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JEE Main 2021 (25 Jul, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2021 (25 Jul, Shift 1)

Q60JEE Main 2021 · 25 JUL · SHIFT 1Medium

Law of Radioactive Decay

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as:

(where $\lambda$ is the decay constant)

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Answer: (d)

Quarter decayed: $N = \frac{3}{4}N_0 = N_0e^{-\lambda t_1}$ , so $t_1 = \frac{1}{\lambda}\ln\frac{4}{3}$ .
Half decayed: $t_2 = \frac{1}{\lambda}\ln2$ .
$t_2 - t_1 = \frac{1}{\lambda}\ln\left(2\times\frac{3}{4}\right) = \frac{\ln\frac{3}{2}}{\lambda}$ .
So the answer is (d).

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