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A solution containing active cobalt Co 27 60 having an activity of 0 .8 μCi and decay constant λ is injected in an animal's body. When 1 c m 3 blood is drawn from the animal's body after 10 h of injection, the activity was found to be 300 dpm (decays per minute), then the total volume of blood in the animal's body is close to [ 1 Ci = 3 .7 × 10 10 dps (decays per second) and at t = 10 h the value of e - λ t = 0.84 ]

Options

  1. A4   L
  2. B6   L
  3. C5   L
  4. D7   L

Correct answer

C. 5   L

Step-by-step solution

Let total volume of blood is v , initial activity A 0 = 0 . Q μ C i its activity at time t A = A o e − λ t activity of x volume A 1 = A V X = X A o V e - λ t V = X A 0 A 1 e - λ t V = 1 c m 3 8 × 10 - 7 × 3.7 × 10 10 300 60 0.84 = 4.97 × 10 3 c m 2 = 4.97 litre

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