Question

I need help answering this question:
Cesium 139 is a radioactive isotope. 10.0 ug of pure Cs-139 (isotopic mass = 138.913364u) has an activity of 1460.2 Curies. What is the half-life of Cs-137 in minutes?

Answer 1

Answer on Question #77417, Chemistry / Inorganic Chemistry

Question:

Cesium-139 is a radioactive isotope. 10.0 ug of pure Cs-139 (isotopic mass = 138.913364u) has an activity of 1460.2 Curies. What is the half-life of Cs-139 in minutes?

Solution:

Amount of Cs-139: 10.0 / 138.913364 = 0.072 umol = 7.2·10⁻⁸ mol

Quantity of atoms of Cs-139: 7.2·10⁻⁸ · 6.022·10²³ = 4.33584·10¹⁶ atoms

1 Curie = 3.7·10¹⁰ decays per second

Activity: 1460.2 · 3.7·10¹⁰ = 5.40274·10¹³ decays per second

Decay constant: λ = 5.40274·10¹³ / 4.33584·10¹⁶ = 1.246·10⁻³ s⁻¹

Half-life: t₁/₂ = ln(2) / λ = 0.693 / 1.246·10⁻³ = 556.18 s = 9.27 min

Answer:

9.27 min

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