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
✓
Answer
${{\text{N}}_1} = {{\text{N}}_0}{{\text{e}}^{ - 10\lambda t}}$ ; $\mathrm{N}_{2}=\mathrm{N}_{0} \mathrm{e}^{-\lambda \mathrm{t}}$
$\frac{1}{e}=\frac{N_{1}}{N_{2}}=e^{-9 \lambda t}$
$\Rightarrow 9 \lambda t=1$
$\Rightarrow t=\frac{1}{9 \lambda}$
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