(A) From the graph, at $t = 0 \, hr$, the initial decay rate $R_0 = 200 \, \text{decays/sec}$.At $t = 2 \, hr$, the decay rate $R = 100 \, \text{decay

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$\frac{25}{2} \, \text{decays/sec}$

(A) From the graph, at $t = 0 \, hr$, the initial decay rate $R_0 = 200 \, \text{decays/sec}$.At $t = 2 \, hr$, the decay rate $R = 100 \, \text{decays/sec}$.Since the decay rate becomes half of its initial value in $2 \, hr$, the half-life $T_{1/2} = 2 \, hr$.The decay rate at any time $t$ is given by $R = R_0 \left( \frac{1}{2} \right)^{t/T_{1/2}}$.For $t = 8 \, hr$, $R = 200 \left( \frac{1}{2} \right)^{8/2} = 200 \left( \frac{1}{2} \right)^4 = \frac{200}{16} = \frac{25}{2} \, \text{decays/sec}$.

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

Difficult

The decay rate for a certain mass of a radioactive substance measured at different times varies with time as shown in the figure. The count rate at $t = 8 \, hr$ will be:

A
$\frac{25}{2} \, \text{decays/sec}$
B
$50 \, \text{decays/sec}$
C
$500 \, \text{decays/sec}$
D
$750 \, \text{decays/sec}$

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Nuclei

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

The half-life of a radioactive substance is $T$. The time taken for all the nuclei to disintegrate will be

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If $f$ denotes the ratio of the number of nuclei decayed $(N_{d})$ to the number of nuclei at $t=0$ $(N_{0})$,then for a collection of radioactive nuclei,the rate of change of $f$ with respect to time is given as: [$\lambda$ is the radioactive decay constant]

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In a radioactive substance at $t = 0$,the number of atoms is $8 \times 10^4$. Its half-life period is $3 \ years$. The number of atoms $1 \times 10^4$ will remain after an interval of ........... $years$.

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If $M_0$ is the initial mass of a radioactive substance with a half-life of ${t_{1/2}} = 5 \text{ years}$,what is the amount of substance remaining after $15 \text{ years}$?

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In a radioactive material,the fraction of active material remaining after time $t$ is $\frac{9}{16}$. The fraction that was remaining after $\frac{t}{2}$ is:

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The decay rate for a certain mass of a radioactive substance measured at different times varies with time as shown in the figure. The count rate at $t = 8 \, hr$ will be:

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