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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?
Verified Answer
Half-life of a radioactive substance A is 4 days. The probability of a...
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 a...
Solution:
Half-Life
The half-life of a radioactive substance is the time taken for half of the radioactive nuclei to decay.
Given:
Half-life of radioactive substance A is 4 days.
To Find:
Probability of a nucleus that, from the given sample that it will decay in two half-lives.
Solution:
Let N0 be the initial number of radioactive nuclei.
After one half-life, the number of radioactive nuclei will become N0/2.
After two half-lives, the number of radioactive nuclei will become N0/2 × 1/2 = N0/4.
The probability of decay of a radioactive nucleus in one half-life is 1/2.
Therefore, the probability of a nucleus decaying in two half-lives is (1/2)×(1/2) = 1/4.
The probability of a nucleus not decaying in two half-lives is (1−1/4) = 3/4.
Therefore, the probability of a nucleus that, from the given sample that it will decay in two half-lives is 3/4.
Hence, the correct option is (b) 3/4.
Half-Life
The half-life of a radioactive substance is the time taken for half of the radioactive nuclei to decay.
Given:
Half-life of radioactive substance A is 4 days.
To Find:
Probability of a nucleus that, from the given sample that it will decay in two half-lives.
Solution:
Let N0 be the initial number of radioactive nuclei.
After one half-life, the number of radioactive nuclei will become N0/2.
After two half-lives, the number of radioactive nuclei will become N0/2 × 1/2 = N0/4.
The probability of decay of a radioactive nucleus in one half-life is 1/2.
Therefore, the probability of a nucleus decaying in two half-lives is (1/2)×(1/2) = 1/4.
The probability of a nucleus not decaying in two half-lives is (1−1/4) = 3/4.
Therefore, the probability of a nucleus that, from the given sample that it will decay in two half-lives is 3/4.
Hence, the correct option is (b) 3/4.
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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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