Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
The half life of ${ }_{92}^{238} \mathrm{U}$ against $\alpha$-decay is $13.86 \times 10^{16} \mathrm{~s}$. The activity of $1 \mathrm{~g}$ sample of ${ }_{92}^{238} \mathrm{U}$ is
PhysicsNuclear PhysicsAP EAMCETAP EAMCET 2018 (22 Apr Shift 2)
Options:
  • A $1.26 \times 10^4 \mathrm{~s}^{-1}$
  • B $1.26 \times 10^{-4} \mathrm{~s}^{-1}$
  • C $12.6 \times 10^4 \mathrm{~s}^{-1}$
  • D $12.6 \times 10^{-4} \mathrm{~s}^{-1}$
Solution:
2006 Upvotes Verified Answer
The correct answer is: $1.26 \times 10^4 \mathrm{~s}^{-1}$
Activity of a sample is
$\begin{aligned}
R & =\left|\frac{d N}{d t}\right|=\mid-\lambda N \models \lambda N=\frac{0.6931}{T_{1 / 2}} \times N \\
& =\frac{0.6931}{T_{1 / 2}} \times n \times N_A=\frac{0.6931}{T_{1 / 2}} \times \frac{m}{M} \times N_A
\end{aligned}$
With values, we get $R=1.26 \times 10^4 \mathrm{~s}^{-1}$

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.