A pure radioactive isotope of mass number 60 has half-life 10 h. A sample contains 1.0 μg of the isotope. Take Avogadro constant = 6.0×10²³ mol⁻¹ and ln2 = 0.693. The initial activity is closest to:
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Question

A pure radioactive isotope of mass number 60 has half-life 10 h. A sample contains 1.0 μg of the isotope. Take Avogadro constant = 6.0×10²³ mol⁻¹ and ln2 = 0.693. The initial activity is closest to:

Options

G1 Physics · Accepted Answer

Sample mass: m = 1.0 μg = 1.0×10⁻⁶ g. Number of moles: n = 1.0×10⁻⁶ ÷ 60 = 1.6667×10⁻⁸ mol. Number of radioactive nuclei: N₀ = nN(A) = 1.6667×10⁻⁸×6.0×10²³ ≈ 1.0×10¹⁶. Half-life: T₁⁄₂ = 10 h = 36000 s. Decay constant: λ = 0.693 ÷ 36000 ≈ 1.925×10⁻⁵ s⁻¹. Initial activity: A₀ = λN₀ ≈ 1.925×10⁻⁵×10¹⁶ = 1.925×10¹¹ Bq. Therefore the closest option is 1.93×10¹¹ Bq. Correct option: B.