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JEE Main 2022 (26 Jun, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2022 (26 Jun, Shift 2)

Q46JEE Main 2022 · 26 JUN · SHIFT 2Easy

Law of Radioactive Decay

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:

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Answer: (d)

For two parallel decays the decay constants add: $\lambda = \lambda_1 + \lambda_2$ , so $\frac{1}{T} = \frac{1}{T_1} + \frac{1}{T_2}$ .
$T = \frac{T_1T_2}{T_1+T_2} = \frac{3.0\times4.5}{7.5} = 1.8$ h.
So the answer is (d) 1.80 hours.

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