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Chapter%201%20Solns0

Chapter%201%20Solns0 - CHAPTER 1 1.1(a Radiation may pass...

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CHAPTER 1 1.1 (a) Radiation may pass through a metal foil. (b) All light (electromagnetic radiation) travels at the same speed; the slower speed supports the particle model. (c) This observation supports the radiation model. (d) This observation supports the particle model; electromagnetic radiation has no mass and no charge. 1.3 microwaves < visible light < ultraviolet light < x-rays < γ -rays 1.5 All of these can be determined using E = h ν and νλ = c . For example, in the first entry frequency is given, so: 8 -1 -7 14 -1 2.998×10 m s = 3.4×10 m = 340 nm 8.7×10 s c λ υ = = ; and ( 29 ( 29 -34 -14 -1 -19 6.626×10 J s 8.7×10 s = 5.8×10 J E h ν = = Frequency (2 s.f.) Wavelength (2 s.f.) Energy of photon (2 s.f.) Event 8.7 × 10 14 Hz 340 nm 5.8 × 10 -19 J Suntan 5.0 × 10 14 Hz 600 nm 3.3 × 10 -19 J Reading 300 MHz 1 m 2 × 10 -25 J Microwave popcorn 1.2 × 10 17 Hz 2.5 nm 7.9 × 10 -17 J Dental X-ray
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1.13 (a) false. The total intensity is proportional to 4 . T (Stefan-Boltzmann Law) (b) true; (c) false. Photons of radio-frequency radiation are lower in energy than photons of ultraviolet radiation. 1.15 (a) Use the de Broglie relationship, 1 1 ( ) . hp h mv λ - - = = 28 31 e 3 1 1 6 1 (9.109 39 10 g) (1 kg/1000 g) 9.109 39 10 kg (3.6 10 km s ) (1000 m km ) 3.6 10 m s m - - - - - = = = 1 34 31 6 1 10 ( ) 6.626 08 10 J s (9.109 39 10 kg) (3.6 10 m s ) 2.0 10 m h mv λ - - - - - = = = (b) 34 16 1 17 (6.626 08 10 J s) (2.50 10 s ) 1.66 10 J E h ν - - - = = ״� = (c) The photon needs to contain enough energy to eject the electron from the surface as well as to cause it to move at 3 1 3.6 10 km s . - The energy involved is the kinetic energy of the electron, which equals 1 2 2 . mv
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17 2 photon 17 31 6 1 2 17 18 17 1 1.66 10 J 2 1 1.66 10 J (9.109 39 10 kg) (3.6 10 m s ) 2 1.66 10 J 5.9 10 J 2.25 10 J E mv - - - - - - - = + =2200 + 9 = + = But we are asked for the wavelength of the photon, which we can get from E hv = and c v λ = or 1 . E hc λ - = 17 2 2 34 2 1 8 1 1 9 2.25 10 (6.62608 10 ) (2.99792 10 ) 8.8 10 8.8 kg m s kg m s m s m nm λ λ - - - - - - - = � � � � = = (d) 8.6 nm is in the x-ray/gamma ray region.
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