A radioactive substance has a half-life of 20 hours. What fraction of the original radioactive nuclei will remain after 80 hours?
Question 1 Report
A radioactive substance has a half-life of 20 hours. What fraction of the original radioactive nuclei will remain after 80 hours?
Answer Details
The half-life of a radioactive substance is the time taken for half of the radioactive nuclei to decay. After one half-life, half of the radioactive nuclei have decayed and only half remain. Similarly, after two half-lives, only a quarter of the original radioactive nuclei remain, and after three half-lives, only an eighth remain.
In this question, the half-life is given as 20 hours, and the time elapsed is 80 hours, which is 4 times the half-life. Therefore, the number of half-lives that have passed is 4.
So, after 4 half-lives, the fraction of the original radioactive nuclei remaining is (1/2) x (1/2) x (1/2) x (1/2) = 1/16.
Therefore, the answer is: 1/16 of the original radioactive nuclei will remain after 80 hours.
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