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FIU CHM 4130 - Key_for Chapter_ 7

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CHAPTER 7 7-1. Equation 7-17 can be written w = Δλeff/D–1. For a prism monochromator the linear dispersion D decreases continuously with increasing wavelength. The reciprocal linear dispersion D–1 thus increases as the wavelength becomes longer. Hence, if Δλeff is to remain constant, w, the slit width, must be decreased accordingly. For a grating instrument, D–1 is essentially constant over a considerable wavelength range. Thus, w does not need to be varied with a grating monochromator. 7-2. For qualitative analysis, it is important to resolve as many absorption bands as possible for identification purposes. This consideration often means that slit widths should be as narrow as possible. On the other hand, for quantitative methods, better signal-to-noise ratios, and hence higher precision, can be obtained with wider slit widths. 7-3. !!!!7-6. Spontaneous emission occurs when a species loses all or part of its excess energy in the form of fluorescence or phosphorescence radiation. Because the process is random and can occur in any direction, the radiation is incoherent. Stimulated emission is brought about by interaction of excited species with externally produced photons that have energies exactly matching the energy of a transition. The photons produced are in phase with those stimulating the emission, and coherent radiation is the result. 7-7. A four-level laser system has the advantage that population inversion is achieved more easily than with a three-level system. In a four-level system, it is only necessary to maintain a number of excited species that exceeds the number in an intermediate energy level that is higher in energy than the ground state. If the lifetime of the intermediate state is brief, a relatively few excited species is required for population inversion. 7-8. The effective bandwidth of a filter is the width in wavelength units of the band transmitted by the filter when measured at one-half the peak height. ! Skoog/Holler/Crouch Chapter 7Principles of Instrumental Analysis, 6th ed. Instructor’s Manual 1 CHAPTER 7 7-1. Equation 7-17 can be written w = 'Oeff/D–1. For a prism monochromator the linear dispersion D decreases continuously with increasing wavelength. The reciprocal linear dispersion D–1 thus increases as the wavelength becomes longer. Hence, if 'Oeff is to remain constant, w, the slit width, must be decreased accordingly. For a grating instrument, D–1 is essentially constant over a considerable wavelength range. Thus, w does not need to be varied with a grating monochromator. 7-2. For qualitative analysis, it is important to resolve as many absorption bands as possible for identification purposes. This consideration often means that slit widths should be as narrow as possible. On the other hand, for quantitative methods, better signal-to-noise ratios, and hence higher precision, can be obtained with wider slit widths. 7-3. (a) Omax = 2.90 u 103/T = 2.90 u 103/5000 K = 0.58 Pm or 580 nm (b) Omax = 2.90 u 103/3000 K = 0.967 Pm or 967 nm (c) Omax = 2.90 u 103/1500 K = 1.93 Pm 7-4. (a) Et = DT4 = 5.69 u 10–8 W m-2 K–4 u (5000 K)4 = 3.56 u 107 W m–2 (b) Et = 5.69 u 10–8 W m-2 K–4 u (3000 K)4 =4.61 u 106 W m–2 (c) Et = 5.69 u 10–8 W m-2 K–4 u (1500 K)4 = 2.88 u 105 W m–2 7-5. (a) Omax = 2.90 u 103/T =2.90 u 103/2870 = 1.01 Pm or 1010 nm Omax = 2.90 u 103/3500 = 0.829 Pm or 829 nm (b) Et = 5.69 u 10–8 W m-2 K–4 u (2870 K)4 = 3.86 u 106 W m–2 u 10–4 m2/cm2 = 3.86 u 102 W cm–27-10.!!!!7-12. !!7-13. ! Principles of Instrumental Analysis, 6th ed. Chapter 7 37-10. From Equation 7-5, d = On/2n. If first-order interference is used, one end of the wedge would have a thinckness d of d = 700 nm u 1/(2 u 1.32) = 265 nm or 0.265 Pm. This thickness would also transmit second-order radiation of 700/2 = 350 nm, which would be absorbed by the glass plates supporting the wedge. The other end of the wedge should have a thickness of d = 400 u 1/(2 u 1.32) = 1.52 nm or 0.152 Pm Thus, a layer should be deposited with is 0.265 Pm on one end and which tapers linearly over 10.0 cm to 0.152 Pm at the other end. 7-11. The dispersion of glass for visible radiation is considerably greater than that for fused silica or quartz (see Figure 6-9). 7-12. nO = d (sin i + sin r) (Equation 7-6) d = nO/(sin i + sin r) = 1 u 400 nm/(sin 45 + sin 5) = 400 nm/(0.707 + 0.087) = 503.7 nm lines/mm = 61 line nm 10 = 1985503.7 nm mmu 7-13. For first-order diffraction, Equation 7-13 takes the form O/'O = nN = 1 u 15.0 mm u 84.0 lines/mm = 1260 In order to obtain the resolution in units of cm–1, we differentiate the equation O = 1/Q 2211 = or = ddOOQQQ''Q Thus, 'O = 2/QQ' Substituting for O and 'O in the first equation gives Principles of Instrumental Analysis, 6th ed. Chapter 7 37-10. From Equation 7-5, d = On/2n. If first-order interference is used, one end of the wedge would have a thinckness d of d = 700 nm u 1/(2 u 1.32) = 265 nm or 0.265 Pm. This thickness would also transmit second-order radiation of 700/2 = 350 nm, which would be absorbed by the glass plates supporting the wedge. The other end of the wedge should have a thickness of d = 400 u 1/(2 u 1.32) = 1.52 nm or 0.152 Pm Thus, a layer should be deposited with is 0.265 Pm on one end and which tapers linearly over 10.0 cm to 0.152 Pm at the other end. 7-11. The dispersion of glass for visible radiation is considerably greater than that for fused silica or quartz (see Figure 6-9). 7-12. nO = d (sin i + sin r) (Equation 7-6) d = nO/(sin i + sin r) = 1 u 400 nm/(sin 45 + sin 5) = 400 nm/(0.707 + 0.087) = 503.7 nm lines/mm = 61 line nm 10 = 1985503.7 nm mmu 7-13. For first-order diffraction, Equation 7-13 takes the form O/'O = nN = 1 u 15.0 mm u 84.0 lines/mm = 1260 In order to obtain the resolution in units of cm–1, we differentiate the equation O = 1/Q 2211 = or = ddOOQQQ''Q Thus, 'O = 2/QQ' Substituting for O and 'O in the first equation gives Principles of Instrumental Analysis, 6th ed. Chapter 7 37-10. From Equation 7-5, d = On/2n. If first-order interference is used, one end of the wedge would have a thinckness d of d = 700 nm u 1/(2 u 1.32) = 265 nm or 0.265 Pm. This thickness would also transmit second-order radiation of 700/2 = 350 nm, which would be absorbed by the glass plates supporting the wedge. The other end of the wedge should have a thickness


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