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chp12hwsolCOMPLETE

chp12hwsolCOMPLETE - CHAPTER 12 QUANTUM MECHANICS AND...

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CHAPTER 12 QUANTUMMECHANICS AND ATOMIC THEORY Light and Matter 21. v = ~ = 3.00 X 10 8 mls = 3.0 x 10 10 s' A 1.0 X 10- 2 m E = hv = 6.63 X 10- 34 J s x 3.0 X 10 10 S-1 = 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 Wave b: A = 1.6 X 10- m = 2.0 x 10-4 m 8 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. 8 v = ~ = 3.00 X 10 m/s = 1.5 X 10\2 S-l A 2.0 X 10- 4 m E = hc = 6.63 X 10- 34 J s x 3.00 X 10 8 m/s = 9.9 x 10- 22 J A 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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456 CHAPTER 12 QUANTUM MECHANICS AND ATOMIC THEORY 8 a. A = ~ = 3.00 x 10 mls = 5.0 x 10- 6 m 23. V 6.0 X 10 13 S-1 b. From Figure 12.3, this is infrared EMR. c. E = hv = 6.63 x 10- 34 J s x 6.0 x 10 13 S -1 = 4.0 x 10-- 20 J/photon 20 23 4.0 X 10- J x 6.022 X 10 photons = 2.4 x 10 4 J/mol photon mol lO l3 d. Frequency and photon energy are directly related (E = hv). Because 5.4 x S·I EMR has a lower frequency than 6.0 x 10 13 S-I EMR, the 5.4 x 10 13 s -1 EMR will have less energetic photons. 34 8 E = hv = hc = 6.63 X 10- J s x 3.00 X 10 mls = 8.0 x 10,18 J/photon 1m A. 25 nm x ~~---c;-- 1 X 10 9 nm 23 8.0 X 10- 18 J x 6.02 x 10 photons = 4.8 x 10 6 llmol photon mol 25. The energy needed to remove a single electron is: 279.7 kJ x 1 mol = 4.645 x 10- 22 kl = 4.645 x 10- 19 J 10 23 mol 6.0221 x 34 8 E = hc A. = hc = 6.6261 X 10- 1 s x 2.9979 X 10 mls == 4.277 x 10- 7 m == 427.7 nm A 'E 4.645 X 10,19 J 26. Referencing Figure 12.3 of the text, 2.12 x 10- 10 m electromagnetic radiation is X rays. 8 A = ~ = 2.9979 X 10 mls = 2.799 m v 107.1 x 10 6 S-1 From the wavelength calculated above, 107.1 MHz electromagnetic radiation is FM radio- waves. he 6.626 X 10- 34 J s x 2.998 X 10 8 mls A = - = = 5.00 x 10. 7 m E 3.97 x 10- 19 J The 3.97 x 10,19 J/photon electromagnetic radiation is visible (green) light.
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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 smallest E largest E e The energy to remove a single electron is: 208.4kJ x Imol =3.461 x 10- 22 kJ = 3.461 x 10- 19 J=E mol 6.022 x 10 23 w Energy of254-nm light is: hc 34 8 (6.626 X 10- J s)(2.998 X 10 m/s) = 7.82 x 10- 19 J E = A 254 X 10- 9 m Epholon = E K + E w , E K = 7.82 x 10- 19 J - 3.461 x 10- 19 J = 4.36 x 10- 19 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.
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