Understanding Attenuation Lengths for Radioactive Materials in Hollow Spheres

[Marioqwe]

Hello, I am reading this article in wikipedia http://en.wikipedia.org/wiki/Attenuation_length about attenuation lengths and there is something I'm hoping someone here can explain to me.

Lets say I have one small solid sphere and one big hollow sphere. And let's say I put the small sphere within the hollow part of the big one.
Now, somehow the small sphere is radioactive and it emits gamma rays. The big sphere is made of a different material (not radioactive). Also, let's say I have solved the equation in the wiki article for the length L = -λln(rand(0,1)). Then, I solve for L using λ for the radioactive material. But what happens if this L happens to be big enough to exit the first material and it goes into the second one. Would I have to calculate L again using λ for the non-radioactive material?

 

[mfb]

You want to calculate a random length L (for a single particle) for the flight distance to the point of absorption? In this case, if both materials are equal, just add the lengths in the materials. Alternatively, if L is longer than the flight distance in the inner object, do the same calculation again for the outer object, with a new L' for the length in this material only.

 

[Marioqwe]

You want to calculate a random length L (for a single particle) for the flight distance to the point of absorption?

Exactly.

In this case, if both materials are equal, just add the lengths in the materials. Alternatively, if L is longer than the flight distance in the inner object, do the same calculation again for the outer object, with a new L' for the length in this material only.

Thank you.