zumdahl_chemprin_6e_csm_ch12 (1)

zumdahl_chemprin_6e_csm_ch12 (1) - CHAPTER 12 QUANTUM...

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455 CHAPTER 12 QUANTUM MECHANICS AND ATOMIC THEORY Light and Matter 21. m 10 0 . 1 s / m 10 00 . 3 λ c ν 2 8 × × = = = 3.0 × 10 10 s 1 E = h ν = 6.63 × 10 34 J s × 3.0 × 10 10 s 1 = 2.0 × 10 23 J/photon mol photons 10 02 . 6 photon J 10 0 . 2 23 23 × × = = 12 J/mol 22. The wavelength is the distance between consecutive wave peaks. Wave a shows 4 wave- lengths and wave b shows 8 wavelengths. Wave a : λ = 4 m 10 6 . 1 3 × = 4.0 × 10 4 m Wave b : λ = 8 m 10 6 . 1 3 × = 2.0 × 10 4 m Wave 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. m 10 0 . 2 m/s 10 00 . 3 λ c ν 4 8 × × = = = 1.5 × 10 12 s 1 m 10 0 . 2 m/s 10 00 . 3 s J 10 63 . 6 λ hc E 4 8 34 × × × × = = = 9.9 × 10 22 J 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.
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456 CHAPTER 12 QUANTUM MECHANICS AND ATOMIC THEORY 23. a. λ = 1 13 8 s 10 0 . 6 s / m 10 00 . 3 ν c × × = = 5.0 × 6 10 m b. From Figure 12.3, this is infrared EMR. c . E = h ν = 6.63 × 34 10 J s × 6.0 × 10 13 1 s = 4.0 × 20 10 J/photon mol photons 10 022 . 6 photon J 10 0 . 4 23 20 × × × = 2.4 × 10 4 J/mol d. Frequency and photon energy are directly related (E = hv). Because 5.4 × 10 13 1 s EMR has a lower frequency than 6.0 × 10 13 1 s EMR, the 5.4 × 10 13 1 s EMR will have less energetic photons. 24. nm 10 1 m 1 nm 25 s / m 10 00 . 3 s J 10 63 . 6 λ hc ν h E 9 8 34 × × × × × = = = = 8.0 × 10 18 J/photon mol photons 10 02 . 6 photon J 10 0 . 8 23 18 × × × = 4.8 × 10 6 J/mol 25. The energy needed to remove a single electron is: 23 10 0221 . 6 mol 1 mol kJ 7 . 279 × × = 4.645 × 10 22 kJ = 4.645 × 10 19 J J 10 645 . 4 s / m 10 9979 . 2 s J 10 6261 . 6 E hc λ , λ hc E 19 8 34 × × × × = = = = 4.277 × 10 7 m = 427.7 nm 26. Referencing Figure 12.3 of the text, 2.12 × 10 10 m electromagnetic radiation is X rays. 1 6 8 s 10 1 . 107 s / m 10 9979 . 2 ν c λ × × = = = 2.799 m From the wavelength calculated above, 107.1 MHz electromagnetic radiation is FM radio- waves. J 10 97 . 3 s / m 10 998 . 2 s J 10 626 . 6 E hc λ 19 8 34 × × × × = = = 5.00 × 10 7 m The 3.97 × 10 19 J/photon electromagnetic radiation is visible (green) light.
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CHAPTER 12 QUANTUM MECHANICS AND ATOMIC THEORY 457 The photon energy and frequency order will be the exact opposite of the wavelength ordering because E and ν are both inversely related to λ . From the previously calculated wavelengths, the order of photon energy and frequency is: FM radiowaves < visible (green) light < X rays longest λ s h o r t e s t λ lowest ν h i g h e s t ν s m a l l e s t E l a r g e s t E 27. The energy to remove a single electron is: 23 10 022 . 6 mol 1 mol kJ 4 . 208 × × = 3.461 × 10 22 kJ = 3.461 × 10 19 J = E w Energy of 254-nm light is: m 10 254 ) s / m 10 998 . 2 )( s J 10 626 . 6 ( λ hc E 9 8 34 × × × = = = 7.82 × 10 19 J E photon = E K + E w , E K = 7.82 × 10 19 J 3.461 × 10 19 J = 4.36 × 10 19 J = maximum KE 28.
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zumdahl_chemprin_6e_csm_ch12 (1) - CHAPTER 12 QUANTUM...

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