Search any question & find its solution
Question:
Answered & Verified by Expert
Two radioactive substances $\mathrm{A}$ and $\mathrm{B}$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$ they have the same number of nuclei. The ratio of number of nuclei of A to those of $\mathrm{B}$ will be $(1 / e)^2$ after a time interval.
Options:
Solution:
1450 Upvotes
Verified Answer
The correct answer is:
$\frac{1}{2} \lambda$
According to the question
$\begin{aligned}
\frac{N_A}{N_B} & =\frac{1}{e^{4 \lambda t}} \\
\Rightarrow \quad \frac{1}{e^{4 \lambda t}} & =\frac{1}{e^2} \\
\Rightarrow \quad t & =\frac{1}{2 \lambda}
\end{aligned}$
$\begin{aligned}
\frac{N_A}{N_B} & =\frac{1}{e^{4 \lambda t}} \\
\Rightarrow \quad \frac{1}{e^{4 \lambda t}} & =\frac{1}{e^2} \\
\Rightarrow \quad t & =\frac{1}{2 \lambda}
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.