(D) The number of nuclei remaining at time $t$ is given by the radioactive decay law: $N(t) = N_0 e^{-\lambda t}$.For material $X_1$ with decay consta

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(D) The number of nuclei remaining at time $t$ is given by the radioactive decay law: $N(t) = N_0 e^{-\lambda t}$.For material $X_1$ with decay constant $10 \lambda$: $N_1 = N_0 e^{-10 \lambda t}$.For material $X_2$ with decay constant $\lambda$: $N_2 = N_0 e^{-\lambda t}$.Given that the ratio $N_1 / N_2 = 1 / e$ at time $t$:$\frac{N_1}{N_2} = \frac{N_0 e^{-10 \lambda t}}{N_0 e^{-\lambda t}} = e^{-10 \lambda t + \lambda t} = e^{-9 \lambda t}$.We are given $\frac{N_1}{N_2} = e^{-1}$.Equating the exponents: $-9 \lambda t = -1$.Therefore,$t = \frac{1}{9 \lambda}$.

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

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Two radioactive materials $X_1$ and $X_2$ have decay constants $10 \lambda$ 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 $1 / e$ after a time:

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A
$1 / (10 \lambda)$
B
$1 / (11 \lambda)$
C
$11 / (10 \lambda)$
D
$1 / (9 \lambda)$

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Nuclei

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

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Two radioactive materials $X_1$ and $X_2$ have decay constants $10 \lambda$ 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 $1 / e$ after a time:

Similar Questions

What is a curie?

The half-lives of two radioactive materials $A$ and $B$ are $T$ and $2T$ respectively. If the ratio of the initial masses of the materials $A$ and $B$ is $8:1$,then the time after which the ratio of the masses of the materials $A$ and $B$ becomes $4:1$ is

The activity of a radioactive sample decreases to $(1/3)$ of its original value in $3\, \text{days}$. Then, in $9\, \text{days}$, its activity will become:

At a given instant,a radioactive sample has $N$ active nuclei. If its decay constant is $\lambda$,which of the following relations is incorrect? (Note: $\lambda$ is very small.)

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