The radioactive substance is really the tricky bit. Everything is made up atomic particles whether living or dead but it's the effect of the radiation that can cause change sooooo if you have the cat and the poison in a sealed box with this radioactive material the radiation affects everything in it's sealed environment which includes keeping the cat alive and also causing it's death by shattering the glass bottle of poison. But due to the box being sealed the event going on inside means that the cat is both being kept alive and dead at the same time. This is the paradox we known shouldn't exist. As soon as you open the lid though you will not see this as your own interaction will cause the cat to be seen as either alive or dead.
Do I have to do your homework for you, AGAIN?
Yes. Lucy's love for him is unrequited.