A source contains initially N0 nuclei of a radioactive nuclide. How many of these nuclei have decayed after a time interval of three half-lives?
Correct answer: D. 7N0/8
- A. N0/8
- B. 2N0/3
- C. N0/3
- D. 7N0/8
Explanation
Each half-life reduces the remaining number of nuclei by half. After one half-life, N0/2 nuclei remain. After two half-lives, N0/4 nuclei remain. After three half-lives, N0/8 nuclei remain. Therefore, the number of nuclei that have decayed is the initial amount minus the remaining amount: N0 - N0/8 = 7N0/8. Thus, Option D is correct. The other options are incorrect because they either represent the remaining amount of nuclei or an incorrect calculation of decayed nuclei.
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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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