Question

Two radioactive materials $A_1$ and $A_2$ have decay constants of $10{\lambda }_0$ and ${\lambda }_0$. If initially they have same number
of nuclei, the ratio of number of their decayed nuclei will be $\left(\frac{1}{e}\right)$ after a time

• A. $\frac{1}{{\lambda }_0}$
• B. $\frac{1}{9{\lambda }_0}$
• C. $\frac{1}{10{\lambda }_0}$
• D. $1$

Answer 1

The correct option is B $\frac{1}{9{\lambda }_0}$

$N=N_0{e}^{-\lambda t}$
$\therefore N_1=N_0{e}^{-10{\lambda }_{0}t}$
$N_2=N_0{e}^{-{\lambda }_{0}t}$
$\therefore \frac{N_1}{N_2}\frac{1}{e}=e^{-9{\lambda }_{0}t}$
$9{\lambda }_{0}t=1$
$\Rightarrow t=\frac{1}{9}{\lambda }_0$