When a single photon (light particle) hits something, there’s an actual impact. That means if I shine a flashlight at you from behind, it (very gently) pushes you forwards. The more energy the photon has, the harder the impact.
It’s how your eyes work. The cells in your eyes wait for a specific impact strength that corresponds to red, green, or blue. Those, and most other photons you’ll see in your life, hit very softly, more like a tap.
Radiation, however, is photons that impact *way* harder than most photons. Less of a tap, and more of a speeding bullet. Getting irradiated is basically getting shot by a bunch of atom-sized bullets.
Now, imagine that your cells are like factories. What happens when a factory gets struck by tons of speeding bullets?
The damage is pretty random, and usually bad. Some things might get damaged a little but still be fixable, some might be beyond repair, and it’s possible the whole place needs to be scrapped.
Likewise, sometimes the damage is so extensive that the cell just dies. And if tons of cells around it meet the same fate, that part of the organ stops working correctly.
It’s likely that some cells either don’t get damaged at all, or can fix the damage. However, they might rely on other nearby cells for certain things. So they’ll become less effective at their jobs because they need things from nearby factories that have been shut down. Or if they do the same thing as some dead or damaged cells, they might suddenly find themselves inundated with orders, as their compatriots that would fill them are out of commission.
Meanwhile, sometimes the bullets hit only the anti-cancer mechanisms (those are well beyond ELI5), and the cell becomes cancerous. It’s actually pretty hard to damage a cell in exactly that way; however, with the number of cells that have to get damaged for the radiation poisoning to be noticeable, a few are bound to win the lottery that way.
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