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Unformatted text preview: AP1200 Foundation Physics Imagination is more important than knowledge… Albert Einstein Chapter 7: Modern Physics The past 100 years has seen significant developments in Physics. There were two major areas of development, relativity and quantum mechanics. In this chapter we will cover briefly on topics such as special theory of relativity, Blackbody radiation, the photoelectric effect, the Compton scattering, the de Broglie waves, the uncertainty principle, the early atomic models and some modern quantum theory. 7.1 Blackbody Radiation and Planck’s Hypothesis An object at any temperature emits thermal radiation. Fig. 7.1 Blackbody radiation A black body is an ideal system that absorbs all radiation incidents on it. The nature of the radiation emitted from a black body depends only on its temperature (and independent of the materials, shape or size) (Fig. 7.2). Notice that as the temperature is increased, two things happen; the peak wavelength shifts towards shorter wavelengths, and the total area under the curve increases. This is why the Sun generates visible light, but the much cooler Earth radiates in the infrared. Wein’s displacement law This law describes the wavelength at which the radiation intensity is the greatest when the black body is at absolute temperature T . 3 max 10 898 . 2 × = T λ m.K (7.1) Fig. 7.2 Blackbody radiation spectrum Stefan’s Law The second law says that the total power of radiation emitted increases with temperature (the area under the curve in Fig. 7.2 increases with temperature): 4 T A P ε σ = (7.2) σ (= 5.6696 × 10 8 Wm2 K4 ) is called Stefan’s constant. A is the area of the blackbody (the hole). For a black body, emissivity ε = 1. So if we talk about the total intensity I ( T ), which is defined as P / A , ( 29 4 T T I σ = (for black body only) (7.3) These two laws were empirical. Rayleigh and Jeans tried to develop a theoretical model to describe Fig. 7.2. The RayleighJeans model assumed that molecules in the surface are treated as a set of oscillators that emit electromagnetic waves at all wavelengths. This model correctly explains the intensity of blackbody radiation at the long wavelength end of the spectrum, but fails to explain the intensity at the short wavelength end of the spectrum (Fig. 7.3). This became known as the ultraviolet catastrophe. Fig. 7.3 RayleighJean’s law In 1900, Planck was able to guess the correct formula. It took him 6 years to find the formula and then he struggled with the physical interpretation. ( 29  = 1 exp 2 , 5 2 T k hc hc T I B λ λ π λ . (7.4) The formula fits the data over the whole spectrum, and over all temperatures. The constant h (6.626 × 10 34 J.s) was tuned so that his formula fit the experimental data over all wavelengths....
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This note was uploaded on 04/17/2011 for the course AP 1200 taught by Professor Michela.vanhove during the Spring '10 term at City University of Hong Kong.
 Spring '10
 MichelA.VanHove

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