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Dassinia
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Hello
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 ?
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
Homework Statement
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 ?
Homework Equations
The Attempt at a Solution
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
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