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Calculate the half width in nanometers for Doppler broadening of the 4s to 4p transition for atomic Nickel at 361.939 nm at a temperature of 20.000 K in both wavelength and frequency units.

Calculate the half width in nanometers for Doppler broadening of the 4s to 4p transition for atomic Nickel at 361.939 nm at a temperature of 20.000 K in both wavelength and frequency units.

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Calculate the half width in nanometers for Doppler broadening of the 4s to 4p transition for atomic Nickel at 361.939 nm at a temperature of 20.000 K in both wavelength and frequency units.

8-12 In a study of line broadening mechanisms in low-pressure laser-induced plasmas, Gornushkina et al." present the following expression for the half width for Doppler broadening AAp of an atomic line. SkT In 2 Aao(T) = AoV Me where A, is the wavelength at the center of the emission line, k is Boltzmann's constant, Tis 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]1/² vm Avp = 2 M where Av, is the Doppler half width and v, 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
Transcribed Image Text:8-12 In a study of line broadening mechanisms in low-pressure laser-induced plasmas, Gornushkina et al." present the following expression for the half width for Doppler broadening AAp of an atomic line. SkT In 2 Aao(T) = AoV Me where A, is the wavelength at the center of the emission line, k is Boltzmann's constant, Tis 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]1/² vm Avp = 2 M where Av, is the Doppler half width and v, 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
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