Final answer:
Using the half-life of phosphorus-32 which is 14.3 days, it takes 4 half-lives to decay from 40.0 g to 2.5 g, which equates to 57.2 days. None of the answer choices provided matches this calculation.
Step-by-step explanation:
To determine the amount of time that has passed after a given amount of a radioactive isotope has decayed, you use its half-life, which is the time required for half of the isotope to decay. Phosphorus-32 has a half-life of 14.3 days. Starting with a 40.0 g sample, after one half-life (14.3 days), you would have 20.0 g remaining. After another half-life, you would be left with 10.0 g. A third half-life brings you to 5.0 g, and finally, after a fourth half-life, you are left with 2.5 g.
If you calculate the time elapsed, it takes 4 half-lives to get from 40.0 g down to 2.5 g. Thus, the time passed is:
14.3 days/half-life × 4 half-lives = 57.2 days
This value is not listed among the options, suggesting there might be a mistake in the given options or the assumptions made in this calculation.