Final answer:
The half-life of a radioactive isotope is the time it takes for half of the sample to decay to a stable form. One half-life for the given isotope in the example takes 200 years, leading to a reduction of the initial sample to 50%.
Step-by-step explanation:
The concept of half-life is fundamental in understanding the decay of radioactive isotopes. Half-life (T1/2) is defined as the amount of time it takes for one-half of the atoms in a sample of a radioactive isotope to decay into a stable form. Let's consider a specific case:
It takes about 200 years for 100% of our isotope sample to decay to 50%. Thus, the half-life is 200 years. Interestingly, after another 200 years (or 400 years in total), only 25% of the original sample would remain, as each half-life period reduces the existing sample by half.
Each radioactive nuclide has its own characteristic and constant half-life, which is essential for applications like radiocarbon dating and managing nuclear waste. Different isotopes have vastly different half-lives, ranging from fractions of a second to millions of years, depending on the isotope in question.