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The rate of disintegration of a radioactive substance falls from 40 3   dps to 5 3   dps in 6 hours. The half-life of the radioactive substance is

Options

  1. A6 7 hours
  2. B2 hours
  3. C3 hours
  4. D1 hour

Correct answer

B. 2 hours

Step-by-step solution

A = A 0 e - λ t ⇒ 100 = 800 e - λ ( 6 × 60 ) ⇒ e - 350 x = 1 8 ⇒ - 360 λ = ln 1 8 = - ln 8 ⇒ λ = ln 2 3 360 = ln 2 120 ⇒ T 1 / 2 = ln 2 λ = ln 2 ( ln 2 / 120 ) = 120   minutes ⇒ T 1 / 2 = 2   hours

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