Question

The decay constant of ${}_{80}^{197}\text{Hg}$ (electron capture to ${}_{79}^{197}\text{Au}$) is 1.8 $\times {10}^{-4}{\text{S}}^{-1}$. (a) What is the half-life ? (b) What is the average - life ? (c) How much time will it take to convert $25\%$ of this isotope of mercury into gold ?

Answer 1

$\text{Since}{t}_{\frac{1}{2}}=\frac{0.693}{\lambda }[\lambda \to \text{Decay Constant}]$

$\Rightarrow t_{\frac{1}{2}}=\frac{0.693}{1.8\times {10}^{-4}}$

=$3850\text{sec}=64\text{min}$

(b)$\text{Average life}=\frac{t_{\frac{1}{2}}}{0.693}$

=$\frac{64}{0.693}=92\text{min}$

(c)$0.75=e^{-\lambda \tau }$

$\Rightarrow \text{ln}0.75=-\lambda t$

$\Rightarrow t=\frac{ln0.75}{-0.00018}$

$=1598.23\text{sec}$