Question
The table illustrates the decay in mass of a 59-gram sample of Bismuth-212 as time progresses.
Time (seconds) | Bismuth-212 (grams)
0 | 59
60.5 | 29.5
121 | X
After 121 seconds, how many grams of the sample will remain if Bismuth-212 has a half-life of 60.5 seconds?
Time (seconds) | Bismuth-212 (grams)
0 | 59
60.5 | 29.5
121 | X
After 121 seconds, how many grams of the sample will remain if Bismuth-212 has a half-life of 60.5 seconds?
Answers
GPT-4o mini
To find the remaining mass of the Bismuth-212 sample after 121 seconds, given its half-life of 60.5 seconds, we can use the concept of exponential decay.
The half-life is the time it takes for half of the sample to decay. For Bismuth-212:
1. At 0 seconds: 59 grams
2. At 60.5 seconds (one half-life): \( \frac{59}{2} = 29.5 \) grams
3. At 121 seconds (which is two half-lives):
To find the amount remaining after two half-lives, we need to halve the amount remaining after one half-life again:
\[
\text{At 121 seconds} = \frac{29.5}{2} = 14.75 \text{ grams}
\]
Therefore, after 121 seconds, 14.75 grams of the Bismuth-212 sample will remain.
The half-life is the time it takes for half of the sample to decay. For Bismuth-212:
1. At 0 seconds: 59 grams
2. At 60.5 seconds (one half-life): \( \frac{59}{2} = 29.5 \) grams
3. At 121 seconds (which is two half-lives):
To find the amount remaining after two half-lives, we need to halve the amount remaining after one half-life again:
\[
\text{At 121 seconds} = \frac{29.5}{2} = 14.75 \text{ grams}
\]
Therefore, after 121 seconds, 14.75 grams of the Bismuth-212 sample will remain.