Question

Radioactive material $'A'$ has decay constant $' 8 \lambda '$ and material $'B' $ has decay constant $'\lambda'$ Initially they have same number of nuclei. After what time, the ration of number of nuclei of material of material $'B' $ to that $'A'$ will be $e ?$

• A. $\frac{1}{7 \lambda} $
• B. $\frac{1}{8 \lambda} $
• C. $\frac{1}{9 \lambda} $
• D. $\frac{1}{ \lambda} $

Answer 1

Answer: (A)

$N _{ A }= N _{ A _{0}} e ^{(-8 \lambda) t }$
$N _{ B }= N _{ B _{0}} e ^{-\lambda t }$
$N _{ A _{0}}= N _{ B _{0}}$
$\Rightarrow \frac{ N _{ B }}{ N _{ A }}= e$
$\Rightarrow \frac{ e ^{-\lambda t }}{ e ^{-8 \lambda t }}= e ^{1}$
$\Rightarrow e ^{7 \lambda t }= e ^{1}$
$7 \lambda t =1$
$t =\frac{1}{7 \lambda}$