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Concepts Of Physics MCQ Edition [Volume 2]PhysicsThe Nucleus

At a certain time, a specific sample of a radioactive material decays at the rate of 500 per second. After 50 minutes , the count rate falls to 200 per second. Determine the decay constant of the sample.

Options

  1. A1.83 10⁻² s ⁻¹
  2. B3.05 10⁻⁴ s ⁻¹
  3. C1.52 10⁻⁴ s ⁻¹
  4. D6.10 10⁻⁴ s ⁻¹

Correct answer

B. 3.05 10⁻⁴ s ⁻¹

Step-by-step solution

Given initial activity A₀ = 500 s ⁻¹ Activity after time t = 50 minutes = 3000 s is A = 200 s ⁻¹ Using the radioactive decay law for activity, A = A₀ e^ - t Substituting the given values: 200 = 500 e^ - 3000 e^ 3000 = 500 200 = 2.5 Taking natural logarithm on both sides: 3000 = (2.5) = 0.916 3000 = 3.05 10⁻⁴ s ⁻¹

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