Final answer:
Radioactive half-life is the period required for half of a radioactive substance to decay, enabling predictions about the amount of material remaining after a given number of half-lives. It is critical for applications ranging from archaeological dating to nuclear medicine.
Step-by-step explanation:
Radioactive Half-Life
The radioactive half-life is a concept in nuclear physics and chemistry that allows us to predict the decay rate of an unstable atomic nucleus, a process that is not influenced by external conditions such as temperature or pressure. It is defined as the time it takes for half of the initial amount of a radioactive substance to decay. For example, if you start with 100 grams of a radioactive isotope, after one half-life, only 50 grams would remain.
After an integer number (n) of half-lives, the calculation to determine the amount of radioactive substance remaining is quite straightforward. If the original amount of the substance is taken to be 1 or 100%, after n half-lives, the remaining amount of the substance would be (½)n times the original amount. For instance, after two half-lives, (½)2 or 25% of the original substance would remain.
Calculating Material Remaining After n Half-Lives
Let's say we have a radioisotope with a half-life of 4 years. If we start with 80 grams of it:
- After 4 years (1 half-life), 40 grams would remain.
- After 8 years (2 half-lives), 20 grams would remain.
- After 12 years (3 half-lives), 10 grams would remain.
Thus, understanding the half-life of a radioactive substance is crucial for fields such as radioactive dating (like carbon-14 dating), medical diagnostics, and nuclear power generation.