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(d) The expression for the Doppler shift given in the chapter and in Problem 8-8 is an approximation that works at relatively low speeds. The relativistic expression for the Doppler shift is   Show that the relativistic expression is consistent with the equation given in the chapter for low atomic speeds. (e) Calculate the speed that an iron atom undergoing the 4s S 4p transition at 385.9911 nm (3859.911 Å) would have if the resulting line appeared at the rest wavelength for the same transition in nickel. (f) Compute the fraction of a sample of iron atoms at 10,000 K that would have the velocity calculated in (e).

(d) The expression for the Doppler shift given in the chapter and in Problem 8-8 is an approximation that works at relatively low speeds. The relativistic expression for the Doppler shift is   Show that the relativistic expression is consistent with the equation given in the chapter for low atomic speeds. (e) Calculate the speed that an iron atom undergoing the 4s S 4p transition at 385.9911 nm (3859.911 Å) would have if the resulting line appeared at the rest wavelength for the same transition in nickel. (f) Compute the fraction of a sample of iron atoms at 10,000 K that would have the velocity calculated in (e).

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(d) The expression for the Doppler shift given in the chapter and in Problem 8-8 is an approximation that works at relatively low speeds. The relativistic expression for the Doppler shift is  

Show that the relativistic expression is consistent with the equation given in the chapter for low atomic speeds.
(e) Calculate the speed that an iron atom undergoing the 4s S 4p transition at 385.9911 nm (3859.911 Å) would have if the resulting line appeared at the rest wavelength for the same transition in nickel.
(f) Compute the fraction of a sample of iron atoms at 10,000 K that would have the velocity calculated in (e).
(g) Create a spreadsheet to calculate the Doppler half width DlD in nanometers for the nickel and iron lines cited in (b) and (e) from 3000–10,000 K.
(h) Consult the paper by Gornushkin et al. (note 10) and list the four sources of pressure broadening that
they describe. Explain in detail how two of these sources originate in sample atoms.

Challenge Problem 9-23 (a) In an investigation of the influence of experimental variables on detection limits in electrothermal AAS, Cabon and Bihan found several factors to be significant in the optimization of the method." List six of these factors, describe in detail the physical basis for each factor, and discuss why each is important. (b) These workers describe an a priori method for determining the limit of detection (LOD). Compare and contrast this method with the method described in Section 1E-2. How does this method improve on the method as defined by the International Union of Pure and Applied Chemistry (IUPAC) in the "Orange Book"? See http://www.iupac.org/publications/analytical_compendium/. Describe any disadvantages of the method. (c) The investigations described by Cabon and Bihan treated the data using least-squares polynomial smoothing (see Section 5C-2) prior to determining the LOD. Describe precisely how the data were smoothed. What experimental variable was optimized in the smoothing procedure? How was the width of the smoothing window defined? What effect, if any, did the smoothing procedure have on the LOD as determined by these workers? What effect did smoothing have on the determination of the integration window for the instrumental signal? (d) These workers compared the determination of the signal magnitude by integration and by measuring peak signals. What was the outcome of this comparison? Explain why these results were obtained by using your understanding of signal-to-noise enhancement procedures. (e) How were instrument signals integrated? What alternative numerical procedures are available for integrating digital signals? What procedural variable or variables influenced the quality of the integrated signal data? Describe the effect of signal integration on working curves for Pb. (f) What is dosing volume, and what effect did it appear to have on the quality of the results in these procedures? "1. Y. Cabon and A. Le Bihan, Analyst, 1997, 122, 1335, DOI: 10.1039/a701308f.
Transcribed Image Text:Challenge Problem 9-23 (a) In an investigation of the influence of experimental variables on detection limits in electrothermal AAS, Cabon and Bihan found several factors to be significant in the optimization of the method." List six of these factors, describe in detail the physical basis for each factor, and discuss why each is important. (b) These workers describe an a priori method for determining the limit of detection (LOD). Compare and contrast this method with the method described in Section 1E-2. How does this method improve on the method as defined by the International Union of Pure and Applied Chemistry (IUPAC) in the "Orange Book"? See http://www.iupac.org/publications/analytical_compendium/. Describe any disadvantages of the method. (c) The investigations described by Cabon and Bihan treated the data using least-squares polynomial smoothing (see Section 5C-2) prior to determining the LOD. Describe precisely how the data were smoothed. What experimental variable was optimized in the smoothing procedure? How was the width of the smoothing window defined? What effect, if any, did the smoothing procedure have on the LOD as determined by these workers? What effect did smoothing have on the determination of the integration window for the instrumental signal? (d) These workers compared the determination of the signal magnitude by integration and by measuring peak signals. What was the outcome of this comparison? Explain why these results were obtained by using your understanding of signal-to-noise enhancement procedures. (e) How were instrument signals integrated? What alternative numerical procedures are available for integrating digital signals? What procedural variable or variables influenced the quality of the integrated signal data? Describe the effect of signal integration on working curves for Pb. (f) What is dosing volume, and what effect did it appear to have on the quality of the results in these procedures? "1. Y. Cabon and A. Le Bihan, Analyst, 1997, 122, 1335, DOI: 10.1039/a701308f.
where A, is the wavelength at the center of the emission line, k is Boltzmann's constant, T is the absolute temperature, Mis the atomic mass, and c is the velocity of light. Ingle and Crouch" present a similar equation in terms of frequencies. [ 2(In 2)kT]1² vm Avp = 2 M where Av, is the Doppler half width and vm is the frequency at the line maximum. (a) Show that the two expressions are equivalent. (b) Calculate the half width in nanometers for Doppler broadening of the 4s → 4p transition for atomic nickel at 361.939 nm (3619.39 Å) at a temperature of 20,000 K in both wavelength and frequency units. (c) Estimate the natural line width for the transition in (b) assuming that the lifetime of the excited state is 5 x 10-"s. (d) The expression for the Doppler shift given in the chapter and in Problem 8-8 is an approximation that works at relatively low speeds. The relativistic expression for the Doppler shift is AA Show that the relativistic expression is consistent with the equation given in the chapter for low atomic speeds. (e) Calculate the speed that an iron atom undergoing the 4s –→ 4p transition at 385.9911 nm (3859.911 Â) would have if the resulting line appeared at the rest wavelength for the same transition in nickel. (f) Compute the fraction of a sample of iron atoms at 10,000 K that would have the velocity calculated in (e). (9) Create a spreadsheet to calculate the Doppler half width A^, in nanometers for the nickel and iron lines cited in (b) and (e) from 3000–10,000 K. (h) Consult the paper by Gornushkin et al. (note 10) and list the four sources of pressure broadening that they describe. Explain in detail how two of these sources originate in sample atoms.
Transcribed Image Text:where A, is the wavelength at the center of the emission line, k is Boltzmann's constant, T is the absolute temperature, Mis the atomic mass, and c is the velocity of light. Ingle and Crouch" present a similar equation in terms of frequencies. [ 2(In 2)kT]1² vm Avp = 2 M where Av, is the Doppler half width and vm is the frequency at the line maximum. (a) Show that the two expressions are equivalent. (b) Calculate the half width in nanometers for Doppler broadening of the 4s → 4p transition for atomic nickel at 361.939 nm (3619.39 Å) at a temperature of 20,000 K in both wavelength and frequency units. (c) Estimate the natural line width for the transition in (b) assuming that the lifetime of the excited state is 5 x 10-"s. (d) The expression for the Doppler shift given in the chapter and in Problem 8-8 is an approximation that works at relatively low speeds. The relativistic expression for the Doppler shift is AA Show that the relativistic expression is consistent with the equation given in the chapter for low atomic speeds. (e) Calculate the speed that an iron atom undergoing the 4s –→ 4p transition at 385.9911 nm (3859.911 Â) would have if the resulting line appeared at the rest wavelength for the same transition in nickel. (f) Compute the fraction of a sample of iron atoms at 10,000 K that would have the velocity calculated in (e). (9) Create a spreadsheet to calculate the Doppler half width A^, in nanometers for the nickel and iron lines cited in (b) and (e) from 3000–10,000 K. (h) Consult the paper by Gornushkin et al. (note 10) and list the four sources of pressure broadening that they describe. Explain in detail how two of these sources originate in sample atoms.
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