Question

A $0.2ml$ sample of a solution containing 1 x 10${}^{-7}$ curie of tritium ${}_1{H}^3$ is injected into the blood stream of a laboratory animal. After allowing sufficient time for circulation $0.1ml$ of the blood is found to have an activity of $20$ disintegration per minute. What is the blood volume of the animal?

• A. $1.1$ litre
• B. $0.55$ litre
• C. $0.65$ litre
• D. $1.65$ litre

Answer 1

The correct option is A $1.1$ litre

We know

$1$ curie $=3.7\times {10}^{10}dps$
Rate of disintegration in $0.2ml$ soln $={10}^{-7}\times 3.7\times {10}^{10}dps$
$=3.7\times {10}^{3}dps$
Now, tritium gets fully dissolved in the blood stream, whose volume is $x$
As $x$ ml contains $3.7\times {10}^{3}dps$
$\therefore 0.1$ ml will contain $\frac{3.7\times {10}^3}{x}\times 0.1\cdots \cdots \cdots \cdots \cdots \left[A\right]$
and
[A] is equal to $20/60$ dps which is given,
$\Rightarrow \frac{3.7\times {10}^3\times 0.1}{x}=\frac{20}{60}\Rightarrow x=1110$ ml
$\Rightarrow x=1.1$ litres