§4 Radiant exitance Emissive power or irradiance. Stefan-Boltzmann law.

Wien's displacement law

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


- relation irradiance and emittance.

[RE] =J/(m2·s) = W/m2

Law of J.Stephen (Austrian scientist) and L. Boltzmann (German scientist):


σ = 5.67·10-8 W/(m2· K4) - or Stefan- Boltzmann constant or Stefan's constant.

Emissive power of a black body is proportional to the fourth power of the thermodynamic temperature.

Stefan-Boltzmann law, determining the temperature dependence of the RE, is not the answer regarding the spectral composition of the radiation of a black body. From the experimental curves rλ,Т of λ at different T, it follows that the spectral energy distribution of a black body is uneven. All the curves have a maximum, which with increasing T is shifted to shorter wavelengths. The area bounded by the curve of rλ,Т of λ, is RE (this follows from the geometric meaning of the integral) and proportional to T4.

 Wien's displacement law (1864 - 1928): The length of the waves (λmax), which accounts for a maximum capacity of a black body emissivity at a given temperature, is inversely proportional to the temperature T.

Signature: Fig. Dependence emissivity ability rλ,Т  black body of the wavelength λ at different temperaturesb = 2,9· 10-3 m·K - Wien's displacement constant.

Wien's displacement is because as the temperature maximum emissivity is shifted to shorter wavelengths.




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

Stefan-Boltzmann law allows to determine the energy emissive RE black body on its temperature. Wien's displacement law binds the body temperature with a wavelength, which accounts for the maximum emissivity ability. But neither the one nor the other law does not solve the basic problem of how high emissivity, the ability borne by each
λ in the spectrum of a black body at temperature T. For this we need to establish the functional dependence of rλ,Т  of λ and T.
Based on the view of the continuous nature of the emission of electromagnetic waves in the law of equipartition the degrees of freedom was obtained two formulas for the black body emissivity ability:

  • Wien's formula

где а, b = const.

  • Rayleigh-Jeans formula

k = 1,38·10-23 J/K - Boltzmann constant

Experimental analysis showed that for a given temperature of Wien is true for short waves and gives sharp differences with experience in long waves. The Rayleigh-Jeans was true for long waves and is not applicable for short.

Study of the thermal radiation with the aid of the Rayleigh-Jeans showed that in classical physics can not resolve the question of the function characterizing the emissivity of a black body This unsuccessful attempt to explain the laws of black body radiation using the apparatus of classical physics is called "ultraviolet catastrophe."

If you try to calculate the RE by the Rayleigh-Jeans formula, then

- "Ultraviolet catastrophe"


§6 Quantum hypothesis and Planck's formula

In 1900, Max Planck (German scientist) put forward the hypothesis that the emission and absorption of energy is not continuous, but certain small portions - quanta, the photon energy is proportional to the frequency of the oscillations (Planck's formula):

h = 6,625·10-34 J·s - Planck's constant or


Since the emission occurs in portions, the energy of the oscillator (the vibrating atoms, electrons) E takes only the values ??integer multiples of the elementary portions of energy, that is, only discrete values

Е = nЕо = n hν.

Photoelectric effect

The effect of the light into the electrical processes were studied by Hertz in 1887. He experimented with the electric discharge tube and found that the irradiation of UV discharge occurs at a much lower voltage. In the 1889-1895 years. AG Stoletov studied the effects of light on metal, using the following scheme. Two electrodes: the cathode to the study of metal and anode A (scheme Stoletov - metal mesh, the transmitted light) in a vacuum tube connected to the battery, so that by the resistance R can change the value and sign of the voltage applied to them. The irradiation of zinc  cathode current is flowing in the circuit, recorded milliammeter. Irradiating the cathode light of different wavelengths, Stoletov established following pattern:

1. The most significant action has ultraviolet radiation;
2. By the light from the cathode break out the negative charges;
3. Current, due to the action of light, is directly proportional to its intensity.
Lenard and Thomson in 1898 measured the specific charge (e / m), pull up the particles, and found that it is equal to the specific charge of the electron, therefore, taken out of the cathode electrons.


§ 2 The external photoelectric effect. Three Laws of external photoeffect

External photoelectric effect is called electron emission substance exposure to light. Electrons emitted from the material in the external photoeffect, called photoelectrons and formed their current called photocurrent.
With the scheme Stoletov obtained the following dependence of the photocurrent on the applied voltage at a constant luminous flux
Ф (that is, the CVC was obtained - the current-voltage characteristics):

At a certain voltage Usat photocurrent reaches saturation Isat - all the electrons emitted by the cathode reach the anode, therefore, the current saturation Isat determined by the number of electrons emitted by the cathode per unit time under the action of light. The number of photoelectrons released in proportion to the number of incident on the surface of the cathode rays of light. And the number of photons is determined by the light flux Ф, falling to the cathode. The number of photons N, falling for the time t on the surface is given by:

where W - the radiant energy received by the surface in time Δt,

- The energy of the photon,

Фе - luminous flux (radiant power).

1st law of the external photoeffect (law ??Stoletov):

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

Isat ~ Ф, ν = const














Ur – retarding voltage - the voltage at which no single electron can not reach the anode. Consequently, the law of conservation of energy, in this case we can write the energy of the emitted electrons is delaying the electric field energy

therefore, we can find the maximum speed of the emitted photoelectrons Vmax

2 - second law photoelectric effect: maximum initial velocity Vmax photoelectrons does not depend on the intensity of the incident light (from Ф ), and is determined only its frequency ν

 3rd law of the photoelectric effect: for every matter there is a "red edge'' photoelectric effect, that is, the minimum frequency νkp, depending on the chemical nature of matter and the state of its surface, which is still possible photoemission.
The second and third laws of the photoelectric effect can not be explained by the wave nature of light (or the classical electromagnetic theory of light). According to this theory tearing out conduction electrons of a metal is a result of their "swinging" the electromagnetic field of the light wave. With increasing light intensity (
Ф) should increase the energy transferred to electrons in a metal, therefore, be increased Vmax, which is contrary to the 2nd law of the photoelectric effect.

Since by the wave theory of energy transfer is proportional to the intensity of the electromagnetic field intensity (Ф), then any light, the frequency, but large enough intensity would pull electrons from the metal, that is, a photoelectric threshold would not exist, contrary to the 3rd law the photoelectric effect. Photoemission is inertialess. A wave theory can not explain it without inertia.


§3 The Einstein equation for the external photoelectric effect.
The work function

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

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

Incident photon energy hv that is spent on to work out electrons from the metal, and the message ejected photoelectron kinetic energy .

Minimum energy that must be imparted to an electron in order to remove it from the solid into the vacuum is called the work function.

Since the Fermi energy EF to depend on temperature and EF, also changes with temperature, it follows that Asat depends on the temperature.

In addition, the work function is very sensitive to the surface finish. Causing the surface of the film (Ca, Sn, Ba) on W Asat decreases from 4.5 eV for pure W to 1.5 ¸ 2 eV for impurity W.
Einstein's equation explains all thumbnails three laws external photoeffect
1st law: each quantum absorbed by only one electron. Therefore, the number of photoelectrons taken out should be proportional to the intensity of the (
Ф) light

2nd law: Vmax ~ ν and because Asat is independent of Ф, then the Vmax is independent of Ф

3rd Law: Reducing ν decreases Vmax and ν = ν0  Vmax= 0, therefore, 0= Asat, therefore, that there is a minimum frequency from which the possible photoemission.

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