Search any question & find its solution
Question:
Answered & Verified by Expert
A radioactive nucleus A has a single decay mode with half life $\tau_{\mathrm{A}}$. Another radioactive nucleus $\mathrm{B}$ has two decay modes 1 and 2. If decay mode 2 were absent, the half life of $\mathrm{B}$ would have been $\tau_{\mathrm{A}} / 2$. If decay mode 1 were absent, the half life of $\mathrm{B}$ would have been $3 \tau_{\mathrm{A}}$, then the ratio $\tau_{\mathrm{B}} / \tau_{\mathrm{A}}$ is-
Options:
Solution:
2357 Upvotes
Verified Answer
The correct answer is:
$3 / 7$
$\begin{array}{l}
\tau_{\mathrm{B}}=\frac{\tau_{\mathrm{A} / 2} \cdot 3 \tau_{\mathrm{A}}}{\tau_{\mathrm{A} / 2}+3 \tau_{\mathrm{A}}} \\
\frac{\tau_{\mathrm{B}}}{\tau_{\mathrm{A}}}=\frac{3}{7}
\end{array}$
\tau_{\mathrm{B}}=\frac{\tau_{\mathrm{A} / 2} \cdot 3 \tau_{\mathrm{A}}}{\tau_{\mathrm{A} / 2}+3 \tau_{\mathrm{A}}} \\
\frac{\tau_{\mathrm{B}}}{\tau_{\mathrm{A}}}=\frac{3}{7}
\end{array}$
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.