JEE Mains · Physics · STD 12 - 13. Nuclei
A radioactive nucleus \(n_2\) has 3 times the decay constant as compared to the decay constant of another radioactive nucleus \(n_1\). If initial number of both nuclei are the same, what is the ratio of number of nuclei of \(n_2\) to the number of nuclei of \(n_1\), after one half-life of \(n_1\) ?
- A \(1 / 8\)
- B \(8\)
- C \(4\)
- D \(1 / 4\)
Answer & Solution
Correct Answer
(D) \(1 / 4\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{N}_2=\mathrm{N}_0 \mathrm{e}^{-3 \lambda t} \\ & \mathrm{~N}_1=\mathrm{N}_0 \mathrm{e}^{-\lambda \mathrm{t}} \\ & \frac{\mathrm{N}_2}{\mathrm{~N}_1}=\mathrm{e}^{-2 \lambda \mathrm{t}} \\ & \mathrm{t}_{\text {half lifeofN }} \mathrm{t} \\ &…
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