(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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The half-life of a sample of a radioactive substance is $1 \text{ hour}$. If $8 \times 10^{10}$ atoms are present at $t = 0$,then the number of atoms decayed in the duration $t = 2 \text{ hours}$ to $t = 4 \text{ hours}$ will be

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What percentage of original radioactive atoms is left after five half-lives (in $\%$)?

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Two radioactive materials $Y_1$ and $Y_2$ initially contain the same number of nuclei. Their decay constants are $9 \lambda \ s^{-1}$ and $6 \lambda \ s^{-1}$ respectively. The time after which the ratio of the number of undecayed nuclei of $Y_1$ and $Y_2$ becomes $\frac{1}{e}$ is:

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The half-life of a radioactive isotope $X$ is $1.37 \times 10^9 \, y$. It decays to a stable isotope $Y$. In a rock sample from the moon,the ratio of $X$ to $Y$ is $1:7$. The age of the rock is:

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