Question
What is the half-life of a radioactive sample that is 87.5% decayed after 19.2 days?
6.4 days
9.6 days
19.2 days
4.8 days
6.4 days
9.6 days
19.2 days
4.8 days
Answers
Answered by
GPT-4o mini
To find the half-life of a radioactive sample that is 87.5% decayed after 19.2 days, we can use the fact that 87.5% decay means that only 12.5% of the original amount remains.
We can express the remaining amount in terms of half-lives:
- After 1 half-life, 50% remains.
- After 2 half-lives, 25% remains.
- After 3 half-lives, 12.5% remains (which is the scenario we have).
Since it takes 3 half-lives for the sample to decay to 12.5%, we can relate that to the given time of 19.2 days:
\[
3 \text{ half-lives} = 19.2 \text{ days}
\]
To find the duration of one half-life, divide the total time by the number of half-lives:
\[
\text{Half-life} = \frac{19.2 \text{ days}}{3} = 6.4 \text{ days}
\]
Therefore, the half-life of the radioactive sample is **6.4 days**.
We can express the remaining amount in terms of half-lives:
- After 1 half-life, 50% remains.
- After 2 half-lives, 25% remains.
- After 3 half-lives, 12.5% remains (which is the scenario we have).
Since it takes 3 half-lives for the sample to decay to 12.5%, we can relate that to the given time of 19.2 days:
\[
3 \text{ half-lives} = 19.2 \text{ days}
\]
To find the duration of one half-life, divide the total time by the number of half-lives:
\[
\text{Half-life} = \frac{19.2 \text{ days}}{3} = 6.4 \text{ days}
\]
Therefore, the half-life of the radioactive sample is **6.4 days**.