§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.
b = 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
где а, b = const.
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
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.
1. The most significant action has ultraviolet radiation;
§ 2 The external photoelectric effect. Three Laws of external photoeffect
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.
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.
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.
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, hν0= Asat, therefore, that there is a minimum frequency from which the possible photoemission.