Final answer:
The active decay stage is determined by the half-life of a radioactive isotope, and it indicates how quickly it decays into a stable form. For Carbon-14, the half-life is 5,730 years, while for Rubidium-87, it is approximately 48.8 billion years. The half-life varies significantly between different isotopes.
Step-by-step explanation:
The term 'active decay stage' generally refers to the period in which a radioactive isotope is decaying at a significant rate, measurable by its half-life. According to the provided information, the half-life of Carbon-14 (14C) is 5,730 years. It means that after 5,730 years, half of the original number of 14C atoms in a sample would have decayed into nitrogen-14 (14N) atoms. This rate of decay is exponential, meaning that it decreases by one-half every half-life period. The half-life for different radioactive isotopes varies considerably; for instance, Rubidium-87 (87Rb) has a half-life of approximately 48.8 billion years.
Half-life is inversely related to the decay constant, and it is an imperative measure in understanding the activity of radioactive isotopes. A substance's radioactivity—which indicates how quickly a radioactive substance decays—depends on the number of unstable atoms present and their decay rate. In a specific example, the half-life for the decay of 16 million neutrons is 10.25 minutes, suggesting that after roughly four hours, only one neutron is expected to be remaining.