Concepts Of Physics MCQ Edition [Volume 2]PhysicsThe Nucleus

Given that the decay constant of ²³⁸ U is 4.9 10⁻¹⁸ s ⁻¹ , find the half-life of ²³⁸ U .

Options

A2.25 10⁹ y
B6.5 10⁹ y
C9.0 10⁹ y
D4.5 10⁹ y

Correct answer

D. 4.5 10⁹ y

Step-by-step solution

The half-life of a radioactive substance is given by: T_ 1/2 = 2 = 0.693 Substituting = 4.9 10⁻¹⁸ s ⁻¹ : T_ 1/2 = 0.693 4.9 10⁻¹⁸ s = 1.414 10¹⁷ s Converting the half-life from seconds to years ( 1 year 3.154 10^7 s ): T_ 1/2 = 1.414 10¹⁷ 3.154 10^7 y T_ 1/2 4.48 10^9 y 4.5 10^9 y

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