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Kinetics of nuclear reactions or nuclear chemistry

Question

A small quantity of solution containing of $_{11} N a_{}^{24}$ radionuclide $(t_{1 / 2} = 15 h r s)$ of activity $1.0 μ C i$ is injected in to the blood of a person. A sample of the blood of volume $1 c m^{3}$ taken after 5hour shows an activity of 296 dpm. Determine the total volume of the blood in the body of the person. Assume the radioactive solution mixes uniformly in the blood of the person $(1.0 C i = 3.7 \times 10^{10} d p s)$ (antilog of $0.1 ≃ 1.26$ )

Moderate

Solution

$t = \frac{2.303}{λ} \log_{10} (\frac{R_{0}}{R}), λ = \frac{0.693}{15}$
$t = \frac{2.303}{0.693 / 15} \log_{10} (\frac{R_{0}}{296})$
$\log 10 (\frac{R_{0}}{296}) = \frac{5 \times 0.693}{2.303 \times 15}, \frac{R_{0}}{296} = 1.26$
$R_{0} = 373 dpm = \frac{373}{60} d p s$
$If activity (\frac{373}{60}), volume of blood 1 {cm}^{3} .$
$5951.7 {cm}^{3} = 5.951 \approx 6 lts$

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