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JEE Main 2021 (27 Jul, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2021 (27 Jul, Shift 1)

Q59JEE Main 2021 · 27 JUL · SHIFT 1Medium

Law of Radioactive Decay

If 'f' denotes the ratio of the number of nuclei decayed (Nd) to the number of nuclei at t = 0 (N0) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as: [ $\lambda$ is the radioactive decay constant]

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Answer: (c)

Decayed nuclei $N_d = N_0(1 - e^{-\lambda t})$ , so $f = \frac{N_d}{N_0} = 1 - e^{-\lambda t}$ .
$\frac{df}{dt} = \lambda e^{-\lambda t}$ .
So the answer is (c) $\lambda e^{-\lambda t}$ .

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