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

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(A) Initial activity $R_0 = 1 \, \mu Ci = 10^{-6} \times 3.7 \times 10^{10} \, dps = 3.7 \times 10^4 \, dps$.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: $V = \frac{3.7 \times 10^4 \times 0.7927}{4.933} \approx 5945 \, cm^3$.Since $1000 \, cm^3 = 1 \, L$,the total volume $V \approx 5.94 \, L$.

Class 12 Physics Nuclei Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

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$A$ small quantity of solution containing $Na^{24}$ radionuclide of activity $1 \, \mu Ci$ is injected into the blood of a person. $A$ sample of the blood of volume $1 \, cm^3$ taken after $5 \, hours$ shows an activity of $296$ disintegrations 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: ............ $L$ (Take $1 \, Ci = 3.7 \times 10^{10}$ disintegrations per second and $e^{-\lambda t} = 0.7927$; where $\lambda$ is the disintegration constant).

A
$5.94$
B
$2$
C
$317$
D
$1$

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Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

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$A$ radioactive sample consists of two distinct species having an equal number of atoms initially. The mean life time of one species is $\tau$ and that of the other is $5 \tau$. The decay products in both cases are stable. $A$ plot is made of the total number of radioactive nuclei as a function of time. Which of the following figures best represents the form of this plot?

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$A$ certain radioactive element disintegrates with a decay constant of $7.9 \times 10^{-10} / s$. At a given instant of time, if the activity of the sample is equal to $55.3 \times 10^{11}$ disintegration/second, then the number of nuclei at that instant of time is:

Using a nuclear counter, the count rate of emitted particles from a radioactive source is measured. At $t = 0$, it was $1600$ counts per second, and at $t = 8 \, s$, it was $100$ counts per second. The count rate observed, in counts per second, at $t = 6 \, s$ is close to:

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