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
Time (seconds) | Bismuth-212 (grams)
0 | 59
60.5 | 29.5
121 | X
Answers
GPT-4o mini
To determine the mass of Bismuth-212 after 121 seconds, we need to identify the decay process using the data provided.
Given the data:
- At 0 seconds, the mass is 59 grams.
- At 60.5 seconds, the mass is 29.5 grams.
From the data, we can see that the mass of Bismuth-212 decreases significantly over time, and it appears to reduce to half in about 60.5 seconds. This indicates that the half-life of Bismuth-212 is approximately 60.5 seconds.
Now, let's calculate the mass at 121 seconds:
1. After the first half-life (60.5 seconds), the mass is reduced to half:
- After 60.5 seconds: 59 g / 2 = 29.5 g (as shown in the table)
2. After the second half-life (a total of 121 seconds, which is 60.5 seconds + 60.5 seconds):
- After another 60.5 seconds (121 seconds in total): 29.5 g / 2 = 14.75 g
So, \( X \) would be 14.75 grams.
The complete data will now look like this:
- Time (seconds) | Bismuth-212 (grams)
- 0 | 59
- 60.5 | 29.5
- 121 | 14.75
Given the data:
- At 0 seconds, the mass is 59 grams.
- At 60.5 seconds, the mass is 29.5 grams.
From the data, we can see that the mass of Bismuth-212 decreases significantly over time, and it appears to reduce to half in about 60.5 seconds. This indicates that the half-life of Bismuth-212 is approximately 60.5 seconds.
Now, let's calculate the mass at 121 seconds:
1. After the first half-life (60.5 seconds), the mass is reduced to half:
- After 60.5 seconds: 59 g / 2 = 29.5 g (as shown in the table)
2. After the second half-life (a total of 121 seconds, which is 60.5 seconds + 60.5 seconds):
- After another 60.5 seconds (121 seconds in total): 29.5 g / 2 = 14.75 g
So, \( X \) would be 14.75 grams.
The complete data will now look like this:
- Time (seconds) | Bismuth-212 (grams)
- 0 | 59
- 60.5 | 29.5
- 121 | 14.75