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 $\frac{1}{e} ?$

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

Answer 1

Answer: (A)

$\frac{1}{7 \lambda}$

Answer 2

No option is correct
If we take $\frac{N_{A}}{N_{B}}=\frac{1}{e}$
Then
$\frac{N_{A}}{N_{B}}=\frac{e^{-8 \lambda t}}{e^{-\lambda t}}$
$\frac{1}{e}=e^{-7 \lambda t}$
$-1=-7 \lambda t$
$t=\frac{1}{7 \lambda}$