Radiation causes damage to DNA, particularly the DNA of a cell that is actively dividing (since the DNA strand “unzips” into two separate strands as it’s being copied).
This can cause cancer because it can damage the parts of DNA that are responsible for repairing and regulating the whole DNA strand. (Imagine a computer with a bunch of information, including a section on how to recover lost data.) That’s why radiation is dangerous in the first place.
However, cancer cells have two traits that make them especially vulnerable to this effect:
* They multiply much more often than normal cells, which means they’re duplicating their DNA much more often.
* They almost always have already lost the ability to repair their DNA effectively (because that’s how they became cancerous in the first place).
As a result, radiation therapy damages cancer cells much more than it damages normal cells. The hope is that it damages the cancer cells to the point of death before it triggers a new cancerous mutation in healthy cells. It usually does, but not always, and secondary cancers do happen sometimes (but, well, you already had cancer in the first place).
EDIT: As others note, radiation therapy is also targeted – the goal is to expose the cancer to it and not healthy cells. But that targeting isn’t perfect, and it does expose healthy cells to some extent too.
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