Nucleus A decays into nucleus B with a half-life of 10 s. At t = 0 s, there are 1000 A nuclei and no B nuclei. At what time will there be 750 B nuclei? 20 s 10 s 14 s 30 s
Question
Nucleus A decays into nucleus B with a half-life of 10 s. At t = 0 s, there are 1000 A nuclei and no B nuclei. At what time will there be 750 B nuclei? 20 s 10 s 14 s 30 s
Solution
To solve this problem, we need to understand the concept of half-life in nuclear decay. The half-life is the time it takes for half of the nuclei in a sample to decay.
Given:
- The half-life of nucleus A is 10 seconds.
- Initially, there are 1000 A nuclei and no B nuclei.
After one half-life (10 seconds), half of the A nuclei will have decayed into B nuclei. So, we will have 500 A nuclei and 500 B nuclei.
After two half-lives (20 seconds), half of the remaining A nuclei (i.e., 250) will have decayed. So, we will have 250 A nuclei and 750 B nuclei.
Therefore, it will take 20 seconds for there to be 750 B nuclei.
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