Does this imply that every time a radioactive atom decays in the body a cancer results?
Or does it mean that once in a while such an event may cause a cancer?
The statement is meaningless without an estimate of the risk per event.
Let's consider the source of the nearly 8000 radioactive events that take place in our bodies every second.
In spite of the frequently stated phrases that "all radiation is harmful" and that "there is no safe dose of radiation", we humans contain, survive, and thrive with rather remarkable quantities of radioactive materials in our bodies.
This is not unexpected, for we do live on a somewhat radioactive planet.
How do these radioactive atoms get into our bodies? Potassium-40 is the most radioactive of the normal body radioelements, and enters the body within all the food we eat.
Potassium is an abundant element, is an essential constituent for plant growth, is found in most soils, and is thus incorporated in growing plants. The level of potassium in the body is maintained by a homeostatic process.
Since many of the radium daughters emit alpha particles, which can produce a lot of damage, this alpha energy is multiplied by a factor to account for this increased damage.
These include familiar isotopes that are found in the fallout from nuclear weapons, such as Cesium-137 and Strontium-90.
Other primordial radioelements may be present, such as Rn, is always present in the air we breath.
In actuality, most of the alpha particles never reach a sensitive tissue, such as a cell, and thus most of this energy is wasted.
Indeed, most of the times an alpha particle does hit a cell, it kills the cell, but dead cells don't give rise to malignancies.