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£> ( CHAPTER 12 QUANTUM MECHANICS AND ATOMIC THEORY Light and Matter 8 v = ~ = 3.00 X 10 mls = 3.0 x 10 10 S-1 21. A. 1.0 X 10- 2 m E = hv = 6.63 X 10- 34 J s x 3.0 X 10 10 S-l = 2.0 x 10- 23 J/photon 2.0 X 10- 23 J _ 6.02 X 10 23 photons ----'---- = 12 J/mol photon mol The wavelength is the distance between consecutive wave peaks. Wave a shows 4 wave- lengths and wave b shows 8 wavelengths. 3 Wave a: A. = 1.6 X 10- m = 4.0 x 10- 4 m 4 3 b: A. = 1.6 X 10- m = 2.0 x 10-4 m 8 a has the longer wavelength. Because frequency and photon energy are both inversely proportional to wavelength, wave b will have the higher frequency and larger photon energy since it has the shorter wavelength. 8 v = ~ = X 10 mls = 1.5 x 10 12 S-I A. 2.0 X 10- 4 m E = he = 6.63 x 10- 34 J s x 3.00 X 10 8 mls = 9.9 x 10- 22 J Ie 2.0 X 10- 4 m Because both waves are examples of electromagnetic radiation, both waves travel at the same speed, c, the speed of light. From Figure 12.3 of the text, both of these waves represent infrared electromagnetic radiation. 455
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457 CHAPTER 12 QUANTUM MECHANICS AND ATOMIC THEORY The photon energy and frequency order will be the exact opposite of the wavelength ordering because E and v are both inversely related to A. From the previously calculated wavelengths, the order of photon energy and frequency is: FM radiowaves < visible (green) light < X rays longest A. shortest A lowest v highest v C0 smallest E The energy In remnve a single electron is: largest E 208.4 kJ x 1mol = 3.461 x 10- 22 kJ = 3.461 x 10- 19 J = E; mol 6.022 x 10 23 Energy of 254-nm light is: 8 hc (6.626 X 10- 34 J s)(2.998 X 10 m/s) = 7.82 x 10- 19 J E =-= ')." 254 X 10- 9 m Ephoton = E K + E w , E K = 7.82 X 10- 19 J - 3.461 x 10- J = 4.36 X 10- J = maximum KE 28. Planck's discovery that heated bodies give off only certain frequencies of light and Einstein's study of the photoelectric effect support the quantum theory of light. The wave-particle duality is summed up by saying all matter exhibits both particulate and wave properties. Electromagnetic radiation, which was thought to be a pure waveform, transmits energy as if it has particulate properties. Conversely, electrons, which were thought to be particles, have a wavelength associated with them. This is true for all matter. Some evidence supporting wave properties of matter are: 1. Electrons can be diffracted like light. 2. The electron microscope uses electrons in a fashion similar to the way in which light is used in a light microscope. However, wave properties of matter are only important for small particles with a tiny mass, e.g., electrons. The wave properties of larger particles are not significant. 29. The photoelectric effect refers to the phenomenon in which electrons are emitted from the surface of a metal when light strikes it. The light must have a certain minimum frequency (energy) in order to remove electrons from the surface of a metal. Light having a frequency below the minimum results in no electrons being emitted, whereas light at or higher than the minimum frequency does cause electrons to be emitted. For light having a frequency higher
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This note was uploaded on 09/30/2009 for the course CHEM 1C taught by Professor Roland during the Spring '08 term at UCSC.

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chp12hwsol - &gt; ( CHAPTER 12 Q UANTUM MECHANICS A ND A...

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