nuclear physics - How does an ordinary object become radioactive?

In the 2019 miniseries "Chernobyl", ordinary objects are depicted as being capable of becoming radioactive, such as clothes, water, stones.

How exactly does something composed of a non-radioactive mass, become radioactive?

I'm aware of the differences between alpha, beta, and gamma radiation, and I know how ionizing radiation works.

However, it isn't clear to me how any radiation, including ionizing radiation makes something radioactive in any long-lasting sense of the word.

I can imagine that ionizing radiation excites the atoms in the object, which makes the atom emit a photon until it becomes relaxed again. However, this doesn't sound like something that has a very long lasting effect?

I can also imagine that radioactive particles, such as those from U-235, may stick to clothes or contaminate water. However, this too seems not that plausible, is there really that much U-235 in a nuclear reactor for dust particles to be a considerable problem in this regard?

I'm not arguing that this isn't true, it simply isn't clear to me how the mechanism behind it works. I'm pretty sure this isn't clear to most non-physicists either.

Answer

There are three main effects:

The first, and simplest, is particulate contamination. The uranium fuel rods were pulverized in the explosion and so dust particles contaminated with uranium and other isotopes (fission products in the fuel rods) were scattered to the wind. Don't underestimate the amount of dust and smoke released. There were several tons of highly radioactive material in the core. That makes a lot of dust.

This is what produced the long-travelling dust cloud that triggered detectors in Minsk and Sweden and elsewhere. The dust can get on clothes and can be transferred by touch in the same way any contamination is spread. The problem for health is that each tiny dust particle contains trillions of radioactive atoms that are constantly decaying and emitting radiation. If you get some particles in your lungs, they will sit there radiating away into the surrounding tissues for many years. Not good.

The second effect is from immediate (prompt) gamma radiation from the core. This was what produced the light effect above the reactor and why Legasov wouldn't let the helicopter pilot fly over the core. This is mainly what killed the firemen and the shift crew. Here, you have basically a beam of radiation coming directly from the dense core and the immense rate of decay occurring there.

A third effect, is that the intense radiation (gammas and neutrons) can affect nuclei in stable atoms and activate them. That is, it converts the stable isotopes into radioactive isotopes, which will later decay. This is well-described in the other answers.