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)
30 hours
45 hours
15 hours
60 hours
30 hours
45 hours
15 hours
60 hours
Answers
GPT-4o mini
To determine how many hours have elapsed when only one-eighth of the sodium-24 remains, we can use the concept of half-lives.
The half-life of sodium-24 is approximately 15 hours.
If you start with 1 whole amount of sodium-24 (let's call it 1), here’s how it decays over time:
- After 1 half-life (15 hours), you have \( \frac{1}{2} \) remaining.
- After 2 half-lives (30 hours), you have \( \frac{1}{4} \) remaining.
- After 3 half-lives (45 hours), you have \( \frac{1}{8} \) remaining.
Since we want to find out when only one-eighth is left, we see that this occurs after 3 half-lives.
Thus, the total time elapsed is:
\[ 3 \times 15 \text{ hours} = 45 \text{ hours} \]
So the answer is **45 hours**.
The half-life of sodium-24 is approximately 15 hours.
If you start with 1 whole amount of sodium-24 (let's call it 1), here’s how it decays over time:
- After 1 half-life (15 hours), you have \( \frac{1}{2} \) remaining.
- After 2 half-lives (30 hours), you have \( \frac{1}{4} \) remaining.
- After 3 half-lives (45 hours), you have \( \frac{1}{8} \) remaining.
Since we want to find out when only one-eighth is left, we see that this occurs after 3 half-lives.
Thus, the total time elapsed is:
\[ 3 \times 15 \text{ hours} = 45 \text{ hours} \]
So the answer is **45 hours**.