Prove Attenuation Length = Avg Photon Travel Distance

[strangequark]

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

 

[strangequark]

ok, nevermind, I think I got it...

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

(i think)