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A small amount of solution containing $\mathrm{Na}^{24}$ ruclides with activity 20,500 disintegration per second was injected in the blood stream of a person - The activity of $1 \mathrm{ml}$ of blood sample taken after 5 hour later. was found to be 20 aisintegration $/ \mathrm{min} \cdot t_{1 / 2}=15$ hours. total volume of blood of the person is:
Option: 1
$40 \text { ltr }$

Option: 2
$36 \text { ltr }$

Option: 3
$45 \text { ltr }$

Option: 4
$49 \text { ltr }$

Answers (1)

best_answer

Let volume of blood of person is $V.$

$\mathrm{Na}^{24}$ is uniformly mixed in $V$ volume of blood.
Activity of $\mathrm{Na}^{24}$ & total no. of nuclei

$A_0=$ Activity of $\mathrm{Na}^{24}$ of 1 ml sample

$=\frac{20500}{\mathrm{Vme}} \times 1 \mathrm{ml}=\frac{20500}{\mathrm{~V}}$
Activity after $5 \, \mathrm{hrs}=\mathrm{Ao} / \mathrm{2}^{\mathrm{n}}.$

$n=\frac{t}{t^{1} / 2}=\frac{5}{15}=1 / 3 . \quad \Rightarrow A=A_0 / 2^{1 / 3}$

$\Rightarrow \frac{20}{60}=\frac{A_0}{2^{1 / 3}} \Rightarrow A=2^{1 / 3} / 3$

$\Rightarrow \frac{20500}{v}=\frac{2^{1 / 3}}{3} \Rightarrow v=\frac{20500 \times 3}{2^{1} / 3} \mathrm{ml}$

$v=48.8\, \, ltr\, \, =49\, ltr .$

Posted by

Kuldeep Maurya

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