Eli5: Why do objects exposed to radiation become radioactive?

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So if radiation is either particles or waves coming from a unstable nucleus, surely things that go near them also wouldn’t become radioactive if they have a stable nucleus? What makes it unstable?

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They are stable in their current state if the particles strike the nucleus they can add to that nucleus and become a different stable or unstable element. They can also break that stable nucleus into other stable and unstable elements. Depending on how fast they are going.

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