In a study of line broadening mechanisms in low-pressure laser-induced

Chapter 8, Problem 8-12

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In a study of line broadening mechanisms in low-pressure laser-induced plasmas,Gornushkina et aj9 present the following expression for the half width forDoppler broadening .lAD of an atomic line.where Ao is the wavelength at the center of the emission line, k is Boltzmann's constant,T is the absolute temperature, At is the atomic mass, and c is the velocity oflight. Ingle and Crouch 10 present a similar equation in terms of frequencies..lV = 2[2(ln2)kT]II2VmDAtewhere .lv" is the Doppler half width and Vm is the frequcncy at the line maximum.(a) Show that the two expressions are equivalent.(b) Calculate the half width in nanometers for Doppler broadening of the 45 ...4p transition for atomic nickel at 361.939 nm (3619.39 A) at a temperaturc of20,000 K in both wavelength and frequency units.(c) Estimate the natural line width for the transition in (b) assuming that the lifetimeof the excited state is 5 X 10'8 s.(d) The expression for the Doppler shift given in the chapter and in 8-8is an approximation that works at relatively low speeds. The relativisticexpression for the Doppler shift is~\j~Show that the relativistic exprcssion is consistent with the equation given inthe chapter for low atomic spceds.(c) Calculate the speed that an iron atom undergoing the 45 ... 4p transition at385.9911 nm (3859.911 A) would have if the resulting line appeared at the restwavelength for the same transition in nickel.(f) Compute the fraction of a sample of iron atoms at 10,000 K that would havethe velocity calculated in (e).(g) Create a spreadsheet to calculate the Doppler half width .lAD in nanometersfor the nickel and iron lines cited in (b) and (e) from 3000 -10,000 K.(h) Consult the paper by Gornushkin et al. (note 9) and list the four sources ofpressure broadening that they describe. Explain in detail how two of thesesources originate in sample atoms.