A radioactive substance has a half-life of 60 minutes. After 3 hours, the fraction of atoms that have decayed would be:
Correct answer: C. 87.5%
- A. 12.5%
- B. 8.5%
- C. 87.5%
- D. 25.1%
Explanation
The half-life of a radioactive substance is the time it takes for half of the radioactive atoms in a sample to decay. So, after 3 hours, which is 180 minutes, 3 half-lives will have passed. This means that 75% of the original radioactive atoms will have decayed, and 25% will remain. The fraction of atoms that have decayed is given by the following formula: f = 1 - (1/2)^n Where f is the fraction of atoms that have decayed, n is the number of half-lives, and 1/2 is the probability that an atom will decay in one half-life. In this case, n = 3. So, the fraction of atoms that have decayed is: f = 1 - (1/2)^3 = 1 - 1/8 = 7/8 = 87.5%
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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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