If radioactivity is so dangerous why do we use it to destroy cancers, and could the treatment cause more damage?
This question shows that you're really thinking and you've come across something that doesn't seem to make sense. As with most things that don't make sense, it's usually because one or more of our assumptions are wrong. In this case, you hit the nail on the head when you said, "If radioactivity is so dangerous...". But, you've really asked two questions here, so let me separate them and try to answer them both.
First, ionizing radiation - whether from radioactive material or produced by devices like x-ray machines - can be harmful. We know that radiation can damage or kill cells in our body. But, like damage done by many other things, when this damage occurs in small amounts spread out over a long time, our bodies are very good at repairing it, with very little chance of any long-term harm. A good example is the damage done by ultraviolet (UV) radiation from the sun. If you receive large doses of UV, you get a sunburn, and if you are exposed this way repeatedly, your chance of getting skin cancer will increase significantly. But, if you keep your exposure low (examples: use sunscreen, don't sunbathe, and wear a hat), your cancer risk will stay small. So, it's a matter of both how much dose, and how fast it is received. It works the same way with ionizing radiation. We all receive small doses of radiation all the time. There is natural radioactivity in the earth, in the air and water, and in our bodies. We receive cosmic radiation from space. We call this background radiation. When doctors treat cancer with radiation, they use very large doses - thousands of times higher than background radiation - and it's received in a short period of time (think of the sunburn example). BUT, here's the twist. Just as you were thinking, very large doses might injure or kill the patient. So, the dose is "focused" on the cancer tumor. The idea is to kill the tumor cells, and try to keep the dose to the rest of the body reasonably low.
Now, for the second question. When a cancer patient is treated with radiation, there is always some dose received by parts of the body that are healthy. Many improvements have been made in the ability to reduce this dose. But, because of the very high doses, location of tumors, and the penetrating nature of the radiation, it's just not possible to completely eliminate this dose. So, the answer to your question is yes, there is some "collateral damage" done by the radiation treatments. And this damage has some risks associated with it. But, as with any medical procedure or treatment, the benefits and risks must be "weighed". When a doctor prescribes radiation treatment for cancer, it is because the disease is serious, and without the treatment, the patient's outlook for recovery is not good. When a patient receives the radiation treatment, the potential benefits of the treatment greatly outweigh the risk involved from the radiation exposure. This same reasoning is used whenever you get a diagnostic x-ray. Here, the doses are much, much lower; but often, the information obtained by taking the x-ray can help save a life.
You can find more information about radiation in medicine at the American College of Radiology, and radiation facts at the Radiation and Health Physics website, or the Health Physics Society website.
And most of all, trust me on the sunscreen...
Keith Welch, Radialogical Controls Group (Other answers by Keith Welch)