Question
If only one-eighth of the sodium-24 remains, roughly how many hours have elapsed, given its half-life is approximately 15 hours?(1 point)
Responses
45 hours
45 hours
15 hours
15 hours
30 hours
30 hours
60 hours
60 hours
Responses
45 hours
45 hours
15 hours
15 hours
30 hours
30 hours
60 hours
60 hours
Answers
GPT-4o mini
To determine how many hours have elapsed for only one-eighth of sodium-24 to remain, we can use the concept of half-lives.
The half-life of sodium-24 is approximately 15 hours.
To go from the original amount to one-eighth of it, we need to undergo three half-lives, because:
- After the first half-life (15 hours), half of the original amount remains (1/2).
- After the second half-life (30 hours), half of that remaining amount is left (1/4).
- After the third half-life (45 hours), half of that remaining amount is left (1/8).
So, it takes 3 half-lives (3 x 15 hours) to reach one-eighth of the original amount.
Thus, the total time that has elapsed is:
3 half-lives × 15 hours = 45 hours.
The correct answer is:
**45 hours.**
The half-life of sodium-24 is approximately 15 hours.
To go from the original amount to one-eighth of it, we need to undergo three half-lives, because:
- After the first half-life (15 hours), half of the original amount remains (1/2).
- After the second half-life (30 hours), half of that remaining amount is left (1/4).
- After the third half-life (45 hours), half of that remaining amount is left (1/8).
So, it takes 3 half-lives (3 x 15 hours) to reach one-eighth of the original amount.
Thus, the total time that has elapsed is:
3 half-lives × 15 hours = 45 hours.
The correct answer is:
**45 hours.**