Final answer:
After two half-lives (3 hours), given a half-life of 1.5 hours for the radioactive isotope, the remaining number of nuclei from an initial 500 would be 125.
Step-by-step explanation:
Calculation of Remaining Nuclei After 3 Hours
The question asks how many nuclei remain after 3 hours if a sample of a radioactive isotope starts with 500 nuclei and has a half-life of 1.5 hours. After one half-life (1.5 hours), the number of remaining nuclei would be half of the original amount, which would be 500 / 2 = 250 nuclei. After two half-lives (3 hours), the remaining nuclei are halved again, so there would be 250 / 2 = 125 nuclei left. This represents two half-lives, and we conclude that the correct answer is (b) 125 nuclei.