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Two radioactive substances, A and B, have half-lives of 20 minutes and 40 minutes, respectively. If both begin with the same number of nuclei, what will be the ratio of the number of nuclei that have decayed in A to the number that have decayed in B after 80 minutes?

1. 1: 4
2. 5: 4
3. 1: 16
4. 4: 1

Correct answer: 5: 4

Solution

After 80 minutes, substance A, with a half-life of 20 minutes, will have gone through 4 half-lives, decaying to 1/16 of its original amount, meaning 15/16 have decayed. Substance B, with a half-life of 40 minutes, will have gone through 2 half-lives, decaying to 1/4 of its original amount, meaning 3/4 have decayed. The ratio of decayed nuclei for A to B is therefore (15/16): (3/4), which simplifies to 5: 4.

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