Prove Attenuation Length = Avg Photon Travel Distance

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    Attenuation Length
AI Thread Summary
The discussion focuses on proving that the attenuation length, denoted as Λ, equals the average distance a photon travels before being scattered or absorbed. The relevant equations include the number of photons absorbed and the expression for the intensity of photons after traveling a distance x. The attenuation length is defined as Λ = 1/(σρ), where σ is the cross-section and ρ is the density. A participant expresses initial uncertainty about how to approach the problem but later suggests an integral for calculating the average distance traveled by photons. The conversation highlights the relationship between attenuation length and photon travel distance in the context of scattering and absorption.
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Homework Statement



Show that the attenuation length, \Lambda, is just equal to the average distance a photon travels before being scattered or absorbed.

Homework Equations



my book gives:

number of photons absorbed = \sigma\rho I(x) dx

number of photons present after a thickness x = I(x)=I(0)e^{-\sigma \rho x}

attenuation length = \Lambda = \frac{1}{\sigma\rho}

The Attempt at a Solution



i'm really not sure where to go here... some idea on how to get started would be very much appreciated... thanks
 
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ok, nevermind, I think I got it...

x_{avg}=\int^{\infty}_{0}x \sigma \rho e^{\sigma \rho} dx

(i think)
 
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