If you start with 16 atoms of a parent radioisotope, after how many half-lives will only 2 atoms of the parent remain, on average?

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BlackTom AI · Accepted Answer

Starting with 16 atoms and repeatedly applying a half-life reduction, we track the number of parent nuclei after each half-life. 
Option 3: After 3 half-lives, 16 -> 8 (1st), 8 -> 4 (2nd), 4 -> 2 (3rd). This matches the target of ending with 2 atoms on average, so this option aligns with the exponential decay rule. 
Option 2: After 2 half-lives, 16 -> 8 (1st), 8 -> 4 (2nd). This leaves 4 atoms, not 2, so this is too early and does not satisfy the condition. 
Option 8: After 8 half-lives, the count would be 16 / 2^8 = 16 / 256 = 0.0625 atoms on average. Since we’re counting discrete atoms, the expectation would be less than 1 atom on average, which clearly does not yield exactly 2 atoms; this option overestimates the number of half-lives needed. 
Option 16: After 16 half-lives, the remaining atoms would be 16 / 2^16 ≈ 0.000244, far fewer than 2; this is far beyond what would yield 2 atoms and shows the wrong end of the decay timeline. 
Option 9: After 9 half-lives, the remaining count would be 16 / 2^9 = 16 / 512 ≈ 0.03125 atoms on average, again far from 2 and not matching the required condition. 
In summary, only the progression for 3 half-lives yields exactly 2 atoms remaining, while the other options misplace the count either by stopping too early, or overshooting to much smaller values, or applying an unrealistic fractional expectation.

EESC1120.01|.02 Summer 2025 Our Home Amongst the Cosmos [Kruckenberg] Week 5 Quiz

If you start with 16 atoms of a parent radioisotope, after how many half-lives will only 2 atoms of the parent remain, on average?

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