Final answer:
In Chemistry, applying the concept of half-life to a 250 nanograms sample of a radioisotope with a 12-hour half-life results in approximately 3.9 nanograms remaining after 72 hours.
Step-by-step explanation:
The subject of this question is Chemistry and it relates to the concept of radioactive decay and half-life calculations. Given a radioisotope with a half-life of 12 hours, we want to determine how much of the original 250 nanograms sample will remain after 72 hours. Since 72 hours is equal to 6 half-lives (72 hours ÷ 12 hours/half-life = 6 half-lives), we can calculate the remaining amount as follows:
- After the first half-life (12 hours), the sample would be reduced to half its original amount, so 125 nanograms would remain.
- After the second half-life (24 hours), half of that amount would remain, so 62.5 nanograms would remain.
- After the third half-life (36 hours), this process continues and we would be left with 31.25 nanograms.
- After the fourth half-life (48 hours), the remaining amount would be 15.625 nanograms.
- After the fifth half-life (60 hours), it would be 7.8125 nanograms.
- Finally, after the sixth half-life (72 hours), the sample would be halved again, leaving 3.90625 nanograms.
Thus, the correct answer to how much of the original 250 nanograms sample will remain after 72 hours is approximately 3.9 nanograms (Option b).