JEE Main2018PhysicsNuclear PhysicsActual
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
- A4   L
- B6   L
- C5   L
- D7   L
Correct answer
C. 5   L
Step-by-step solution
Let the 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 , the 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   cm 3 8 × 10 - 7 × 3.7 × 10 10 300 60   0.84 = 4.97 × 10 3   cm 2 = 4.97   liter = 5   L .