Chapter 8: Q. 8.1 (page 208)
Why is the CaOH spectrum in Figure 8-8 so much broader than the sodium emission line shown in Figure 8-4?
The spectrum of CaOH is broader due to transitions between vibrational and rotational states, whereas shifts between electronic energy levels occur in sodium.
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In high-temperature sources, sodium atoms emit a doublet with an average wavelength of 1139 nm. The transition responsible is from the 4s to 3p state. Set up a spreadsheet to calculate the ratio of the number of excited atoms in the 4s state to the number in the ground 3s state over the temperature range from an acetylene-oxygen flame (3000ยฐC) to the hottest part of an inductively coupled plasma source 8750ยฐC).
In a study of line broadening mechanisms in low-pressure laser-induced plasmas, Gornushkina et al.10 present the following expression for the half width for Doppler broadening of an atomic line.
where is the wavelength at the center of the emission line, k is Boltzmannโs constant, T is the absolute temperature, M is the atomic mass, and c is the velocity of light. Ingle and Crouch11 present a similar
equation in terms of frequencies.
where is the Doppler half width and 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 4s4p transition for atomic nickel at 361.939 nm (3619.39 ร ) 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 .
(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 4p transition at 385.9911 nm (3859.911 ร ) 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 in nanometers for the nickel and iron lines cited in (b) and (e) from 3000โ10,000 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.
For Na atoms and Mg+ ions, compare the ratios of the number of atoms or ions in the 3p excited state to the number in the ground state in
(a) a natural gasโair flame (1800 K).
(b) a hydrogen-oxygen flame (2950 K).
(c) an inductively coupled plasma source (7250 K).
What determines natural line widths for atomic emission and absorption lines? About how broad are these widths, typically?
In the concentration range of 500 to 2000 ppm of U, there is a linear relationship between absorbance at 351.5 nm and concentration. At lower concentrations, the relationship is nonlinear unless about 2000 ppm of an alkali metal salt is introduced into the sample. Explain.
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