(D) The activity of a radioactive sample at time $t$ is given by $A(t) = A_0 (1/2)^n$,where $n = t / T_{1/2}$ is the number of half-lives elapsed.For

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(D) The activity of a radioactive sample at time $t$ is given by $A(t) = A_0 (1/2)^n$,where $n = t / T_{1/2}$ is the number of half-lives elapsed.For nuclide $X$ at $t = 48$ years:Number of half-lives $n_X = 48 / 24 = 2$.Activity $A_X = A_0 (1/2)^2 = A_0 / 4$.For nuclide $Y$ at $t = 48$ years:Number of half-lives $n_Y = 48 / 16 = 3$.Activity $A_Y = A_0 (1/2)^3 = A_0 / 8$.The total activity of the mixture is the sum of the individual activities:$A_{total} = A_X + A_Y = A_0 / 4 + A_0 / 8 = (2 A_0 + A_0) / 8 = 3 A_0 / 8$.

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

Medium

Samples of two radioactive nuclides,$X$ and $Y$,each have equal activity $A_0$ at time $t = 0$. $X$ has a half-life of $24$ years and $Y$ has a half-life of $16$ years. The samples are mixed together. What will be the total activity of the mixture at $t = 48$ years?

A
$\frac{1}{2} A_0$
B
$\frac{1}{4} A_0$
C
$\frac{3}{16} A_0$
D
$\frac{3}{8} A_0$

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Nuclei

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

$A$ radioactive substance is being produced at a constant rate of $10 \text{ nuclei/s}$. The decay constant of the substance is $0.5 \text{ s}^{-1}$. After what time will the number of radioactive nuclei become $10$? Initially,there are no nuclei present. Assume the decay law holds for the sample.

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The decay constant of a radioisotope is $\lambda$. If its activity at times $t_1$ and $t_2$ are $A_1$ and $A_2$ respectively,then the number of nuclei that have decayed during the time interval $(t_1 - t_2)$ is:

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Two radioactive materials $X_1$ and $X_2$ have decay constants $5\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $\frac{1}{e}$ after a time:

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For a radioactive element,the mean life is $\tau$. At time $t = 0$,the number of nuclei decaying per unit time is $n$. The number of nuclei that have decayed between time $0$ and $t$ is:

Medium

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The half-life $(T)$ and the disintegration constant $(\lambda)$ of a radioactive substance are related as:

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Samples of two radioactive nuclides,$X$ and $Y$,each have equal activity $A_0$ at time $t = 0$. $X$ has a half-life of $24$ years and $Y$ has a half-life of $16$ years. The samples are mixed together. What will be the total activity of the mixture at $t = 48$ years?

Similar Questions

$A$ radioactive substance is being produced at a constant rate of $10 \text{ nuclei/s}$. The decay constant of the substance is $0.5 \text{ s}^{-1}$. After what time will the number of radioactive nuclei become $10$? Initially,there are no nuclei present. Assume the decay law holds for the sample.

The decay constant of a radioisotope is $\lambda$. If its activity at times $t_1$ and $t_2$ are $A_1$ and $A_2$ respectively,then the number of nuclei that have decayed during the time interval $(t_1 - t_2)$ is:

Two radioactive materials $X_1$ and $X_2$ have decay constants $5\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $\frac{1}{e}$ after a time:

For a radioactive element,the mean life is $\tau$. At time $t = 0$,the number of nuclei decaying per unit time is $n$. The number of nuclei that have decayed between time $0$ and $t$ is:

The half-life $(T)$ and the disintegration constant $(\lambda)$ of a radioactive substance are related as:

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