Final answer:
To find the half-life of element C, we note that the mass goes from 20.0 grams to 5.0 grams in 50 years, indicating two half-life periods have occurred. Thus, each half-life is 25.0 years (50 years / 2).
Step-by-step explanation:
The problem presents a radioactive decay situation and asks us to find the half-life of element C. With an initial amount of 20.0 grams and 5.00 grams remaining after 50.0 years, we can calculate the number of half-lives that have occurred using the following steps:
- Determine the number of times the mass has been halved: 20.0g to 10.0g (1 half), 10.0g to 5.0g (2 halves).
- Since the mass has been halved twice over 50.0 years, each half-life corresponds to 50.0 years / 2 = 25.0 years.
Therefore, the correct answer is (C) 25.0 years. This is the time it takes for half of the radioactive isotopes of element C to decay.