Q. A small quantity of solution containing $Na^{24}$ radio nuclide of activity $1\ microcurie$ is injected into the blood of a person. A sample of the blood of volume $1cm^{3}$ taken after 5 hours shows an activity of 296 disintegration per minute. What will be the total volume of the blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of the person (Take $1\ curie = 3.7 \times 10^{10}$ disintegration per second and $e^{- \lambda t} = 0.7927;$ where $\lambda =$ disintegration constant)
A) $5.94\ litre$
B) $2\ litre$
C) $317\ litre$
D) $1\ litre$
Explanation
(a) $R_{0} =$ Initial activity = 1 micro curie $= 3.7 \times 10^{4}d\ ps$
$r =$ Activity in $1\ cm^{3}$ of blood at $t = 5\ hr$
$= \frac{296}{60}dps = 4.93dps$
$R =$ Activity of whole blood at time $t = 5\ hr$
Total volume should be $V = \frac{R}{r} = \frac{R_{0}e^{- \lambda t}}{r}$
$= \frac{3.7 \times 10^{4} \times 0.7927}{4.93} = 5.94 \times 10^{3}cm^{3} = 5.94\ litre$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.