One-half of the nuclei of a given radioisotope decays during one half-life. Why doesn't the remaining half decay during the next halflife?

The half-life of a radioisotope is the time it takes for half of its unstable nuclei to decay. This means that if we start with a certain mass of the isotope, after one half-life, its mass would have reduced by half. Keep in mind that the decay is a random process and follows an exponential decay pattern.

Radioactive decay is a statistical process because the decay of any particular nucleus is purely random. However, when we observe a large number of nuclei, we can see a pattern of decay. This pattern follows the exponential decay law.

The number of radioactive nuclei present affects the rate of decay. According to the decay law, the decay rate is proportional to the number of radioactive nuclei present. Mathematically, it can be represented as: dN/dt = -λN Where dN/dt is the decay rate, λ is the decay constant, and N is the number of radioactive nuclei.

Since the decay rate depends on the number of radioactive nuclei present, as the number of radioactive nuclei decreases, the rate of decay also decreases. This means that during the next half-life, the remaining undecayed nuclei will decay at a slower rate than the initial nuclei. After one half-life, half of the initial nuclei would have decayed, and the remaining half will decay slower due to the reduced number of radioactive nuclei. After the second half-life, only half of the remaining radioactive nuclei from the first half-life would have decayed, leaving 25% of the initial nuclei undecayed. This process continues for multiple half-lives, leading to a continuous decrease in the number of undecayed nuclei. In conclusion, the remaining half of a radioisotope's nuclei do not decay during the next half-life because the rate of decay is proportional to the number of radioactive nuclei present, and as the number of radioactive nuclei decreases, the rate of decay decreases as well. This process results in a continuous decrease in the number of undecayed nuclei with each half-life.