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?

Question

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.

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?单项选择题

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