Consequences to a medium after ionising radiation has passed through?

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So I fully understand how alpha and beta can ionise different media. I also get why they can penetrate different media, but, what are the consequences (changes), if at all, to the media if after "absorption" or "penetration"

a) What happens to a medium after radiation has passed through it?

e.g. if a beta particle penetrates a sheet of paper does it ionise the paper at all on the way through? Can a beta particle ionise an atom in a sheet of paper and have enough energy to pass through as well?

b) What happens to a medium if the radiation is "absorbed"?

Does this word "absorbed" simply mean:

1) the particle no longer has enough KE to be ionising due to collisions with the medium and it has not done any ionising in that medium

2) the particle no longer has enough KE to be ionising due to collisions with the medium but it might have done some ionising in that medium (we don't know)

3) the particle no longer has enough KE to be ionising due to collisions with the medium due to ionising atom(s) in that medium.

I hope these questions make sense, many thanks.
 
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what are the consequences (changes), if at all, to the media if after "absorption" or "penetration"
Depends on the material and the radiation. You can get chemical reactions, you can disturb the lattice of solid materials, and so on.

e.g. if a beta particle penetrates a sheet of paper does it ionise the paper at all on the way through?
It does, and the corresponding energy loss can be described with the Bethe-formula.
Can a beta particle ionise an atom in a sheet of paper and have enough energy to pass through as well?
If the sheet is not too thick and/or the energy is sufficient, sure.

Does this word "absorbed" simply mean:
Usually the third for alpha and beta radiation. Other energy losses are possible, as well.