医学物理学9Word下载.docx

1、9.1 Blackbody radiation and Planck hypothesis 9.1.1 Historical recall: studies on light Without question, geometric optics is the earliest theory to describe the phenomenon of light and it is still used today. As you know, there are several basic laws and equations in geometric optics and they are s

2、till useful today in explaining the optical instrument. You might notice that light paths are all straight lines in geometric optics. In the early of 18th century, based on the existing knowledge of light at that time, Newton proposed his corpuscular theory of light to explain the light travels alon

3、g a straight line in the space or uniform medium. In such a theory, light is regarded as a stream of particles that set up disturbances in the aether （which is recognized as the medium of light propagation）of space. Newtons corpuscular （微粒的） theory is the first one to try to explain the nature of li

4、ght but there exist many other interesting and beautiful effects that cannot be explained by Newtons corpuscular theory such as light bending around corners. Therefore it is not a correct theory. It is known that the Geometric optics is just a phenomenon, macroscopic and application study on light.

5、That light travels in a straight line in space or medium is just a physical model used to study light in geometric optics and it is the superficial phenomenon of light and it has nothing to do with the property of light. The wave nature of light is based on the experiments of interference and diffra

6、ction of light. Such a phenomenon can be explained by Huygens principle and these phenomena put Newtons corpuscular theory of light into history. The complete wave theory of light was finally given by Maxwell （James Clerk） who showed that light formed the part of electromagnetic waves. The famous ex

7、periments to show light has wave property are Thomas Yangs double-slit interference experiment and Fraunhofer Single slit diffraction experiment. In 1801, Thomas Young did a double-slit interference experiment of light and showed that a wave theory was essential to interpret this type of phenomenon.

8、 And from then, Newtons corpuscular theory of light has been considered as a wrong theory for the explanation of the nature of light. Another famous experiment was done by Fraunhofer Single-slit diffraction. It should be also explained by wave theory of light. In the middle of 19th century, lights a

9、re recognized as part of electromagnetic spectrum and its space and time dependence follows the laws given in Maxwell equations which were considered as a complete theory for electromagnetic waves. Therefore, light belongs to electromagnetic waves and it does have the wave properties. Most physicist

10、s thought Physics skyscraper had been completely built and some minor problems like blackbody radiation and light speed would be soon found out using existing physics theory. However, Genius physicists thought that the blackbody radiation and light speed were the two patches of clouds in physics sky

11、. In fact, the “minor” problems had shaken the “skyscraper” of classical physics. In order to explain the quantum nature of light, we have to understand how the following three problems to be solved: blackbody radiation, photoelectric effect and Compton Effect. Among the three problems, blackbody ra

12、diation is the most important one. 9.1.2 Basic concepts of blackbody radiation Types of heat energy transmission are conduction, convection and radiation. Conduction is transfer of heat energy by molecular vibrations not by actual motion of material. For example, if you hold one end of an iron rod （

13、铁杆） and the other end of the rod is put on a flame, you will feel hot some time later. We can say that the heat energy reaches your hand by heat conduction.Convection is transfer of heat by actual motion of material. The hot-air furnace, the hot-water heating system, and the flow of blood in the bod

14、y are examples.Radiation The heat reaching the earth from the sun cannot be transferred either by conduction or convection since the space between the earth and the sun has no material medium. The energy is carried by electromagnetic waves that do not require a material medium for propagation. The k

15、ind of heat transfer is called thermal radiation. Blackbody radiation problem was found in the research of thermal radiation.Blackbody is defined as the body that can absorb all energies that fall on it. This is like a black hole. No lights or material can get away from it as long as it is trapped.

16、A large cavity with a small hole on its wall can be taken as a blackbody （cf. Fig.12-1 the model of blackbody in your textbook）. Blackbody radiation: Any radiation that enters the hole is absorbed in the interior of the cavity, and the radiation emitted from the hole is called blackbody radiation. 9

17、.1.3 Two successful laws1. Stefan and Boltzmanns law: it is found that the radiation energy is proportional to the fourth power of the associated temperature. 1. （9.1）where M（T） is radiation energy and actually it is the area under each curve, is called Stefans constant determined by experiment and

18、T is absolute temperature.2. Wiens displacement law: the peak of the curve shifts towards longer wavelength as the temperature falls. （cf. Fig. 12.2 the spectrum curves of blackbody radiation in your textbook） （9.2） is the peak value of the curve M（T） and b is called Weins constant. This law is quit

19、e useful while measuring the temperature of a blackbody with a very high temperature. You can see the example for how to measure the temperature on the surface of the sun. The above laws describes the blackbody radiation very well. 9.1.4 Problems exist in blackbody radiation and three formulas The p

20、roblem existing in the relation is between the radiation power M（T） and the wavelength . Blackbody radiation has nothing to do with both the material used in the blackbody concave wall and the shape of the concave wall. Two typical blackbody radiation formulas: one is given by Rayleigh and Jeans and

21、 the other is given by Wein. 1. Rayleigh and Jeans formula: In 1890, Rayleigh and Jeans obtained a formula using the classical electromagnetic （Maxwell） theory and the classical equipartition theorem of energy （能均分定理） in thermotics （热学）. The formula is given by （9.3）whereis radiation power, C1 is a

22、constant number to be determined, is the wavelength of blackbody radiation, T is the absolute temperature. Rayleigh-Jeans formula was correct for very long wavelength in the far infrared but hopelessly wrong in the visible light and ultraviolet region. Maxwells electromagnetic theory and thermodynam

23、ics are known as correct theory. The failure in explaining blackbody radiation puzzled physicists! It was regarded as ultraviolet Catastrophe （disaster）.2. Weins formula : Later on in 1896, Wein derive another important formula using thermodynamics. （9.4）where C2 and C3 are constants to be determine

24、d. Unfortunately, this formula is only valid in the region of short wavelengths. 3. Planks empirical formula: In 1900, after studying the above two formulas carefully, Planck proposed （提出） an empirical formulaFig. 9.1 Blackbody radiation（9.5）where c is light velocity, k is Boltzmens constant, e is t

25、he base of natural logarithms. It is surprising that the experience formula can describe the curve of blackbody radiation exactly for all wavelengths. 9.1.5 Derivations from Plancks formula1. Rayleigh and Jeans formula;For very large wavelength, the Rayleigh-Jeans formula can be obtained from Planck

26、s formula;2. Weins formula;For smaller wavelength of blackbody radiation, the Weins formula can be achieved also from Plancks experience formula;3. Stefan and Boltzmanns law;Integrating Plancks formula with respect to wavelength, the Stefan and Boltzmanns law can be obtained as well.4. Wiens displac

27、ement law.Finally, according to the basic mathematical theory and differentiating the Plancks formula with respect to wavelength, Wiens displacement law can also derived!9.1.6 Plancks Hypotheses1. The molecules and atoms composing the blackbody concave can be regarded as the linear harmonic oscillat

28、or with electrical charge;2. The oscillators can only be in a special energy state. All these energies must be the integer multiples of a smallest energy （0 = h）. Therefore the energies of the oscillators are E = n h with n = 1, 2, 3, 3. derivation of Plancks fumula （omitted）4. h was named photon by Einstein and （9.6）is called Planck-Einstein quantization law. h is called Planck constant. （9.7） The rel