Question

The mean lives for $\alpha$ and $\beta$ decay of a radioactive substance are $1620years$ and $405years$ respectively. The time in which $\frac{3}{4}th$ of the material will decay , if it simultaneously emits $\alpha$ and $\beta$ particles is

• A. $449years$
• B. $199years$
• C. $\infty$
• D. $99years$

Answer 1

The correct option is A $449years$

Let us assume $\frac{3}{4}$ decays in time $t$ implies $\frac{1}{4}$ is left.
Total decay constant $=\frac{1}{1620}+\frac{1}{405}=\frac{1}{324}$
Now, $\frac{1}{4}=e^{-\lambda t}$
$\therefore e^{\lambda t}=4$
So, $t=\frac{1}{\lambda }ln4=1.3862\times 324=449years$