Chapter 27

# Chapter 27 - CHAPTER 27 Quick Quizzes 1(b Some energy is...

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C HAPTER 27 Quick Quizzes 1. (b). Some energy is transferred to the electron in the scattering process. Therefore, the scattered photon must have less energy (and hence, lower frequency) than the incident photon. 2. (c). Conservation of energy requires the kinetic energy given to the electron be equal to the difference between the energy of the incident photon and that of the scattered photon. 3. (c). Conservation of momentum requires the momentum of the incident photon equal the vector sum of the momenta of the electron and the scattered photon. Since the scattered photon moves in the direction opposite that of the electron, the magnitude of the electron’s momentum must exceed that of the incident photon. 4. (c). Two particles with the same de Broglie wavelength will have the same momentum p = mv . If the electron and proton have the same momentum, they cannot have the same speed because of the difference in their masses. For the same reason, remembering that 2 2 KE p m = , they cannot have the same kinetic energy. Because the kinetic energy is the only type of energy an isolated particle can have, and we have argued that the particles have different energies, Equation 27.15 tells us that the particles do not have the same frequency. 5. (b). The Compton wavelength, C e hmc λ = , is a combination of constants and has no relation to the motion of the electron. The de Broglie wavelength, e hmv = , is associated with the motion of the electron through its momentum. 355

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CHAPTER 27 Problem Solutions 27.1 From Wien’s displacement law, (a) 22 9 0.2898 10 mK 0 .2898 mK 970 m max T λ −− × ⋅× == × , or 3 2.99 10 K 3000 K (b) 9 145 m T × × , or 4 2.00 20 000 K 27.2 Using Wien’s displacement law, (a) 2 4 ×⋅ = 7 2.898 m ~100 nm Ultraviolet (b) 2 7 m × 1 ~10 nm -rays γ 27.3 (a) The wavelength of maximum radiation is given by 2 7 9.99 m= 2900 K × 999 nm (b) The peak wavelength is in the infrared , far from the visible region of the electromagnetic spectrum. 27.4 () 34 15 19 1.00 eV 6.63 Js 4.14 eV s 1.60 J Eh f f f ⎛⎞ × = × ⎜⎟ ⎝⎠ × (a) ( )( ) 12 -1 eV s 620 10 s E ⋅ × = 2.57 eV (b) ( )( ) 9-1 eV s 3.10 E × = 5 1.28 eV × (c) ( )( ) 6-1 eV s 46. 01 0 s E × = 7 1.91 × 356
CHAPTER 27 (d) 8 7 12 3.00 10 m s 4.84 10 m 620 10 Hz c f λ × == = × = × ( ) 484 nm visible light, blue 8 2 9 10 m s 9.68 m 3.10 c f × = × = × ( ) 9.67 cm microw aves 8 6 10 m s 46. 01 0 Hz c f × = × ( ) 6.52 m rad iow aves 27.5 ( ) ( ) 34 8 19 6.63 Js 3.00 10 m s 1.00 eV 1.60 J hc Eh f f λλ ×⋅ × ⎛⎞ === ⎜⎟ ⎝⎠ × , which yields 6 1.24 me V E ×⋅ = (a) 6 2 V 5.00 m E × 5 2.49 eV × (b) 6 9 V 500 m E × 2.49 eV (c) 6 9 V m E × 249 eV 27.6 The energy of a single photon is () ( ) 8 9 10 m s 3.38 J 589. 31 0 m E γ = × × The number of photons emitted by the lamp in 1.00 s t ∆ = is ( )( ) 1000 J s 1.00 s J t E N EE γγ ℘⋅ ∆ = = 21 2.96 × × 357

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CHAPTER 27 27.7 The energy of a single photon is ( )( ) 34 6- 12 6.63 10 Js 99. 71 0 s6 .
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Chapter 27 - CHAPTER 27 Quick Quizzes 1(b Some energy is...

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