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CHAPTER 21 OPTICAL PROPERTIES PROBLEM SOLUTIONS 21.1 Similarities between photons and phonons are: 1) Both may be described as being wave-like in nature. 2) The energy for both is quantized. Differences between photons and phonons are: 1) Phonons are elastic waves that exist within solid materials. Photons are electromagnetic energy packets that may exist in solid materials, as well as in other media. 2) There is a considerable disparity between the velocities of photons and phonons. The velocity of a photon is the same as the velocity of light in the particular medium; for a phonon, its velocity is that of sound. 21.2 From the classical perspective, electromagnetic radiation is wave-like in character, and the possible energies of the radiation are continuous. From the quantum-mechanical perspective, electromagnetic radiation is dual-like in character (being both wave-like and particle-like), and not all energies are possible (i.e., energy is quantized). 21.3 In order to compute the frequency of a photon of orange light, we must use Equation (21.2) as ν = c λ = 3x10 8 m/s 6x10 7 m = 5 x 10 14 s -1 Now, for the energy computation, we employ Equation (21.3) as follows: E = hc λ = 6.63 x 10 34 J-s ( ) 8 ( ) 7 m = 3.31 x 10 -19 J (2.07 eV) 21.4 Opaque materials are impervious to light transmission; it is not possible to see through them. Light is transmitted diffusely through translucent materials (there is some internal light scattering). Objects are not clearly distinguishable when viewed through a translucent material. 1
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Virtually all of the incident light is transmitted through transparent materials, and one can see clearly through them. 21.5 (a) The phenomenon of electronic polarization by electromagnetic radiation is described in Section 21.4. (b) Two consequences of electronic polarization in transparent materials are absorption and refraction. 21.6 (a) In ionic materials, the larger the size of the component ions the greater the degree of electronic polarization. (b) Upon consultation of Table 12.3 we find that the Ba 2+ , Ca 2+ , Na + , and K + ions are all greater in size than the Si 4+ ion (0.136, 0.100, 0.102, and 0.0.138 nm, respectively, versus 0.040 nm), and, therefore, all of these ions will increase the index of refraction when added to SiO 2 . 21.7 (a) The electron band structures of metals are such that empty and available electron states are adjacent to filled states. Electron excitations from filled to empty states are possible with the absorption of electromagnetic radiation having frequencies within the visible spectrum, according to Equation (21.6). The light energy is totally absorbed or reflected, and, since none is transmitted, the material is opaque. (b) Metals are transparent to high-frequency x-ray and γ -ray radiation since the energies of these types of radiation are greater than for visible light; electron excitations corresponding to these energies are not possible because energies for such transitions are to within an energy band gap beyond the highest partially-filled energy band.
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