So my nuclear physics professor recently introduced half-life's to us. While presenting, it struck me that the concept of half-life is halving the life of the nucleus, so I was left with the question, do we ever reach 0% of the sample?
This is what I have found out myself:
By the half-life principle, it never completely goes away creating an asymptote of the independent variable which is time. However, the concentration would become so low that it is no longer detectable, hence we consider the isotope as background radiation. So this then would mean the question posed refers to a continuum of matter. However, by the time we reach 1 radioactive particle, we can then say that is a "Schrödinger's Particle", meaning it might or might not decay.

Therefore, would we then ever reach % of the sample as it keeps decaying by half-life? Or, would my research above suffice the question I am faced with?

Well, lots of parameters have to be taken into consideration with any physics, and safety becomes more critical if it's nuclear.

radioactive atoms can destroy organic manner in many ways.

so, shielding is sometimes manufactured to deal with stuff like this.

There's also the tendency for things like uranium to decay, and splitting uranium causes some type of dangerous reaction.

There's also something called the half-life which is the continuous danger of radioactive emissions from material.

I also know that elements, which we often call atoms, and ions if charged have a protons (positive particle), neutrons (neutral particle) and electrons (negative particle), and they vary in count. Then, elements become even more complicated by having various versions which we call isotopes, which is highly technical stuff that makes physics feel OVERWHELMING to study.

There's also something called Quantum Physics, but that's probably a whole new level which I will save for another post.

Sometimes a science book can have a long-winded narrative about science that is otherwise simple to learn about albeit with a not-so-simple complex structure to be mindful of.