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JEE Main 2021 (20 Jul, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2021 (20 Jul, Shift 2)

Q65JEE Main 2021 · 20 JUL · SHIFT 2Medium

Law of Radioactive Decay

For a certain radioactive process the graph between In R and t(sec) is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately:

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Answer: (d)

$\ln R = \ln R_0 - \lambda t$ , so the slope of the line is $-\lambda$ .
From the graph, $\ln R$ falls from 6 to 0 in 40 s: $\lambda = \frac{6}{40} = 0.15\text{ s}^{-1}$ .
$T = \frac{0.693}{0.15} \approx 4.62$ s.
So the answer is (d) 4.62 sec.

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