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JEE Main 2021 (31 Aug, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2021 (31 Aug, Shift 1)

Q69JEE Main 2021 · 31 AUG · SHIFT 1Medium

Law of Radioactive Decay

A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B versus time is:

(Assume that at t = 0, there are no B atoms in the sample)

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Answer: (d)

$\frac{dN_B}{dt} = \lambda_A N_A - \lambda_B N_B$ , with $N_B = 0$ at $t = 0$ .
At first B grows smoothly as A decays; later A is nearly used up and B decays away.
So $N_B$ rises from zero, reaches a smooth maximum and then falls towards zero.
So the answer is (d).

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