(B) The number of nuclei remaining at time $t$ is given by $N(t) = N_0 e^{-\lambda t}$.For substance $A$, $N_A = N_0 e^{-5 \lambda t}$.For substance $

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(B) The number of nuclei remaining at time $t$ is given by $N(t) = N_0 e^{-\lambda t}$.For substance $A$, $N_A = N_0 e^{-5 \lambda t}$.For substance $B$, $N_B = N_0 e^{-\lambda t}$.Given the ratio $\frac{N_A}{N_B} = (1/e)^2 = e^{-2}$.Substituting the expressions:$\frac{N_0 e^{-5 \lambda t}}{N_0 e^{-\lambda t}} = e^{-2}$$e^{-5 \lambda t + \lambda t} = e^{-2}$$e^{-4 \lambda t} = e^{-2}$Equating the exponents:$-4 \lambda t = -2$$t = \frac{2}{4 \lambda} = \frac{1}{2 \lambda}$.

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

Medium

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$, they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

WBJEE 2012 All WBJEE

A
$\frac{1}{\lambda}$
B
$\frac{1}{2 \lambda}$
C
$\frac{1}{3 \lambda}$
D
$\frac{1}{4 \lambda}$

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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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$A$ sample contains $16\, g$ of a radioactive material, the half-life of which is $2\, days$. After $32\, days$, the amount of radioactive material left in the sample is:

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Define the decay constant and state its $SI$ unit.

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The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

DifficultTS EAMCET 2012

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$A$ radioactive nucleus is being produced at a constant rate $\alpha$ per second. Its decay constant is $\lambda$. If $N_0$ is the number of nuclei at time $t = 0$,then the maximum number of nuclei possible is:

Medium

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The count rate of a Geiger-Muller counter for the radiation of a radioactive material with a half-life of $30\, minutes$ decreases to $5\, s^{-1}$ after $2\, hours$. The initial count rate was..........$s^{-1}$.

MediumAIPMT 1995

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Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$, they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

Similar Questions

$A$ sample contains $16\, g$ of a radioactive material, the half-life of which is $2\, days$. After $32\, days$, the amount of radioactive material left in the sample is:

Define the decay constant and state its $SI$ unit.

The half-life of $Ra^{226}$ is $1620$ years. Calculate the number of atoms that decay in one second in $1 \ g$ of radium (Avogadro number $= 6.023 \times 10^{23}$).

$A$ radioactive nucleus is being produced at a constant rate $\alpha$ per second. Its decay constant is $\lambda$. If $N_0$ is the number of nuclei at time $t = 0$,then the maximum number of nuclei possible is:

The count rate of a Geiger-Muller counter for the radiation of a radioactive material with a half-life of $30\, minutes$ decreases to $5\, s^{-1}$ after $2\, hours$. The initial count rate was..........$s^{-1}$.

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