Question

Two radioactive materials $A$ and $B$ have decay constants $10\lambda$ and $\lambda$, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of $A$ to that of $B$ will be $1/e$ after a time:

• A. $\frac{11}{10\lambda }$
• B. $\frac{1}{9\lambda }$
• C. $\frac{1}{10\lambda }$
• D. $\frac{11}{11\lambda }$

Answer 1

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

$N_1=N_0{e}^{-10\lambda t}$
$N_2=N_0{e}^{-\lambda t}$
$\frac{1}{e}=\frac{N_1}{N_2}=e^{-9\lambda t}$
$\Rightarrow 9\lambda t=1$
$t=\frac{1}{9\lambda }$