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Unformatted text preview: Chapter 38 p. 1 CHAPTER 38 – Early Quantum Theory and Models of the Atom Note: At the atomic scale, it is most convenient to have energies in electronvolts and wavelengths in nanometers. A useful expression for the energy of a photon in terms of its wavelength is E = hf = hc / λ = (6.63 × 10 –34 J ∙ s)(3.00 × 10 8 m/s)(10 –9 nm/m) /(1.60 × 10 –19 J/eV) λ ; E = (1.24 × 10 3 eV ∙ nm)/ λ . 1. We find the temperature for a peak wavelength of 440 nm: T = (2.90 × 10 –3 m ∙ K)/ λ P = (2.90 × 10 –3 m ∙ K)/(440 × 10 –9 m) = 6.59 × 10 3 K . 2. ( a ) The temperature for a peak wavelength of 25.0 nm is T = (2.90 × 10 –3 m ∙ K)/ λ P = (2.90 × 10 –3 m ∙ K)/(25.0 × 10 –9 m) = 1.16 × 10 5 K . ( b ) We find the peak wavelength from λ P = (2.90 × 10 –3 m ∙ K)/ T = (2.90 × 10 –3 m ∙ K)/(2800 K) = 1.04 × 10 –6 m = 1.04 μ m . Note that this is not in the visible range. 3. Because the energy is quantized, E = nhf , the difference in energy between adjacent levels is ? E = hf = (6.63 × 10 –34 J ∙ s)(8.1 × 10 13 Hz) = 5.4 × 10 –20 J = 0.34 eV . 4. ( a ) We find the peak wavelength from λ P = (2.90 × 10 –3 m ∙ K)/ T = (2.90 × 10 –3 m ∙ K)/(273 K) = 1.06 × 10 –5 m = 10.6 μ m . This wavelength is in the infrared . ( b ) We find the peak wavelength from λ P = (2.90 × 10 –3 m ∙ K)/ T = (2.90 × 10 –3 m ∙ K)/(3300 K) = 8.79 × 10 –7 m = 879 nm . This wavelength is in the near infrared . ( c ) We find the peak wavelength from λ P = (2.90 × 10 –3 m ∙ K)/ T = (2.90 × 10 –3 m ∙ K)/(4 K) = 7.25 × 10 –4 m = 0.73 mm . This wavelength is in the far infrared . 5. ( a ) The potential energy on the first step is U 1 = mgh = (58.0 kg)(9.80 m/s 2 )(0.200 m) = 114 J . ( b ) The potential energy on the second step is U 2 = mg 2 h = 2 U 1 = 2(114 J) = 228 J . ( c ) The potential energy on the third step is U 3 = mg 3 h = 3 U 1 = 3(114 J) = 342 J . ( d ) The potential energy on the n th step is U n = mgnh = nU 1 = n (114 J) = 114 n J . ( e ) The change in energy is ? E = U 2 – U 6 = (2 – 6)(114 J) = – 456 J ....
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 Spring '08
 ROSS
 Energy, Kinetic Energy, Mass, Photon, ev

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