges of which light wings are attached. The whole device was placed in a glass vessel, from which the air was pumped out. Light falls on the wings located on one side of the rod. The value of pressure can be judged by the angle of twist of the thread. The difficulty of accurately measuring the pressure of light was due to the fact that it was impossible to pump out all the air from the vessel. During the experiment, the movement of air molecules began, caused by unequal heating of the wings and walls of the vessel. Wings cannot be hung absolutely vertically. Heated air flows rise up, act on the wings, which leads to additional torques. Also, the twisting of the thread is affected by the non-uniform heating of the sides of the wings. The side facing the light source heats up more than the opposite side. Molecules bouncing off the hotter side impart more momentum to the winglet.



Rice. 4. Lebedev device



Rice. 5. Lebedev device

Lebedev managed to overcome all difficulties, despite low level experimental technology at that time. He took a very large vessel and very thin wings. The wing consisted of two pairs of thin platinum circles. One of the circles of each pair was shiny on both sides. The other sides had one side coated with platinum black. At the same time, both pairs of circles differed in thickness.

To exclude convection currents, Lebedev directed beams of light to the wings from one side or the other. Thus, the forces acting on the wings were balanced (Fig. 4-5).



Rice. 6. Lebedev device



Rice. 7. Lebedev device

Thus, the pressure of light on solid bodies was proved and measured (Fig. 6-7). The value of this pressure coincided with Maxwell's predicted pressure.

Three years later, Lebedev managed to make another experiment - to measure the pressure of light on gases (Fig. 8).



Rice. 8. Installation for measuring the pressure of light on gases

Lord Kelvin: “Perhaps you know that all my life I fought with Maxwell, not recognizing his light pressure, and now your Lebedev forced me to surrender before his experiments.”

The advent of the quantum theory of light made it possible to more simply explain the cause of light pressure.

Photons have momentum. When absorbed by their body, they transfer their impulse to it. Such an interaction can be regarded as an absolutely inelastic impact.

A force acts on the surface from each photon:



Light pressure on the surface:



Interaction of a photon with a mirror surface

In the case of this interaction, an absolutely elastic interaction is obtained. When a photon falls on a surface, it is reflected from it with the same speed and momentum with which it fell on this surface. The momentum change will be twice as large as when a photon falls on a black surface, the light pressure will double.

In nature, there are no substances whose surface would completely absorb or reflect photons. Therefore, to calculate the pressure of light on real bodies, it is necessary to take into account that some of the photons will be absorbed by this body, and some will be reflected.

Lebedev's experiments can be regarded as experimental evidence that photons have momentum. Although under normal conditions the light pressure is very small, its effect can be significant. Based on the pressure of the Sun, a sail was developed for spaceships, which will allow you to move in space under the pressure of light (Fig. 11).



Rice. 11. Spaceship sail

The pressure of light, according to Maxwell's theory, arises as a result of the action of the Lorentz force on electrons that make oscillatory motions under the influence of the electric field of an electromagnetic wave.

From the point of view of quantum theory, the pressure of light arises as a result of the interaction of photons with the surface on which they fall.

The calculations that were carried out by Maxwell coincided with the results that Lebedev produced. This vividly proves the quantum-wave dualism of light.

Crookes' experiments

Lebedev first discovered the pressure of light experimentally and was able to measure it. The experiment was incredibly difficult, but there is a scientific toy - the Crookes experiment (Fig. 12).



Rice. 12. Crookes experiment

A small propeller, consisting of four petals, is located on the needle, which is covered with a glass cap. If this propeller is illuminated with light, it starts to rotate. If you look at this propeller in the open air, when the wind blows on it, its rotation would not surprise anyone, but in this case, the glass dome does not allow air currents to act on the propeller. Therefore, the cause of its movement is light.

English physicist William Crookes accidentally created the first light spinner.

In 1873, Crookes decided to determine the atomic weight of the element Thallium and weigh it on a very accurate balance. To prevent random air currents from distorting the weighing pictures, Crookes decided to hang the rocker arms in a vacuum. I did it and was amazed, since its thinnest scales were sensitive to heat. If the heat source was under the object, it reduced its weight, if above, it increased it.

Having improved this accidental experience of his, Crookes came up with a toy - a radiometer (light mill). The Crookes radiometer is a four-bladed impeller balanced on a needle inside a glass bulb with a slight vacuum. When a light beam hits the blade, the impeller begins to rotate, which is sometimes incorrectly explained by light pressure. In fact, the cause of torsion is the radiometric effect. The emergence of a repulsive force due to the difference kinetic energies gas molecules impinging on the illuminated (heated) side of the blade and on the opposite unlit (colder) side.

1. The pressure of light and the pressure of circumstances ().
2. Pyotr Nikolaevich Lebedev ().
3. Crookes radiometer ().

CBETA PRESSURE, the pressure exerted by light on reflecting and absorbing bodies, particles, as well as individual molecules and atoms; one of the ponderomotive actions of light associated with the transfer of an electromagnetic field momentum to a substance. The hypothesis of the existence of light pressure was first put forward by I. Kepler in the 17th century to explain the deviation of comet tails from the Sun. The theory of light pressure within the framework of classical electrodynamics was given by J. K. Maxwell in 1873. In it, light pressure is explained by the scattering and absorption of an electromagnetic wave by particles of matter. In the framework of the quantum theory of light pressure - the result of the transfer of momentum by photons to the body.

With normal incidence of light on the surface of a solid body, the pressure of light p is determined by the formula:

p = S(1 + R)/c, where

S is the energy flux density (light intensity), R is the coefficient of reflection of light from the surface, c is the speed of light. Under normal conditions, light pressure is hardly noticeable. Even in a powerful laser beam (1 W/cm 2 ) the light pressure is on the order of 10 -4 g/cm 2 . A laser beam wide in cross section can be focused, and then the force of light pressure at the focus of the beam can hold a milligram particle in weight.

Experimentally, the pressure of light on solids was first studied by P. N. Lebedev in 1899. The main difficulties in the experimental detection of light pressure were to distinguish it against the background of radiometric and convective forces, the magnitude of which depends on the pressure of the gas surrounding the body and, in insufficient vacuum, can exceed the pressure of light by several orders of magnitude. In Lebedev's experiments in an evacuated (pressure of the order of 10 -4 mm Hg) glass vessel, on a thin silver thread, the beams of a torsion balance were suspended with thin disk-wings fixed on them, which were irradiated. The wings were made from various metals and mica with identical opposite surfaces. By sequentially irradiating the anterior and posterior surfaces of wings of different thicknesses, Lebedev was able to level out the residual effect of radiometric forces and obtain satisfactory agreement (with an error of ± 20%) with Maxwell's theory. In 1907-10 Lebedev investigated the pressure of light on gases.

Light pressure plays a large role in astronomical and atomic phenomena. The pressure of light in stars, along with the pressure of gas, keeps them stable by counteracting the forces of gravity. The action of light pressure explains some forms of comet tails. When a photon is emitted by atoms, the so-called light return occurs, and the atoms receive the momentum of the photon. In condensed media, the pressure of light can induce a current of charge carriers (see Entrainment of electrons by photons). They are trying to use the pressure of solar radiation to create a kind of space propulsion device - the so-called solar sail.

Specific features of light pressure are found in rarefied atomic systems during resonant scattering of intense light, when the frequency of laser radiation is equal to the frequency of the atomic transition. Having absorbed a photon, the atom receives a momentum in the direction of the laser beam and goes into an excited state. Further, by spontaneously emitting a photon, the atom acquires momentum (light output) in an arbitrary direction. With subsequent absorption and spontaneous emission of photons, the atom constantly receives impulses directed along the light beam, which creates light pressure.

The force F of the resonant pressure of light on an atom is defined as the momentum transmitted by the photon flux with density N per unit time: F = Nћkσ, where ћk = 2πћ/λ is the momentum of one photon, σ ≈ λ 2 is the absorption cross section of the resonant photon, λ is the wavelength light, k - wave number, ћ - Planck's constant. At relatively low radiation densities, the resonant light pressure is directly proportional to the light intensity. At high photon flux densities N, saturation of the absorption and saturation of the resonant pressure of light occurs (see Saturation effect). In this case, the pressure of light is created by photons spontaneously emitted by atoms with an average frequency γ (the reciprocal of the lifetime of an excited atom) in a random direction. The force of light pressure ceases to depend on the intensity, but is determined by the speed of spontaneous emission acts: F≈ћkγ. For typical values ​​of γ ≈ 10 8 s -1 and λ ≈0.6 µm, the light pressure force is F≈5·10 -3 eV/cm; when saturated, the resonant pressure of light can create an acceleration of atoms up to 10 5 g (g is the acceleration of free fall). Such strong forces make it possible to selectively control atomic beams by varying the frequency of light and differently affecting atoms with slightly different resonant absorption frequencies. In particular, it is possible to compress the Maxwellian velocity distribution by removing high-speed atoms from the beam. The laser light is directed towards the atomic beam, while selecting the frequency and shape of the radiation spectrum so that the light pressure slows down fast atoms with a large shift in the resonant frequency (see the Doppler effect). The resonant pressure of light can be used to separate gases: when a two-chamber vessel filled with a mixture of two gases is irradiated, the atoms of one of which are in resonance with radiation, the resonant atoms under the action of light pressure will pass into the far chamber.

The resonant pressure of light on atoms placed in the field of an intense standing wave has some features. From a quantum point of view, a standing wave formed by counter-flows of photons causes jolts of the atom due to the absorption of photons and their stimulated emission. The average force acting on the atom is not equal to zero due to the inhomogeneity of the field at the wavelength. From the classical point of view, the pressure force of light is due to the action of a spatially inhomogeneous field on the atomic dipole induced by it. This force is minimal at nodes where no dipole moment is induced and at antinodes where the field gradient vanishes. The maximum light pressure force is equal in order of magnitude to F≈ ±Ekd (the signs refer to the in-phase and anti-phase motion of dipoles with moment d relative to the field with strength E). This force can reach gigantic values: d≈ 1 debye, λ≈0.6 µm and E≈ 10 6 V/cm, force F≈5∙10 2 eV/cm. The field of a standing wave stratifies a beam of atoms passing through a beam of light, since dipoles oscillating in antiphase move along different trajectories, like atoms in the Stern-Gerlach experiment. Atoms moving along the laser beam are affected by the radial force of light pressure due to the radial inhomogeneity of the light field density. Both in a standing and in a traveling wave, not only the deterministic motion of atoms occurs, but also their diffusion in the phase space, since the absorption and emission of photons are quantum random processes. The resonance pressure of light can also be experienced by quasiparticles in solids: electrons, excitons, etc.

Lit .: Lebedev P. N. Sobr. op. M., 1963; Ashkin A. Pressure of laser radiation // Uspekhi fizicheskikh nauk. 1973. Vol. 110. Issue. 1; Kazantsev A.P. Resonance light pressure // Ibid. 1978. Vol. 124. Issue. 1; Letokhov VS, Minogin VG Pressure of laser radiation on atoms. M., 1986.

S. G. Przhibelsky.

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. Quantum electromagnetic radiation exists only by propagating at the speed of light, while possessing 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. The Lorentz force from the magnetic field of the wave is directed along the direction of wave propagation and is force of light pressure. The 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.

Determine the pressure of light on the surface using quantum theory 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 radiation direction 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 optical phenomena- interference, diffraction, polarization indicates 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 x-ray radiation when it is scattered by matter. 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 Zе (Z is the serial number of the element in the periodic table, e is 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 Earth 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 =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.

In the transition of electrons from more high levels to 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 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 ).

13.2. Light and microparticles as objects of quantum theory

13.2.3. light pressure

Light exerts pressure on the surface.

The pressure of light is equal to the momentum that photons transmit to a unit area of ​​the surface located perpendicular to the photon beam per unit time:

p = (1 + ρ) p γ (N / t) S ,

where ρ is the reflectance of the surface; N /t is the number of photons incident on the surface every second (per unit time); p γ - photon momentum, p γ = h ν/c or p γ = h λ ; S is the area of ​​the surface located perpendicular to the incident photon beam.

Reflection coefficient is the fraction of photons reflected from the surface; the reflection coefficient is determined by the ratio

ρ = N neg N ,

where N is the number of photons incident on the surface; N neg - the number of photons reflected from the surface.

For surfaces with different properties, the reflection coefficient has different values:

• for a mirror surface ρ = 1;
• blackened surface ρ = 0.

Absorption coefficient is the fraction of photons absorbed by the surface; the absorption coefficient is determined by the ratio

ρ * = N deep N ,

where N absorb - the number of photons absorbed by the surface.

For surfaces with different properties, the absorption coefficient has different values:

• for a mirror surface ρ * = 0;
• blackened surface ρ * = 1.

Light pressure force to the surface

F = ps

where p is the light pressure; S is the area of ​​the surface located perpendicular to the incident photon beam.

The pressure force is related to the power of the photon beam by the formula

F = (1 + ρ) P c ,

where ρ is the reflection coefficient; P is the power of the photon beam, P = Nh ν/t = Nhc /λt ; ν is the photon frequency; λ is the wavelength of the photon; c is the speed of light in vacuum; h - Planck's constant, h = 6.626 ⋅ 10 −34 J ⋅ s; N /t is the number of photons falling on the surface every second.

Force of light pressure on a surface does not depend on surface area, but is determined only by the power of the incident beam and the reflective properties of the surface.

Example 6. Every second, 1.0 ⋅ 10 19 photons with a wavelength of 560 nm fall on a certain surface. With a normal incidence on an area of ​​10 cm 2, light exerts a pressure of 20 μPa. Find the absorption coefficient of this surface.

Solution . The light pressure is equal to the momentum that all photons transmit to a unit area of ​​the surface located perpendicular to the photon beam per unit time:

p = (1 + ρ) p γ (N / t) S = (1 + ρ) h N λ S t ,

where ρ is the reflection coefficient; p γ - momentum of one photon, p γ = h /λ; λ is the wavelength of light incident on the surface, λ = 560 nm; h - Planck's constant, h = 6.63 ⋅ 10 −34 J ⋅ s; N /t is the number of photons incident on the surface every second, N /t = 1.0 ⋅ 10 19 s −1 ; S is the surface area located perpendicular to the incident photon beam, S = 10 cm 2 .

Let us express the reflection coefficient of the surface from here:

ρ = p λ S h (N / t) − 1 ,

where p is the pressure of light on the surface, p = 20 µPa.

The absorption and reflection coefficients of the same surface are related by the formula

where ρ is the reflectance of the surface; ρ* is the absorption coefficient of the same surface.

this implies

ρ * = 1 − ρ,

or taking into account the explicit form of the expression for the reflection coefficient

ρ * = 1 − (p λ S h (N / t) − 1) = 2 − p λ S h (N / t) .

Let's calculate:

ρ * = 2 − 20 ⋅ 10 − 6 ⋅ 560 ⋅ 10 − 9 ⋅ 10 ⋅ 10 − 4 6.63 ⋅ 10 − 34 ⋅ 1.0 ⋅ 10 19 = 0.31.

The absorption coefficient of this surface is 0.31.

The absorption coefficient is the fraction of photons absorbed by the surface; therefore, it can be argued that 31% of the photons incident on the surface are absorbed by this surface.