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JEE Main 2022 (26 Jul, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2022 (26 Jul, Shift 1)

Q48JEE Main 2022 · 26 JUL · SHIFT 1Medium

Law of Radioactive Decay

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is:

$($ Take $\log_{10} 1.88 = 0.274)$

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Answer: (c)

$\lambda = \frac{2.303}{t}\log_{10}\frac{R_0}{R}$ .
$\frac{R_0}{R} = \frac{4250}{2250} \approx 1.88$ , so $\lambda = \frac{2.303}{10}\times0.274$ .
$\lambda \approx 0.063\text{ min}^{-1}$ , so the answer is (c).

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