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Introductory Physics Homework Help
Spectral Analysis of Gas Atoms: Temperature Calculation
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[QUOTE="Dassinia, post: 4585383, member: 487299"] Hello [h2]Homework Statement [/h2] A gas of atoms, each of mass m, is maintained in a box at temperature T. The atoms emit light which passes (in the x-direction) through a window in the box and can be observed as a spectral line in a spectroscope. A stationary atom would emit light at the sharply de¯ned frequency vo. But because of the Doppler effect the frequency of the light emitted from an atom with horizontal velocity vx is not simply vo but rather v=vo(1+vx/c) Calculate the relative intensity distribution I(Δ) of the light measured in the spectroscope. The spectrum of a gas atom elitting at 638, nm follows a gauss distribution with σ=1.5 GHz What is the gas temperature ? [h2]Homework Equations[/h2] [h2]The Attempt at a Solution[/h2] So we have G(K)=Go exp(-(K-Ko)²/(2σ²)) Go a constant and σ=Ko*√(k*T/(mc²)) So I have to calculate I(Δ) = 1/2 ∫ Go exp(-(K-Ko)²/(2σ²)) * cos(KΔ) dK from 0 to infinity The result is given and we're supposed to find that I(Δ) = Io cos(Ko Δ) exp (-1/2 (σΔ)²) I tried integration by parts but I can't get to the result .. b/ T=σ²*m*c²/(Ko²*k) k=1/lambda and Ko=2pi*vo=2pic/lambda Replacing we obtain the temperature in fuction of the mass tHANKS [/QUOTE]
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Spectral Analysis of Gas Atoms: Temperature Calculation
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