AP EAMCET · PHYSICS · Nuclear Physics
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
- 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 \(12.6 \times 10^{-4} \mathrm{~s}^{-1}\)
Answer & Solution
Correct Answer
(A) \(1.26 \times 10^4 \mathrm{~s}^{-1}\)
Step-by-step Solution
Detailed explanation
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,…
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