Question

Two radioactive materials $A$ and $B$ have decay constants $10 \lambda$ and $\lambda$, respectively. It 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. $\frac{1}{11 \lambda}$

Answer 1

Answer: (B)

$\frac{1}{9 \lambda}$

Answer 2

$N_{1} = N_{0} e^{-10 \lambda t}$
$N_{2} = N_{0} e^{-\lambda t}$
$\frac{1}{e} = \frac{N_{1}}{N_{2}} =e^{-9 \lambda t}$
$\Rightarrow 9\lambda t = 1$
$t = \frac{1}{9\lambda}$