§ 4 Energy luminosity. Stefan-Boltzmann law.

Wien's displacement law

RE(integrated energy luminosity) - energy luminosity determines the amount of energy emitted from a single surface per unit time in the entire frequency range from 0 to ∞ at a given temperature T.

Connection energy luminosity and emissivity

[R e ] \u003d J / (m 2 s) \u003d W / m 2

The law of J. Stefan (Austrian scientist) and L. Boltzmann (German scientist)

Where

σ \u003d 5.67 10 -8 W / (m 2 K 4) - Stef-on-Boltzmann constant.

The energy luminosity of a black body is proportional to the fourth power of thermodynamic temperature.

Stefan-Boltzmann's law, defining dependenceREon temperature, does not give an answer regarding the spectral composition of the radiation of a completely black body. From the experimental dependence curvesrλ ,T from λ at various T it follows that the distribution of energy in the spectrum of a blackbody is uneven. All curves have a maximum, which with increasing T shifts towards shorter wavelengths. Area bounded by dependency curverλ ,T from λ, is equal to RE(this follows from the geometric meaning of the integral) and is proportional to T 4 .

Wien's displacement law (1864 - 1928): Length, waves (λ max), which accounts for the maximum emissivity of an a.ch.t. at a given temperature, is inversely proportional to the temperature T.

b\u003d 2.9 10 -3 m K - Wien's constant.

The Wien shift occurs because as the temperature increases, the maximum emissivity shifts towards shorter wavelengths.

§ 5 Rayleigh-Jeans formula, Wien's formula and ultraviolet catastrophe

The Stefan-Boltzmann law allows you to determine the energy luminosityREa.h.t. by its temperature. Wien's displacement law relates body temperature to the wavelength at which the maximum emissivity falls. But neither one nor the other law solves the main problem of how great is the radiative ability per each λ in the spectrum of an A.Ch.T. at a temperature T. To do this, you need to establish a functional dependencyrλ ,T from λ and T.

Based on the concept of the continuous nature of the emission of electromagnetic waves in the law of uniform distribution of energies over degrees of freedom, two formulas were obtained for the emissivity of an a.ch.t.:

  • Wine formula

Where A, b = const.

  • Rayleigh-Jeans formula

k =1.38·10 -23 J/K - Boltzmann's constant.

Experimental verification showed that for a given temperature Wien's formula is correct for short waves and gives sharp discrepancies with experience in the region of long waves. The Rayleigh-Jeans formula turned out to be correct for long waves and not applicable for short ones.

The study of thermal radiation using the Rayleigh-Jeans formula showed that within the framework of classical physics it is impossible to solve the problem of the function characterizing the emissivity of an AChT. This unsuccessful attempt explanation of the radiation laws of A.Ch.T. with the help of the apparatus of classical physics, it was called the “ultraviolet catastrophe”.

If we try to calculateREusing the Rayleigh-Jeans formula, then

  • “ ultraviolet catastrophe”

§6 Quantum hypothesis and Planck's formula.

In 1900, M. Planck (a German scientist) put forward a hypothesis according to which the emission and absorption of energy does not occur continuously, but in certain small portions - quanta, and the quantum energy is proportional to the oscillation frequency (Planck's formula):

h \u003d 6.625 10 -34 J s - Planck's constant or

Where

Since the radiation occurs in portions, the energy of the oscillator (oscillating atom, electron) E takes only values ​​that are multiples of an integer number of elementary portions of energy, that is, only discrete values

E = n E o = nhν .

PHOTOELECTRIC EFFECT

The influence of light on the course of electrical processes was first studied by Hertz in 1887. He conducted experiments with an electric spark gap and found that when irradiated with ultraviolet radiation, the discharge occurs at a much lower voltage.

In 1889-1895. A.G. Stoletov studied the effect of light on metals using the following scheme. Two electrodes: cathode K made of the metal under study and anode A (in Stoletov's scheme - a metal mesh that transmits light) in a vacuum tube are connected to the battery so that with the help of resistance R you can change the value and sign of the voltage applied to them. When the zinc cathode was irradiated, a current flowed in the circuit, which was recorded by a milliammeter. By irradiating the cathode with light of various wavelengths, Stoletov established the following basic laws:

  • The strongest effect is exerted by ultraviolet radiation;
  • Under the action of light, negative charges escape from the cathode;
  • The strength of the current generated by the action of light is directly proportional to its intensity.

Lenard and Thomson in 1898 measured the specific charge ( e/ m), ejected particles, and it turned out that it is equal to the specific charge of the electron, therefore, electrons are ejected from the cathode.

§ 2 External photoelectric effect. Three laws of the external photoelectric effect

The external photoelectric effect is the emission of electrons by a substance under the influence of light. Electrons escaping from a substance with an external photoelectric effect are called photoelectrons, and the current they generate is called photocurrent.

Using the Stoletov scheme, the following dependence of the photocurrent onapplied voltage at constant luminous flux F(that is, the I–V characteristic was obtained - current-voltage characteristic):

At some voltageUHphotocurrent reaches saturationI n - all electrons emitted by the cathode reach the anode, hence the saturation currentI n is determined by the number of electrons emitted by the cathode per unit time under the action of light. The number of released photoelectrons is proportional to the number of light quanta incident on the cathode surface. And the number of light quanta is determined by the luminous flux F falling on the cathode. Number of photonsNfalling over timet to the surface is determined by the formula:

Where W- radiation energy received by the surface during the time Δt,

photon energy,

F e -luminous flux (radiation power).

1st law of external photoelectric effect (Stoletov's law):

At a fixed frequency of the incident light, the saturation photocurrent is proportional to the incident light flux:

Ius~ Ф, ν =const

Uh - retarding voltage is the voltage at which no electron can reach the anode. Therefore, the law of conservation of energy in this case can be written: the energy of the emitted electrons is equal to the retarding energy of the electric field

therefore, one can find top speed outgoing photoelectronsVmax

2nd law of photoelectric effect : maximum initial speedVmaxphotoelectrons does not depend on the intensity of the incident light (on F), but is determined only by its frequency ν

3rd law of photoelectric effect : for every substance there is "red border" photo effect, that is, the minimum frequency ν kp , depending on the chemical nature of the substance and the state of its surface, at which the external photoelectric effect is still possible.

The second and third laws of the photoelectric effect cannot be explained using the wave nature of light (or the classical electromagnetic theory of light). According to this theory, the pulling out of conduction electrons from the metal is the result of their "rocking" by the electromagnetic field of the light wave. As the light intensity increases ( F) the energy transmitted by the electron of the metal should increase, therefore, it should increaseVmax, and this contradicts the 2nd law of the photoelectric effect.

Since, according to the wave theory, the energy transmitted by the electromagnetic field is proportional to the intensity of light ( F), then any light; frequency, but a sufficiently high intensity would have to pull out electrons from the metal, that is, the red border of the photoelectric effect would not exist, which contradicts the 3rd law of the photoelectric effect. The external photoelectric effect is inertialess. And the wave theory cannot explain its inertialessness.

§ 3 Einstein's equation for the external photoelectric effect.

Work function

In 1905, A. Einstein explained the photoelectric effect on the basis of quantum concepts. According to Einstein, light is not only emitted by quanta in accordance with Planck's hypothesis, but propagates in space and is absorbed by matter in separate portions - quanta with energy E0 = hv. Quanta electromagnetic radiation called photons.

Einstein's equation (the law of conservation of energy for the external photo effect):

Incident photon energy hv is spent on pulling out an electron from the metal, that is, on the work function A out, and to communicate kinetic energy to the emitted photoelectron.

The smallest energy that must be imparted to an electron in order to remove it from a solid body into a vacuum is called work function.

Since the energy of Ferm to E Fdepends on temperature and E F, also changes with temperature, then, therefore, A out temperature dependent.

In addition, the work function is very sensitive to surface finish. Applying a film to the surface Sa, SG, Wa) on WA outdecreases from 4.5 eV for pureW up to 1.5 h 2 eV for impurityW.

Einstein's equation makes it possible to explain in c e three laws of the external photo-effect,

1st law: each quantum is absorbed by only one electron. Therefore, the number of ejected photoelectrons should be proportional to the intensity ( F) Sveta

2nd law: Vmax~ ν and since A out does not depend on F, then andVmax does not depend on F

3rd law: As ν decreases,Vmax and for ν = ν 0 Vmax = 0, therefore,hν 0 = A out, therefore, i.e. there is a minimum frequency, starting from which the external photoelectric effect is possible.

d Φ e (\displaystyle d\Phi _(e)), emitted by a small area of ​​the surface of the radiation source, to its area d S (\displaystyle dS) : M e = d Φ e d S . (\displaystyle M_(e)=(\frac (d\Phi _(e))(dS)).)

They also say that the energy luminosity is the surface density of the emitted radiation flux.

Numerically, the energy luminosity is equal to the time-averaged modulus of the component of the Poynting vector perpendicular to the surface. In this case, averaging is carried out over a time that significantly exceeds the period of electromagnetic oscillations.

The emitted radiation can originate in the surface itself, then one speaks of a self-luminous surface. Another variant is observed when the surface is illuminated from outside. In such cases, some part of the incident flux necessarily returns as a result of scattering and reflection. Then the expression for the energy luminosity has the form:

M e = (ρ + σ) ⋅ E e , (\displaystyle M_(e)=(\rho +\sigma)\cdot E_(e),)

Where ρ (\displaystyle \rho ) And σ (\displaystyle \sigma )- coefficient reflection and coefficient scattering of the surface, respectively, and - its irradiance .

Other names of energy luminosity, sometimes used in the literature, but not provided for by GOST: - emissivity And integral emissivity.

Spectral density of energy luminosity

Spectral density of energy luminosity M e , λ (λ) (\displaystyle M_(e,\lambda )(\lambda))- the ratio of the magnitude of the energy luminosity d M e (λ) , (\displaystyle dM_(e)(\lambda),) per small spectral interval d λ , (\displaystyle d\lambda ,) enclosed between λ (\displaystyle \lambda ) And λ + d λ (\displaystyle \lambda +d\lambda ), to the width of this interval:

M e , λ (λ) = d M e (λ) d λ . (\displaystyle M_(e,\lambda )(\lambda)=(\frac (dM_(e)(\lambda))(d\lambda )).)

The SI unit of measure is W m −3 . Since the length waves of optical radiation is usually measured in nanometers, then in practice W m −2 · nm −1 is often used.

Sometimes in literature M e , λ (\displaystyle M_(e,\lambda )) are called spectral emissivity.

Light analogue

M v = K m ⋅ ∫ 380 n m 780 n m M e , λ (λ) V (λ) d λ , (\displaystyle M_(v)=K_(m)\cdot \int \limits _(380~nm)^ (780~nm)M_(e,\lambda )(\lambda)V(\lambda)d\lambda ,)

Where K m (\displaystyle K_(m))- maximum luminous efficiency of radiation, equal in the SI system to 683 lm / W. Its numerical value follows directly from the definition of the candela.

Information about other basic energy photometric quantities and their light analogs is given in the table. The designations of the quantities are given according to GOST 26148-84.

SI energy photometric quantities
Name (synonym) Value designation Definition SI unit notation Light quantity
Energy radiation (radiant energy) Q e (\displaystyle Q_(e)) or W (\displaystyle W) Energy carried by radiation J Light energy
Flux radiation (radiant flux) Φ (\displaystyle \Phi ) or P (\displaystyle P) Φ e = d Q e d t (\displaystyle \Phi _(e)=(\frac (dQ_(e))(dt))) Tue Light flow
Strength radiation (energy strength of light) I e (\displaystyle I_(e)) I e = d Φ e d Ω (\displaystyle I_(e)=(\frac (d\Phi _(e))(d\Omega ))) Tue sr −1 The power of light
Volumetric radiation energy density U e (\displaystyle U_(e)) U e = d Q e d V (\displaystyle U_(e)=(\frac (dQ_(e))(dV))) J m −3 Volumetric density of light energy
Energy brightness L e (\displaystyle L_(e)) L e = d 2 Φ e d Ω d S 1 cos ⁡ ε (\displaystyle L_(e)=(\frac (d^(2)\Phi _(e))(d\Omega \,dS_(1)\, \cos\varepsilon))) W m −2 sr −1 Brightness
Integral energy brightness e (\displaystyle \Lambda _(e)) Λ e = ∫ 0 t L e (t ′) d t ′ (\displaystyle \Lambda _(e)=\int _(0)^(t)L_(e)(t")dt") J m −2 sr −1 Integral brightness
Irradiation (energy illumination) E e (\displaystyle E_(e)) E e = d Φ e d S 2 (\displaystyle E_(e)=(\frac (d\Phi _(e))(dS_(2)))) W m −2

The spectral density of energy luminosity (brightness) is a function showing the distribution of energy luminosity (brightness) over the radiation spectrum.
Bearing in mind that:
Energy luminosity is the surface density of the energy flux emitted by the surface
Energy brightness is the amount of flux emitted by a unit area per unit solid angle in a given direction

Completely black body- physical idealization used in thermodynamics, a body that absorbs all electromagnetic radiation falling on it in all ranges and reflects nothing. Despite the name, a black body itself can emit electromagnetic radiation of any frequency and visually have a color. The radiation spectrum of a black body is determined only by its temperature.

Absolutely black body

Completely black body- this is a physical abstraction (model), which is understood as a body that completely absorbs all electromagnetic radiation falling on it

For a completely black body

gray body

gray body- this is a body whose absorption coefficient does not depend on frequency, but depends only on temperature

For the gray body

Kirchhoff's law for thermal radiation

The ratio of the emissivity of any body to its absorption capacity is the same for all bodies at a given temperature for a given frequency and does not depend on their shape and chemical nature.

Temperature dependence of the spectral density of the energy luminosity of a black body

dependence of the spectral energy density of the radiation L (T) of a black body on the temperature T in the microwave radiation range, is set for the temperature range from 6300 to 100000 K.

Wien's displacement law gives the dependence of the wavelength at which the radiation flux of black body energy reaches its maximum, on the temperature of the black body.

B=2.90*m*K

Stefan-Boltzmann law

Rayleigh jeans formula

plank formula

constant plank

photo effect- this 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.

Laws of the photoelectric effect:

Wording 1st law of photoelectric effect: the number of electrons ejected by light from the surface of a metal per unit time at a given frequency is directly proportional to the light flux illuminating the metal.

According to 2nd law of photoelectric effect, the maximum kinetic energy of electrons ejected by light increases linearly with the frequency of light and does not depend on its intensity.

3rd law of photoelectric effect: for each substance there is a red border of the photoelectric effect, that is, the minimum frequency of light (or maximum wavelengthλ 0), at which the photoelectric effect is still possible, and if , then the photoelectric effect no longer occurs.

Photon- an elementary particle, a quantum of electromagnetic radiation (in the narrow sense - light). It is a massless particle that can only exist by moving at the speed of light. The electric charge of a photon is also equal to zero.

Einstein's equation for the external photoelectric effect

Photocell- an electronic device that converts photon energy into electrical energy. The first photoelectric cell based on the external photoelectric effect was created by Alexander Stoletov in late XIX century.

energy mass and momentum of a photon

light pressure is the pressure produced by electromagnetic light waves falling on the surface of a body.

The pressure p exerted by the wave on the metal surface could be calculated as the ratio of the resultant Lorentz forces acting on free electrons in the surface layer of the metal to the surface area of ​​the metal:

The quantum theory of light explains light pressure as a result of the transfer of their momentum by photons to atoms or molecules of matter.

Compton effect(Compton effect) - the phenomenon of changing the wavelength of electromagnetic radiation due to its elastic scattering by electrons

Compton wavelength

De Broglie's hypothesis is that the French physicist Louis de Broglie put forward the idea of ​​ascribing wave properties to an electron. Drawing an analogy between a quantum, de Broglie suggested that the motion of an electron or some other particle with a rest mass is associated with a wave process.

De Broglie's hypothesis establishes that a moving particle with energy E and momentum p corresponds to a wave process whose frequency is equal to:

and the wavelength:

where p is the momentum of the moving particle.

Davisson-Jermer experiment- a physical experiment on electron diffraction, conducted in 1927 by American scientists Clinton Davisson and Lester Germer.

The reflection of electrons from a single crystal of nickel was studied. The setup included a nickel single crystal ground at an angle and mounted on a holder. A beam of monochromatic electrons was directed perpendicularly to the plane of the section. The electron velocity was determined by the voltage across electron gun:

A Faraday cup connected to a sensitive galvanometer was installed at an angle to the incident electron beam. According to the readings of the galvanometer, the intensity of the electron beam reflected from the crystal was determined. The entire setup was in a vacuum.

In the experiments, the intensity of the electron beam scattered by the crystal was measured as a function of the scattering angle, the azimuthal angle , and the electron velocity in the beam.

Experiments have shown that there is a pronounced selectivity (selectivity) of electron scattering. At different values angles and velocities, intensity maxima and minima are observed in the reflected beams. Maximum condition:

Here is the interplanar distance.

Thus, the diffraction of electrons on the crystal lattice of a single crystal was observed. The experiment was a brilliant confirmation of the existence of wave properties in microparticles.

wave function, or psi function is a complex-valued function used in quantum mechanics to describe the pure state of a system. It is the expansion coefficient of the state vector in terms of the basis (usually the coordinate one):

where is the coordinate basis vector, and is the wave function in the coordinate representation.

physical meaning wave function is that, according to the Copenhagen interpretation quantum mechanics probability density of finding a particle at a given point in space in this moment time is considered to be equal to the square of the absolute value of the wave function of this state in the coordinate representation.

Heisenberg uncertainty principle(or Heisenberg) in quantum mechanics - a fundamental inequality (uncertainty relation), which sets the limit on the accuracy of the simultaneous determination of a pair of physical observables characterizing a quantum system (see physical quantity), described by non-commuting operators (for example, coordinates and momentum, current and voltage, electric and magnetic fields). The uncertainty relation [* 1] sets a lower limit for the product of the standard deviations of a pair of quantum observables. The uncertainty principle, discovered by Werner Heisenberg in 1927, is one of the cornerstones of quantum mechanics.

Definition If there are several (many) identical copies of the system in a given state, then the measured values ​​of position and momentum will obey a certain probability distribution - this is a fundamental postulate of quantum mechanics. By measuring the magnitude of the standard deviation of the position and the standard deviation of the momentum, we find that:

Schrödinger equation

Potential hole is the region of space where there is a local minimum of the potential energy of the particle.

tunnel effect, tunneling- overcoming a potential barrier by a microparticle in the case when its total energy (remaining unchanged during tunneling) is less than the barrier height. The tunnel effect is a phenomenon of exclusively quantum nature, impossible and even completely contrary to classical mechanics. An analogue of the tunnel effect in wave optics can be the penetration of a light wave into a reflecting medium (at distances of the order of the wavelength of a light wave) under conditions when, from the point of view of geometric optics, complete internal reflection. The phenomenon of tunneling underlies many important processes in atomic and molecular physics, in the physics of the atomic nucleus, solid state, etc.

Harmonic oscillator in quantum mechanics, it is a quantum analogue of a simple harmonic oscillator, while considering not the forces acting on the particle, but the Hamiltonian, that is, the total energy of the harmonic oscillator, and the potential energy is assumed to be quadratically dependent on the coordinates. Accounting for the following terms in the expansion of the potential energy with respect to the coordinate leads to the concept of an anharmonic oscillator.

The study of the structure of atoms showed that atoms consist of a positively charged nucleus, in which almost all of the mass is concentrated. h of the atom, and negatively charged electrons moving around the nucleus.

Bohr-Rutherford planetary model of the atom. In 1911, Ernest Rutherford, having done a series of experiments, came to the conclusion that the atom is a kind of planetary system in which electrons move in orbits around a heavy positively charged nucleus located in the center of the atom ("Rutherford's model of the atom"). However, such a description of the atom came into conflict with classical electrodynamics. The fact is that, according to classical electrodynamics, an electron, when moving with centripetal acceleration, must radiate electromagnetic waves, and, consequently, lose energy. Calculations showed that the time it takes for an electron in such an atom to fall onto the nucleus is absolutely negligible. To explain the stability of atoms, Niels Bohr had to introduce postulates, which boiled down to the fact that an electron in an atom, being in some special energy states, does not radiate energy (“the Bohr-Rutherford model of the atom”). Bohr's postulates showed that classical mechanics is not applicable to describe the atom. Further study of the radiation of the atom led to the creation of quantum mechanics, which made it possible to explain the vast majority of the observed facts.

Emission spectra of atoms usually obtained with high temperature light source (plasma, arc or spark), in which the evaporation of a substance occurs, the splitting of its molecules into individual atoms and excitation of atoms to glow. Atomic analysis can be both emission - the study of emission spectra, and absorption - the study of absorption spectra.
The emission spectrum of an atom is a set of spectral lines. The spectral line appears as a result of monochromatic light emission during the transition of an electron from one electronic sublevel allowed by the Bohr postulate to another sublevel different levels. This radiation is characterized by the wavelength K, the frequency v, or the wave number co.
The emission spectrum of an atom is a set of spectral lines. The spectral line appears as a result of monochromatic light emission during the transition of an electron from one electronic sublevel allowed by the Bohr postulate to another sublevel of different levels.

Bohr model of the atom (Bohr model)- the semiclassical model of the atom proposed by Niels Bohr in 1913. He took as a basis the planetary model of the atom put forward by Rutherford. However, from the point of view of classical electrodynamics, an electron in Rutherford's model, moving around the nucleus, would have to radiate continuously, and very quickly, having lost energy, fall onto the nucleus. To overcome this problem, Bohr introduced the assumption, the essence of which is that electrons in an atom can only move along certain (stationary) orbits, while being in which they do not radiate, and radiation or absorption occurs only at the moment of transition from one orbit to another. Moreover, only those orbits are stationary, when moving along which the momentum of the electron's momentum is equal to an integer number of Planck's constants: .

Using this assumption and the laws classical mechanics, namely, the equality of the force of attraction of an electron from the nucleus and the centrifugal force acting on a rotating electron, he obtained the following values ​​for the radius of a stationary orbit and the energy of an electron located in this orbit:

Here is the electron mass, Z is the number of protons in the nucleus, is the dielectric constant, e is the electron charge.

It is this expression for the energy that can be obtained by applying the Schrödinger equation, solving the problem of the motion of an electron in the central Coulomb field.

The radius of the first orbit in the hydrogen atom R 0 \u003d 5.2917720859 (36) 10 −11 m, now called the Bohr radius, or atomic unit of length and is widely used in modern physics. The energy of the first orbit, eV, is the ionization energy of the hydrogen atom.

Bohr's postulates

§ An atom can only be in special stationary, or quantum, states, each of which corresponds to a certain energy. In a stationary state, an atom does not radiate electromagnetic waves.

§ An electron in an atom, without losing energy, moves along certain discrete circular orbits, for which the angular momentum is quantized: , where are natural numbers, and is Planck's constant. The stay of an electron in orbit determines the energy of these stationary states.

§ When an electron moves from an orbit (energy level) to an orbit, an energy quantum is emitted or absorbed, where are the energy levels between which the transition is made. When moving from the upper level to the lower one, energy is emitted, and when moving from the lower to the upper one, it is absorbed.

Using these postulates and the laws of classical mechanics, Bohr proposed a model of the atom, now called the Bohr model of the atom. Later, Sommerfeld extended Bohr's theory to the case of elliptical orbits. It is called the Bohr-Sommerfeld model.

Franc and hertz experiments

experience has shown that electrons transfer their energy to mercury atoms in batches , and 4.86 eV is the smallest possible portion that can be absorbed by a mercury atom in the ground energy state

Balmer formula

To describe the wavelengths λ of the four visible lines of the hydrogen spectrum, I. Balmer proposed the formula

where n = 3, 4, 5, 6; b = 3645.6 Å.

Currently, for the Balmer series, they use special case Rydberg formulas:

where λ is the wavelength,

R≈ 1.0974 10 7 m −1 - Rydberg constant,

n- the main quantum number of the initial level - a natural number greater than or equal to 3.

hydrogen atom An atom that contains one and only one electron in its electron shell.

X-ray radiation- electromagnetic waves, the photon energy of which lies on the electromagnetic wave scale between ultraviolet radiation and gamma radiation, which corresponds to wavelengths from 10 −2 to 10 3 Å (from 10 −12 to 10 −7 m)

x-ray tube- an electrovacuum device designed to generate X-rays.

Bremsstrahlung- electromagnetic radiation emitted by a charged particle during its scattering (deceleration) in electric field. Sometimes in the concept bremsstrahlung» also include the radiation of relativistic charged particles moving in macroscopic magnetic fields(in accelerators, in outer space), and call it magnetic bremsstrahlung; however, the term "synchrotron radiation" is more commonly used in this case.

CHARACTERISTIC RADIATION- roentgen. line spectrum radiation. characteristic of the atoms of each element.

chemical bond - the phenomenon of interaction of atoms, due to the overlap of electron clouds of binding particles, which is accompanied by a decrease in the total energy of the system.

molecular spectrum- emission (absorption) spectrum arising from quantum transitions between energy levels of molecules

Energy level - energy eigenvalues ​​of quantum systems, that is, systems consisting of microparticles (electrons, protons and other elementary particles) and subject to the laws of quantum mechanics.

Quantum number n – The main thing . It determines the energy of an electron in a hydrogen atom and one-electron systems (He +, Li 2+, etc.). In this case, the electron energy

Where n takes values ​​from 1 to ∞. The less n, the greater the energy of interaction of the electron with the nucleus. At n= 1 hydrogen atom is in the ground state, at n> 1 - in excited.

selection rules in spectroscopy, they call restrictions and prohibitions on transitions between levels of a quantum mechanical system with the absorption or emission of a photon, imposed by conservation laws and symmetry.

multi-electron atoms called atoms with two or more electrons.

Zeeman effect- splitting of lines of atomic spectra in a magnetic field.

Discovered in 1896 by Zeeman for sodium emission lines.

The essence of the phenomenon of electron paramagnetic resonance lies in the resonant absorption of electromagnetic radiation by unpaired electrons. An electron has a spin and an associated magnetic moment.

Energy luminosity of the body R T, numerically equal to the energy W radiated by the body in the entire wavelength range (0 per unit of body surface, per unit of time, at body temperature T, i.e.

Emissivity of the body rl ,T numerically equal to the energy of the body dWl radiated by the body from a unit of body surface, per unit of time at body temperature T, in the wavelength range from l to l +dl, those.

This value is also called the spectral density of the energy luminosity of the body.

Energy luminosity is related to the emissivity by the formula

absorbency body al ,T- a number showing what fraction of the energy of radiation incident on the surface of a body is absorbed by it in the wavelength range from l to l +dl, those.

The body for which al ,T=1 over the entire wavelength range, is called a black body (black body).

The body for which al ,T=const<1 over the entire wavelength range is called gray.

Where- spectral density energy luminosity, or emissivity of the body .

Experience shows that the emissivity of a body depends on the temperature of the body (for each temperature, the maximum radiation lies in its own frequency range). Dimension .



Knowing the emissivity, you can calculate the energy luminosity:

called absorption capacity of the body . It also strongly depends on temperature.

By definition, it cannot be greater than one. For a body that completely absorbs radiation of all frequencies, . Such a body is called absolutely black (this is an idealization).

Body for which and is less than unity for all frequencies,called gray body (this is also an idealization).

There is a certain relationship between the emitting and absorbing ability of the body. Let's mentally carry out the following experiment (Fig. 1.1).

Rice. 1.1

Let there be three bodies inside a closed shell. The bodies are in a vacuum, therefore, the exchange of energy can occur only due to radiation. Experience shows that after some time such a system will come to a state of thermal equilibrium (all bodies and the shell will have the same temperature).

In this state, a body with a greater radiative capacity loses more energy per unit time, but, therefore, this body must also have a greater absorbing capacity:

Gustav Kirchhoff in 1856 formulated law and suggested black body model .

The ratio of emissivity to absorptivity does not depend on the nature of the body, it is the same for all bodies.(universal)function of frequency and temperature.

, (1.2.3)

Where - universal Kirchhoff function.

This function has a universal, or absolute, character.

The quantities and themselves, taken separately, can change extremely strongly when passing from one body to another, but their ratio constantly for all bodies (at a given frequency and temperature).

For an absolutely black body, therefore, for it, i.e. Kirchhoff's universal function is nothing but the radiance of a completely black body.

Absolutely black bodies do not exist in nature. Soot or platinum black have absorbing power, but only in a limited frequency range. However, a cavity with a small opening is very close in its properties to a completely black body. The beam that got inside, after multiple reflections, is necessarily absorbed, and the beam of any frequency (Fig. 1.2).

Rice. 1.2

The emissivity of such a device (cavity) is very close to f(ν, ,T). Thus, if the walls of the cavity are maintained at a temperature T, then radiation coming out of the hole is very close in spectral composition to the radiation of a completely black body at the same temperature.

Expanding this radiation into a spectrum, we can find the experimental form of the function f(ν, ,T) (Fig. 1.3), at different temperatures T 3 > T 2 > T 1 .

Rice. 1.3

The area covered by the curve gives the energy luminosity of a black body at the appropriate temperature.

These curves are the same for all bodies.

The curves are similar to the velocity distribution function of molecules. But there, the areas covered by the curves are constant, while here, with increasing temperature, the area increases significantly. This suggests that energy compatibility is highly dependent on temperature. Maximum radiation (emissivity) with increasing temperature is shifting towards higher frequencies.

The laws of thermal radiation

Any heated body emits electromagnetic waves. The higher the temperature of a body, the shorter the waves it emits. A body in thermodynamic equilibrium with its radiation is called absolutely black (AChT). The radiation of a black body depends only on its temperature. In 1900, Max Planck derived a formula by which, at a given temperature, a completely black body can calculate the intensity of its radiation.

The Austrian physicists Stefan and Boltzmann established a law expressing the quantitative relationship between the total emissivity and the temperature of a black body:

This law is called Stefan-Boltzmann law . The constant σ \u003d 5.67 ∙ 10 -8 W / (m 2 ∙ K 4) was called Stefan-Boltzmann constant .

All Planck curves have a markedly pronounced maximum attributable to the wavelength

This law is called Wien's law . So, for the Sun T 0 = 5800 K, and the maximum falls on the wavelength λ max ≈ 500 nm, which corresponds to the green color in the optical range.

As the temperature increases, the blackbody radiation maximum shifts to the short-wavelength part of the spectrum. A hotter star radiates most of its energy in the ultraviolet range, a less hot one in the infrared.

Photoelectric effect. Photons

photoelectric effect was discovered in 1887 by the German physicist G. Hertz and experimentally studied by A. G. Stoletov in 1888–1890. The most complete study of the phenomenon of the photoelectric effect was carried out by F. Lenard in 1900. By this time, the electron had already been discovered (1897, J. Thomson), and it became clear that the photoelectric effect (or, more precisely, the external photoelectric effect) consists in pulling electrons out of matter under the influence of light falling on it.

The layout of the experimental setup for studying the photoelectric effect is shown in fig. 5.2.1.

The experiments used a glass vacuum vessel with two metal electrodes, the surface of which was thoroughly cleaned. A voltage was applied to the electrodes U, the polarity of which could be changed using a double key. One of the electrodes (cathode K) was illuminated through a quartz window with monochromatic light of a certain wavelength λ. At a constant luminous flux, the dependence of the photocurrent strength was taken I from the applied voltage. On fig. 5.2.2 shows typical curves of such a dependence obtained at two intensity values luminous flux incident on the cathode.

The curves show that at sufficiently high positive voltages at the anode A, the photocurrent reaches saturation, since all the electrons ejected by light from the cathode reach the anode. Careful measurements have shown that the saturation current I n is directly proportional to the intensity of the incident light. When the voltage across the anode is negative, the electric field between the cathode and anode slows down the electrons. The anode can only reach those electrons whose kinetic energy exceeds | EU|. If the anode voltage is less than - U h, the photocurrent stops. measuring U h, it is possible to determine the maximum kinetic energy of photoelectrons:

Numerous experimenters have established the following basic laws of the photoelectric effect:

  1. The maximum kinetic energy of photoelectrons increases linearly with increasing light frequency ν and does not depend on its intensity.
  2. For every substance there is a so-called red border photo effect , i.e., the lowest frequency ν min at which an external photoelectric effect is still possible.
  3. The number of photoelectrons pulled out by light from the cathode in 1 s is directly proportional to the light intensity.
  4. The photoelectric effect is practically inertialess, the photocurrent appears instantly after the start of cathode illumination, provided that the light frequency ν > ν min .

All these laws of the photoelectric effect fundamentally contradicted the ideas of classical physics about the interaction of light with matter. According to wave concepts, when interacting with an electromagnetic light wave, an electron would have to gradually accumulate energy, and it would take a considerable time, depending on the intensity of light, for the electron to accumulate enough energy to fly out of the cathode. Calculations show that this time should have been calculated in minutes or hours. However, experience shows that photoelectrons appear immediately after the start of illumination of the cathode. In this model, it was also impossible to understand the existence of the red boundary of the photoelectric effect. The wave theory of light could not explain the independence of the energy of photoelectrons from the intensity of the light flux and the proportionality of the maximum kinetic energy to the frequency of light.

Thus, the electromagnetic theory of light proved unable to explain these regularities.

A way out was found by A. Einstein in 1905. A theoretical explanation of the observed laws of the photoelectric effect was given by Einstein on the basis of M. Planck's hypothesis that light is emitted and absorbed in certain portions, and the energy of each such portion is determined by the formula E = h v, where h is Planck's constant. Einstein took the next step in the development of quantum concepts. He came to the conclusion that light has a discontinuous (discrete) structure. electromagnetic wave consists of separate portions - quanta, subsequently named photons. When interacting with matter, a photon transfers all of its energy h for one electron. Part of this energy can be dissipated by an electron in collisions with atoms of matter. In addition, part of the electron energy is spent on overcoming the potential barrier at the metal–vacuum interface. To do this, the electron must do the work function A depending on the properties of the cathode material. The maximum kinetic energy that a photoelectron emitted from the cathode can have is determined by the energy conservation law:

This formula is called Einstein's equation for the photoelectric effect .

Using the Einstein equation, one can explain all the regularities of the external photoelectric effect. From the Einstein equation follows linear dependence maximum kinetic energy on frequency and independence on light intensity, existence of a red border, inertialess photoelectric effect. The total number of photoelectrons leaving the cathode surface in 1 s should be proportional to the number of photons falling on the surface in the same time. It follows from this that the saturation current must be directly proportional to the intensity of the light flux.

As follows from the Einstein equation, the slope of the straight line expressing the dependence of the blocking potential U h from the frequency ν (Fig. 5.2.3), is equal to the ratio of Planck's constant h to the charge of an electron e:

Where c is the speed of light, λcr is the wavelength corresponding to the red border of the photoelectric effect. For most metals, the work function A is a few electron volts (1 eV = 1.602 10 -19 J). In quantum physics, the electron volt is often used as a unit of energy. The value of Planck's constant, expressed in electron volts per second, is

Among metals, alkaline elements have the lowest work function. For example, sodium A= 1.9 eV, which corresponds to the red border of the photoelectric effect λcr ≈ 680 nm. Therefore, connections alkali metals used to create cathodes in photocells designed to detect visible light.

So, the laws of the photoelectric effect indicate that light, when emitted and absorbed, behaves like a stream of particles called photons or light quanta .

The photon energy is

it follows that the photon has momentum

Thus, the doctrine of light, having completed a revolution lasting two centuries, again returned to the ideas of light particles - corpuscles.

But this was not a mechanical return to Newton's corpuscular theory. At the beginning of the 20th century, it became clear that light has a dual nature. When light propagates, its wave properties appear (interference, diffraction, polarization), and when interacting with matter, corpuscular (photoelectric effect). This dual nature of light is called wave-particle duality . Later, the dual nature was discovered in electrons and other elementary particles. classical physics can't give visual model combinations of wave and corpuscular properties of micro-objects. The motion of micro-objects is controlled not by the laws of classical Newtonian mechanics, but by the laws of quantum mechanics. The theory of radiation of a completely black body, developed by M. Planck, and quantum theory Einstein's photoelectric effect is at the heart of this modern science.

Thermal radiation of bodies is called electromagnetic radiation that occurs due to that part of the internal energy of the body, which is related to the thermal motion of its particles.

The main characteristics of thermal radiation of bodies heated to a temperature T are:

1. Energy luminosityR (T ) -the amount of energy emitted per unit time per unit surface of the body, in the entire range of wavelengths. Depends on the temperature, nature and state of the surface of the radiating body. In the SI system R ( T ) has the dimension [W/m 2 ].

2. Spectral density of energy luminosityr ( ,T) =dW/ d - the amount of energy emitted by a unit of body surface per unit of time in a unit wavelength interval (near the considered wavelength). Those. this quantity is numerically equal to the energy ratio dW emitted per unit area per unit time in a narrow range of wavelengths from before +d, to the width of this interval. It depends on the temperature of the body, the wavelength, and also on the nature and state of the surface of the radiating body. In the SI system r(, T) has the dimension [W/m 3 ].

Energy luminosity R(T) related to the spectral density of energy luminosity r(, T) in the following way:

(1) [W/m2]

3. All bodies not only radiate, but also absorb electromagnetic waves incident on their surface. To determine the absorption capacity of bodies in relation to electromagnetic waves of a certain wavelength, the concept is introduced monochromatic absorption coefficient-the ratio of the energy of a monochromatic wave absorbed by the body surface to the energy of an incident monochromatic wave:

The monochromatic absorption coefficient is a dimensionless quantity that depends on temperature and wavelength. It shows what fraction of the energy of the incident monochromatic wave is absorbed by the surface of the body. Value  (, T) can take values ​​from 0 to 1.

Radiation in an adiabatically closed system (not exchanging heat with the environment) is called equilibrium. If a small hole is created in the wall of the cavity, the state of equilibrium will change slightly, and the radiation leaving the cavity will correspond to the equilibrium radiation.

If a beam is directed into such a hole, then after repeated reflections and absorption on the walls of the cavity, it will not be able to go back out. This means that for such a hole, the absorption coefficient (, T) = 1.

The considered closed cavity with a small hole serves as one of the models absolutely black body.

Completely black bodya body is called that absorbs all the radiation incident on it, regardless of the direction of the incident radiation, its spectral composition and polarization (without reflecting or transmitting anything).

For a blackbody, the spectral density of energy luminosity is some universal function of wavelength and temperature f(, T) and does not depend on its nature.

All bodies in nature partially reflect the radiation incident on their surface and therefore do not belong to absolutely black bodies. If the monochromatic absorption coefficient of a body is the same for all wavelengths and lessunits((, T) = Т = const<1),then such a body is called gray. The coefficient of monochromatic absorption of a gray body depends only on the temperature of the body, its nature and the state of its surface.

Kirchhoff showed that for all bodies, regardless of their nature, the ratio of the spectral density of energy luminosity to the monochromatic absorption coefficient is the same universal function of wavelength and temperature f(, T) , which is the spectral density of the energy luminosity of a black body :

Equation (3) is Kirchhoff's law.

Kirchhoff's law can be formulated like this: for all bodies of the system that are in thermodynamic equilibrium, the ratio of the spectral density of energy luminosity to the coefficient monochromatic absorption does not depend on the nature of the body, is the same function for all bodies, depending on the wavelength and temperature T.

From the foregoing and formula (3) it is clear that at a given temperature, those gray bodies that have a large absorption coefficient radiate more strongly, and absolutely black bodies radiate most strongly. Since for a completely black body( , T)=1, then formula (3) implies that the universal function f(, T) is the spectral density of the energy luminosity of a black body