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.
This question appeared on the ETEA MDCAT 2013 paper, which you can sit online with every answer explained.
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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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