Final answer:
The half-life of thorium-229 is (b) 3670 years, and understanding half-lives is essential for evaluating the long-term activity of radioactive substances.
Step-by-step explanation:
The half-life of thorium-229 is option b) 3670 years. Half-life is a term used in nuclear physics to describe the time required for one-half of the radioactive nuclei in a sample to decay. In this scenario, understanding half-lives is crucial, as it helps us to determine how long radioactive substances like thorium-229 remain active and potentially hazardous in the environment.
For instance, plutonium-239, which is also a nuclear waste byproduct, has a half-life of approximately 24,100 years, suggesting that it will remain active for a very long time, creating environmental concerns.