Question

A solution containing active cobalt $\_{27}^{60}Co$ having an activity of $0.8\mu Ci$ and decay constant $\lambda$ is injected in an animal's body. When $1c{m}^3$ blood is drawn from the animal's body after $10h$ of injection, the activity was found to be $300dpm$ (decays per minute), then the total volume of blood in the animal's body is close to $[1Ci=3.7\times 10^{10}dps$ (decays per second) and at $t=10h$ the value of $e^{-\lambda t}=0.84]$

• A. $4L$
• B. $6L$
• C. $5L$
• D. $7L$

Answer 1

Answer: (C)

Let the total volume of blood is $\text{v}$ , initial activity $A_0=0.Q\mu C_i$ its activity at time $\text{t}$ , $A=A_o{e}^{-\lambda t}$ , the activity of $\text{x}$ volume, $A^1=\left(\frac{A}{V}\right)X=X\left(\frac{A_o}{V}\right)e^{-\lambda t}$
$\Rightarrow V=X\left(\frac{A_0}{A^1}\right)e^{-\lambda t}\Rightarrow V=\left(1c{m}^3\right)\left(\frac{8\times 10^{-7}\times 3.7\times 10^{10}}{\frac{300}{60}}\right)(0.84)$
$=4.97\times 10^{3}c{m}^2=4.97$ liter $=5$ L.