The number of radioactive nuclei in a particular sample decreases to one-eighth of its original number in 9 days. The half-life of these nuclei is 3 days.
According to radioactive decay law,
n(t) = No [tex]e^{-kt}[/tex]
where n is number at t and No is starting number
when t = 9, n/No = 1/8 = 0.125
so
0.125 = [tex]e^{-k9}[/tex]
ln 0.125 = -9 k
k = 0.231
So,
half life = [tex]t\frac{1}{2}[/tex] = 0.693/k
half life = [tex]t\frac{1}{2}[/tex] = 0.693/0.231
half life = [tex]t\frac{1}{2}[/tex] = 3days
Therefore, when the number of radioactive nuclei in a particular sample decreases to one-eighth of its original number in 9 days. The half-life of these nuclei is 3 days.
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