A radioactive source initially has activity 6400 Bq. After some time its activity becomes 200 Bq. The half-life of the nuclide is 4 h. Find the elapsed time in hours.
Physics · Nuclear physics · radioactivity and law of decay
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Question

A radioactive source initially has activity 6400 Bq. After some time its activity becomes 200 Bq. The half-life of the nuclide is 4 h. Find the elapsed time in hours.

G1 Physics · Accepted Answer

Activity is proportional to the number of undecayed nuclei, so it follows the same half-life law. Activity reduction factor: 6400 ÷ 200 = 32 = 2⁵. Thus five half-lives have elapsed. Elapsed time: t = 5×4 h = 20 h. Hence N = 20.