Modern Physics 3 Question 8
8. A radioactive sample $S _1$ having an activity of $5 \mu Ci$ has twice the number of nuclei as another sample $S _2$ which has an activity of $10 \mu Ci$. The half lives of $S _1$ and $S _2$ can be
(a) $20 yr$ and $5 yr$, respectively
$(2008,3 M)$
(b) $20 yr$ and $10 yr$, respectively
(c) $10 yr$ each
(d) 5 yr each
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Solution:
- Activity of $S _1=\frac{1}{2}$ (activity of $S _2$ )
or $\quad \lambda _1 N _1=\frac{1}{2}\left(\lambda _2 N _2\right)$
or $\quad \frac{\lambda _1}{\lambda _2}=\frac{N _2}{2 N _1}$
or $\quad \frac{T _1}{T _2}=\frac{2 N _1}{N _2} \quad T=$ half - life $=\frac{\ln 2}{\lambda}$
Given $\quad N _1=2 N _2$
$\therefore \quad \frac{T _1}{T _2}=4$
