Question

Two radioactive material $A_1$ and $A_2$ have decay constants of ${\lambda }_0$ and $10{\lambda }_0$. If initially they have same number of nuclei, the ratio of number of their undecayed nuclei will be $\frac{1}{e}$ 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 $\frac{1}{9{\lambda }_0}$

$N_1=N_0{e}^{-{\lambda }_{0}t}{N}_2=N_0{e}^{-10{\lambda }_{0}t}\frac{N_2}{N_1}=\frac{1}{e}\Rightarrow e^{-9{\lambda }_{0}t}=e^{-1}\Rightarrow t=\frac{1}{9{\lambda }_0}$