Modern Physics 3 Question 18
18. The half-life of ${ }^{131} I$ is 8 days. Given a sample of ${ }^{131} I$ at time $t=0$, we can assert that
$(1998,2 M)$
(a) no nucleus will decay before $t=4$ days
(b) no nucleus will decay before $t=8$ days
(c) all nuclei will decay before $t=16$ days
(d) a given nucleus may decay at any time after $t=0$
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Solution:
- Number of nuclei decreases exponentially
$$ \begin{aligned} & \qquad N=N _0 e^{-\lambda t} \\ & \text { and rate of decay }-\frac{d N}{d t}=\lambda N \end{aligned} $$
Therefore, decay process lasts upto $t=\infty$. Therefore, a given nucleus may decay at any time after $t=0$.
