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Half-life of a radioactive substance A is 4 days. The probability of a nucleus that, from the given sample that it will decay in two half-lives is
- a)1/4
- b)3/4
- c)1/2
- d)1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Half-life of a radioactive substance A is 4 days. The probability of ...
After two half-lives 1/4 th fraction of nuclei will remain undecayed. Or, 3/4 th fraction will decay. Hence, the probability that a nucleus decays in two half lives is 3/4
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Half-life of a radioactive substance A is 4 days. The probability of ...
Understanding Half-life
The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei in a sample to decay. For substance A, the half-life is 4 days.
Decay Over Two Half-lives
In two half-lives, which is 8 days for substance A, we can determine the probability of decay as follows:
- First Half-life (4 days): After the first half-life, 50% of the original sample remains. Thus, 50% has decayed.
- Second Half-life (4 days): From the remaining 50%, another half will decay. Therefore, 25% of the original sample remains after the second half-life.
Calculating the Probability of Decay
Now, to find the overall probability that a nucleus will decay in two half-lives:
- Initial Sample: 100% (all nuclei)
- Remaining after Two Half-lives: 25% (after 8 days)
- Decayed Nuclei: 100% - 25% = 75%
The probability that a nucleus will decay in two half-lives is:
- Probability of Decay = Decayed Nuclei / Initial Sample = 75% / 100% = 3/4.
Conclusion
Therefore, the correct answer is option 'B', which indicates that there is a 75% probability (or 3/4) that a nucleus of substance A will decay in two half-lives.
The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei in a sample to decay. For substance A, the half-life is 4 days.
Decay Over Two Half-lives
In two half-lives, which is 8 days for substance A, we can determine the probability of decay as follows:
- First Half-life (4 days): After the first half-life, 50% of the original sample remains. Thus, 50% has decayed.
- Second Half-life (4 days): From the remaining 50%, another half will decay. Therefore, 25% of the original sample remains after the second half-life.
Calculating the Probability of Decay
Now, to find the overall probability that a nucleus will decay in two half-lives:
- Initial Sample: 100% (all nuclei)
- Remaining after Two Half-lives: 25% (after 8 days)
- Decayed Nuclei: 100% - 25% = 75%
The probability that a nucleus will decay in two half-lives is:
- Probability of Decay = Decayed Nuclei / Initial Sample = 75% / 100% = 3/4.
Conclusion
Therefore, the correct answer is option 'B', which indicates that there is a 75% probability (or 3/4) that a nucleus of substance A will decay in two half-lives.
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Half-life of a radioactive substance A is 4 days. The probability of a nucleus that, from the given sample that it will decay in two half-lives isa)1/4b)3/4c)1/2d)1Correct answer is option 'B'. Can you explain this answer?
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