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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:

1. 3.17 × 10¹⁹
2. 3.17 × 10²⁰
3. 3.17 × 10¹⁷
4. 3.17 × 10¹⁸

Correct answer: 3.17 × 10¹⁹

Solution

The decay rate (R) is related to the number of radioactive atoms (N) by R = λN, where λ is the decay constant. The decay constant λ = ln(2) / T₁/₂. Substituting T₁/₂ = 2.2 × 10⁹ s, we get λ = 0.693 / (2.2 × 10⁹) = 3.15 × 10⁻¹⁰ s⁻¹. Using R = λN, we find N = R / λ = (10¹⁰) / (3.15 × 10⁻¹⁰) ≈ 3.17 × 10¹⁹.

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