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I would like your assistance with wrapping up my thoughts regarding the following problem.

Say I have Am-241 nuclide, which emits alpha particle in every decay (for the sake of this discussion, lets assume that 100% of the decays lead to a daughter nuclide, Np-237 + an alpha particle). Lets consider the following setups (see picture below):

On the left hand side, I have a rod (a side view), with a certain thickness, with Am-241 atoms (represented by the red hollow circles) attached to one side of it.

On the right hand side, I have a solid cylinder (a cross section), with Am-241 atoms evenly distributed along the entire volume & surface of the cylinder.

Now, If I would like to calculate the desorption probability of Np-237 (meaning, the probability for Np-237 release from the rod/cylinder into the air, for each decay of Am-241), the left case it is quite straight forward, as there's 50% chance that the Np-237 atom will recoil out of the rod and 50% chance that the Np-237 atom will recoil into the rod (lets say that the Np-237's energy isn't high enough to pass through the rod's thickness and leave it on the other side).

How would I calculate the desorption probability of Np-237 on the second case? Basically, the atoms on the cylinder's surface also have a 50% percent chance to leave the surface, but what about the atoms confined within the volume? How can I mathematically describe the probabilities there?

Would appreciate your assistance :)

Thanks!