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:

  1. 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 $t=0$.



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