The hypothesis states that the fraction of radioactive nuclei after n half-lives is 0.5n.In this expression, the value 0.5 represents

Each half-life leaves half of the radioactive nuclei undecayed, so the remaining fraction is multiplied by 0.5 after every cycle. Thus, in the expression 0.5ⁿ, 0.5 is the fraction remaining after any one half-life cycle. The half-life’s duration is a measure of time, not the fraction 0.5.

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