Q65 / 90 · JEE Main 2018 (15 Apr) · Physics

A solution containing active cobalt Co2760 having an activity of 0.8 μCi and decay constant λ is injected in an animal's body. When 1 cm3 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=3.7×1010 dps(decays per second) and at t=10 h the value of e-λt=0.84]

  • A
    4 L
  • B
    6 L
  • Correct answer
    C
    5 L
  • D
    7 L

Solution

Let the total volume of blood is v, initial activity A0=0.Q μCi its activity at time t,  A= A o e −λt , the activity of x volume,  A1=AVX=XAoVe-λt
⇒V=XA0A1e-λt⇒V=1 cm38×10-7×3.7×101030060 0.84
=4.97×103 cm2=4.97 liter=5 L.
 

Hence, the correct answer is option: 'C'.

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