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JEE Main 2019 (10 Jan, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2019 (10 Jan, Shift 1)

Q79JEE Main 2019 · 10 JAN · SHIFT 1Medium

Law of Radioactive Decay

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = 6 seconds is close to -

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Answer: (a)

Count rate falls as $R = R_0 (1/2)^{t/T}$ .
$1600/100 = 16 = 2^4$ , so 4 half-lives in 8 s, giving $T = 2$ s.
At $t = 6$ s: 3 half-lives, $R = 1600/2^3 = 200$ counts/s.
So the answer is (a) 200.

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