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JEE Main 2022 (24 Jun, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2022 (24 Jun, Shift 2)

Q51JEE Main 2022 · 24 JUN · SHIFT 2Medium

Law of Radioactive Decay

A sample contains 10 $-$ 2 kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1: 2. The ratio of the amounts of A and B after 16 s is $\frac{x}{100}$ . The value of x is ___________.

Numerical answer type. Work it out, then open the answer.

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Answer: 25

In 16 s: A goes through $16/4 = 4$ half-lives, B through $16/8 = 2$ .
Mass of A left $= 10^{-2}/16$ kg; mass of B left $= 10^{-2}/4$ kg.
Ratio of amounts (mass) $= \frac{1/16}{1/4} = \frac{1}{4} = \frac{25}{100}$ .
So $x = 25$ .

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