The half life of a radioactive nucleus is 50 days. The time invertal (t2 - t1) between the time t2 when 2/3 of it has decayed and the time t1 when 1/3 of it had decayed is (a) 30 days (b) 50 days (c) 60 days (d) 15 days

Answer: (b). When 1/3 has decayed, 2/3 remains; when 2/3 has decayed, 1/3 remains. The remaining amount halves between t₁ and t₂, so t₂ - t₁ = T. t₂ - t₁ = 50 days, so the answer is (b).

The half life of a radioactive nucleus is 50 days. The time invertal… | NEET 2012 (AIPMT, Mains)

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Law of Radioactive Decay

The half life of a radioactive nucleus is 50 days. The time invertal (t2 $-$ t1) between the time t2 when $\frac{2}{3}$ of it has decayed and the time t1 when $\frac{1}{3}$ of it had decayed is

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Answer: (b)

When $\frac{1}{3}$ has decayed, $\frac{2}{3}$ remains; when $\frac{2}{3}$ has decayed, $\frac{1}{3}$ remains.
The remaining amount halves between $t_1$ and $t_2$ , so $t_2 - t_1 = T$ .
$t_2 - t_1 = 50$ days, so the answer is (b).

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