So it is out of your body the very instant it is produced. The interesting bit is whether it strikes something on the way out.
Energy is not a constant. As explained previously, an atom functions on the level of chemistry all the time, but releases radiation once, in an instant during decay. So but for all except an single instant in say 30 years, the individual atom is radiologically inert.
Now as hard as it is to believe, on the atomic scale, your body is only very slightly different than empty space. The chances of gamma ray hitting something are quite low. Because alpha particles are a bit bigger, the chances they will hit something are larger.
An atom of cesium is toxic to one molecule of something in your body. Odds are +/- 100% that you have at least one of every type of atom in your body somewhere. In that 137 grams (roughly 0.25 pounds) of cesium 137 contains 6.022 * 10^22 atoms and in that most of the atoms composing your body are lighter than cesium, your body probably contains something between 1 * 10^25 to 1*10^26 atoms (bunches and bunches). When you look through that many atoms, pretty much everything is going to be there every time.
While the chances of hitting something are quite low, even lower are the chances of hitting something that matters. Much of your body is water and hitting a water molecule might ionize it, but a considerable portion of the water in your body is ionized all the time (which is why it has a pH). Ionizing an additional molecule would not be detectable.
If it happens instead to hit a bit of DNA or RNA, depending on where, a cancer could arise. Most defects in DNA will kill the cell, but some cause cancer. This is a very low probability event, but given exposure to enough radiation, it will happen.
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