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JEE Main 2022 (29 Jun, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2022 (29 Jun, Shift 1)

Q45JEE Main 2022 · 29 JUN · SHIFT 1Easy

Law of Radioactive Decay

The activity of a radioactive material is 2.56 $\times$ 10 $-$ 3 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 $\times$ 10 $-$ 5 Ci?

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Answer: (b)

Activity halves every half-life: $A = A_0/2^n$ .
$\frac{A_0}{A} = \frac{2.56\times10^{-3}}{2\times10^{-5}} = 128 = 2^7$ , so $n = 7$ .
$t = nT = 7\times5 = 35$ days.
So the answer is (b) 35 days.

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