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.
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