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A sample has 4 × 10¹⁶ radioactive nuclei of half-life 10 days. The number of atoms decaying in 30 days is

1. 3.9 × 10¹⁶
2. 5 × 10¹⁵
3. 10¹⁶
4. 3.5 × 10¹⁶

Correct answer: 3.9 × 10¹⁶

Solution

The half-life of the sample is 10 days, so in 30 days (3 half-lives), the fraction of undecayed nuclei is (1/2)^3 = 1/8. Initially, there are 4 × 10¹⁶ nuclei, so the remaining nuclei after 30 days are (1/8) × 4 × 10¹⁶ = 0.5 × 10¹⁶. The decayed nuclei are the difference: 4 × 10¹⁶ - 0.5 × 10¹⁶ = 3.9 × 10¹⁶.

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