Question

What happens to the atom(or an atom's identity) when an radioactive discharge happens?

Answer 1

The explanation is as follows.

What happens to atoms after they release radiation?!
As the nucleus emits radiation or disintegrates, the radioactive atom (radionuclide) transforms to a different nuclide. This process is called radioactive decay.
Now each particular type of radioactive discharge affects the atoms in a different way.
There are several types of radioactive decays like alpha decay, beta decay, gamma radiations etc. The detailed explanation of these may be beyond the scope for now.

Hope it answers your question.
All the best!