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If a radioactive isotope has a half-life of 5 years, how much of a 100 g sample will remain after 15 years?

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Topic

Atoms and nuclear radiation

Question

If a radioactive isotope has a half-life of 5 years, how much of a 100 g sample will remain after 15 years?

Answer

12.5 g

Explanation

This question assesses the ability to apply the concept of half-life over multiple periods. The calculation requires understanding how the mass decreases by half for each half-life period.

Common mistake

Misunderstanding Half-Life Calculation

Students often confuse the concept of half-life with the total time for decay, thinking it is the time taken for all radioactive nuclei to decay rather than the time for half to decay.

Emphasize that half-life is the time required for half of the radioactive nuclei in a sample to decay, and practice calculating remaining activity after several half-lives.

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Question 1

A radioactive substance has a half-life of 5 years. If the initial count rate is 80 counts per minute, what will the count rate be after 15 years? Use the smoke alarm context to keep Half-lives and the random nature of radioactive decay distinct from nearby atomic and nuclear radiation ideas.