Radioactive elements decay via first-order kinetics. Consider a certain type of nucleus that has a rate constant of 1.0 × 10^-3 h^-1. A sample contains 5.0 × 10⁹ radioactive nuclides. Calculate the number of nuclides remaining after 39 days have passed. A) 64 B) 7.8 × 10^-11 C) 2.0 × 10⁹ D) 5.0 × 10⁹ E) 2.5 × 10⁹

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Quizplus · Accepted Answer

The number of nuclides remaining can be calculated using the first-order decay formula: N = N₀e^(-kt). Converting 39 days to hours (39 × 24 = 936 hours) and using the given rate constant (k = 1.0 × 10^-3 h^-1), N = 5.0 × 10^9 e^(-0.936) ≈ 2.0 × 10^9.

Radioactive Elements Decay Via First-Order Kinetics