The half-life of a radioactive atom refers to the time it takes for half of a sample of radioactive material to decay. It is important to note that the half-life is a statistical measure and does not depend on individual atoms.
The half-life of a radioactive atom can vary widely, ranging from fractions of a second to billions of years. The specific value depends on the particular radioactive isotope in question. Some isotopes have very short half-lives, while others have extremely long half-lives.
The reason why radioactive decay can happen relatively quickly, even though some isotopes have long half-lives, is due to the probabilistic nature of radioactive decay. Each radioactive atom has a probability of decaying within a given time interval, but the actual time at which an individual atom decays is unpredictable.
Consider a large sample of radioactive material containing a vast number of atoms. In a short period, such as seconds or minutes, some of the atoms will decay, emitting radiation. However, the rate of decay is proportional to the number of radioactive atoms present. As time progresses, more and more atoms will decay, leading to a decrease in the number of remaining radioactive atoms.
In the case of isotopes with long half-lives, the probability of any given atom decaying within a short time frame is relatively low. However, due to the immense number of atoms present in a sample, a significant fraction of atoms can still decay over longer periods. This is why we can observe radioactive decay occurring even though the half-life may be measured in billions of years.
It is important to remember that the half-life is an average characteristic of a large population of radioactive atoms. While individual atoms can decay quickly or slowly, the half-life provides a useful measure for understanding the overall decay behavior of a radioactive substance.