Question
If only one-eighth of the sodium-24 remains, roughly how many hours have elapsed, given its half-life is approximately 15 hours?
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Answers
GPT-4o mini
To determine how many hours have elapsed when only one-eighth of sodium-24 remains, we can use the concept of half-lives.
Sodium-24 has a half-life of 15 hours. This means that after each 15-hour period, the amount of sodium-24 is reduced by half.
1. After 0 half-lives (0 hours), 1 (or 8/8) remains.
2. After 1 half-life (15 hours), 1/2 (or 4/8) remains.
3. After 2 half-lives (30 hours), 1/4 (or 2/8) remains.
4. After 3 half-lives (45 hours), 1/8 remains.
Since we are looking for the point at which only 1/8 remains, we see that this occurs after 3 half-lives.
Now, we simply multiply the number of half-lives by the duration of one half-life:
\[
3 \text{ half-lives} \times 15 \text{ hours/half-life} = 45 \text{ hours}
\]
Thus, approximately 45 hours have elapsed.
Sodium-24 has a half-life of 15 hours. This means that after each 15-hour period, the amount of sodium-24 is reduced by half.
1. After 0 half-lives (0 hours), 1 (or 8/8) remains.
2. After 1 half-life (15 hours), 1/2 (or 4/8) remains.
3. After 2 half-lives (30 hours), 1/4 (or 2/8) remains.
4. After 3 half-lives (45 hours), 1/8 remains.
Since we are looking for the point at which only 1/8 remains, we see that this occurs after 3 half-lives.
Now, we simply multiply the number of half-lives by the duration of one half-life:
\[
3 \text{ half-lives} \times 15 \text{ hours/half-life} = 45 \text{ hours}
\]
Thus, approximately 45 hours have elapsed.