How does the radioactivity of an atom affect the body?
You've asked a very broad question, so we'll have to split it up into smaller chunks in order to give you a reasonable answer. This is a topic that is very much misunderstood by most people and it's hard to give a short answer.
You may know that all of us have radioactive material in our bodies naturally. There has always been radioactive material on earth (in fact, a million years ago, there was more present than there is today), and people have therefore always been exposed to it. There has also always been cosmic radiation bathing our earth from outer space. I like to describe the earth as "a radioactive planet, floating in a sea of radiation." At first, this description may not sound very cozy, but it helps us keep in mind that radiation is a completely normal, natural component of our environment.
So, if radioactive material is everywhere (including in our bodies), it would seem that it might not have any effect on the body. And this is true. So, the first general answer to your question is: radioactive atoms can - and do - reside in the body with no discernible effect on us. And as for the effect of a single radioactive atom on the body, its effect would have to be called "infinitesimal." Our bodies are well adapted to having radioactivity as well as other potentially harmful things in them.
Now let's reword the question a little. "Can radioactive material affect the body?" The answer to this is, YES. As mentioned above, radiation is a "potentially harmful" agent. When radiation interacts with the tissue of our bodies, whether it is from radioactive atoms inside the body or from an external source such as an x-ray machine, it can cause damage to cells. This damage stems from the process of ionization. The radiation from radioactive atoms is called "ionizing radiation" because it causes ionization. Ionization is simply the "knocking off" of electrons from the atoms they are normally said to "orbit." These electrons act as the "glue" that holds atoms together in chemical bonds. So, if some of the electrons get knocked loose by ionizing radiation, some of the chemical bonds get broken. This can result in damage to the cells. Since there is radioactive material in our bodies, this process goes on all the time. But it is going on at a relatively low level. Again, our bodies are marvelously well adapted to repair this damage. There is even some evidence suggesting that because of the way our bodies have adapted to the ever-present radiation environment, we need a low level of radiation to keep certain body systems operating at their peak. But we also know that high levels of radiation can cause illness, injury or death. These effects have been the subject of many studies on the health effects of radiation exposure. Much has been learned about these effects over the years. In general, it is known that as the radiation dose to a person increases, the chances of an effect such as cancer are increased. At low levels, such as those associated with someone who works routinely with radiation (an x-ray technician at a hospital, for example), this chance is very small - in fact it's not measurably different than for someone who receives no radiation above "background" radiation. Limits on exposure have been established to keep the chances of a harmful effect to a minimum. People who work around radiation are educated about these effects and trained to use work practices that minimize their exposure - while understanding that low levels of exposure are unavoidable, in order to pursue these beneficial activities.
The scientific field of radiation protection is known as Health Physics. You can learn more about this field at the Health Physics Society website.
Keith Welch, Radialogical Controls Group (Other answers by Keith Welch)