Question

A solution containing active cobalt having activity of 0.8 ci and decay constant is injected in an animal's body. If 1 cm3 of blood is drawn from the animal's body after 10 hrs of injection, the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body ? (1 ci = 3.7 1010 decays per second and at t = 10 hrs et = 0.84)

Answer 1

Answer will be approximately 5 liters.

$N = N_{0} e^{λt} \\A = A_{0} e^{λt}$

As ,

total volume of blood will be V.

A_{0} = 0.8 μci

t = t_{1},

A = A_{0} e^{λt}

Activity = { A / V }

V  = 1 x A_{0} e^{λt} / A_{1}

V = 1 x 8 x 10^ -7 x 3.7 e ^ 10 x 0.84 / [ 300 / 60 ]

V = 4.97 liters