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JEE Main 2016 · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2016

Q91JEE Main 2016Medium

Law of Radioactive Decay

Half-lives of two radioactive elements $A$ and $B$ are $20$ minutes and $40$ minutes, respectively. Initially, the samples have equal number of nuclei. After $80$ minutes, the ratio of decayed number of $A$ and $B$ nuclei will be:

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Answer: (b)

In 80 min: A goes through 4 half-lives, B through 2.
Decayed A $= \frac{15}{16}N_0$ ; decayed B $= \frac{3}{4}N_0 = \frac{12}{16}N_0$ .
Ratio $= 15 : 12 = 5 : 4$ .
So the answer is (b) $5 : 4$ .

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