A particle radioisotope has a half-life of 5 days. In 15 days, the probability of decay in percentage will be:
Correct answer: B. 87.5%
- A. 67 %
- B. 87.5%
- C. 82.5%
- D. 77%
Explanation
To solve this problem, we first determine how many half-lives have passed in 15 days. Given the half-life of 5 days, 15 days corresponds to 3 half-lives. For each half-life, the remaining quantity of the radioactive substance is halved. Therefore, after 3 half-lives, the remaining quantity is (1/2)³ = 1/8 of the original amount. This means 7/8 of the original amount has decayed. To convert this into a percentage, we calculate (7/8) * 100 = 87.5%. Thus, the probability of decay after 15 days is 87.5%, making Option B the correct choice. The other options do not accurately reflect the decay over three half-lives and are therefore incorrect.
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About Half-life and Rate of Decay
Half-life is the time required for half the unstable nuclei in a sample to decay, and it remains constant for a particular radioactive nuclide. Questions use the exponential decay law, decay constant, activity, remaining quantity and mean life. Radioactive decay is random for individual nuclei but predictable for large samples.
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