The rate of radioactive disintegration at an instant for a radioactive sample of half life 2.2 × 10⁹ s is 10¹⁰ s⁻¹. The number of radioactive atoms in that sample at that instant is, (a) 3.17 × 10¹⁹ (b) 3.17 × 10²⁰ (c) 3.17 × 10¹⁷ (d) 3.17 × 10¹⁸

Answer: (a). R = λ N ⇒ N = (R T)/(0.693). N = 10¹⁰×2.2×10⁹0.693 ≈ 3.17×10¹⁹. So the answer is (a) 3.17×10¹⁹.

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Law of Radioactive Decay

The rate of radioactive disintegration at an instant for a radioactive sample of half life $2.2 \times 10^{9}\text{ s}$ is $10^{10}\text{ s}^{-1}$ . The number of radioactive atoms in that sample at that instant is,

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Answer: (a)

$R = \lambda N \Rightarrow N = \frac{R\,T}{0.693}$ .
$N = \frac{10^{10}\times2.2\times10^9}{0.693} \approx 3.17\times10^{19}$ .
So the answer is (a) $3.17\times10^{19}$ .

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