The rule is that a sample is safe when its radioactivity has dropped below detection limits. So, if radioactive iodine-131 (which has a half-life of 8 days) is injected into the body to treat thyroid cancer, it’ll be “gone” in 10 half-lives, or 80 days.
The great scientist Ernest Rutherford was the first to define the concept of “half-life,” that is, the time it takes for one half of the atoms in a given quantity of a radioactive element (such as plutonium) to decay into another element (such as uranium), or for one isotope of an element (such as carbon-14) to decay into another isotope of that same element (such as carbon-12).
It might take a millisecond, or it might take a century. But if you have a large enough sample, a pattern begins to emerge.
It takes a certain amount of time for half the atoms in a sample to decay.
reported that, “when researchers suggested in August  that the sun causes variations in the decay rates of isotopes of silicon, chlorine, radium and manganese, the physics community reacted with curiosity, but mostly with skepticism” (Ibid.).
Despite this skepticism, there is proof that this is true.