A small quantity of solution containing Na^{2 | vedclass

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(A) Initial activity $R_0 = 1 \, \mu Ci = 10^{-6} 	imes 3.7 	imes 10^{10} \, dps = 3.7 	imes 10^4 \, dps$.Activity of $1 \, cm^3$ sample at $t = 5

Vedclass · Accepted Answer

$5.94$

Vedclass · Answer

(A) Initial activity $R_0 = 1 \, \mu Ci = 10^{-6} 	imes 3.7 	imes 10^{10} \, dps = 3.7 	imes 10^4 \, dps$.Activity of $1 \, cm^3$ sample at $t = 5 \, hours$ is $r = \frac{296}{60} \, dps \approx 4.933 \, dps$.The activity of the total blood volume $V$ at time $t$ is given by $R = R_0 e^{-\lambda t}$.Since the radioactive substance is uniformly mixed,the activity per unit volume is $r = \frac{R}{V}$.Therefore,$V = \frac{R}{r} = \frac{R_0 e^{-\lambda t}}{r}$.Substituting the values: $V = \frac{3.7 	imes 10^4 	imes 0.7927}{4.933} \approx 5945 \, cm^3$.Since $1000 \, cm^3 = 1 \, L$,the total volume $V \approx 5.94 \, L$.

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