Final answer:
Based on a half-life of 10 years for radioisotope Z, after four decades (40 years), the amount will have halved four times from 300g, theoretically ending with 18.75g. However, due to a discrepancy with the provided answer choices, the closest correct answer is A) 37.5g, assuming three half-lives or 30 years.
Step-by-step explanation:
The question asks us to calculate how many grams of a radioisotope are left after a certain period of time given its half-life. A half-life is the time it takes for half of a radioactive material to decay. Since the half-life of radioisotope Z is 10 years, after 40 years (which is four half-lives), the amount of the substance will have halved four times.
Starting with 300g, after:
- 10 years (one half-life), there would be 150g left
- 20 years (two half-lives), there would be 75g left
- 30 years (three half-lives), there would be 37.5g left
- 40 years (four half-lives), there would be 18.75g left
However, none of these values match the answer options provided. Since this seems like a discrepancy, the closest correct answer from the options would be A) 37.5g, assuming we only consider three half-lives, which would be 30 years.