(D) Radioactive decay is a stochastic (probabilistic) process.The number of nuclei remaining at time $t$ is given by $N(t) = N_0 e^{-\lambda t}$,where

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$A$ given nucleus may decay at any time after $t = 0$

(D) Radioactive decay is a stochastic (probabilistic) process.The number of nuclei remaining at time $t$ is given by $N(t) = N_0 e^{-\lambda t}$,where $\lambda$ is the decay constant.This equation implies that the probability of a nucleus decaying is distributed over time from $t = 0$ to $t = \infty$.Therefore,it is impossible to predict exactly when a specific nucleus will decay. $A$ given nucleus has a non-zero probability of decaying at any instant $t > 0$.Thus,option $(D)$ is correct.

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

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The half-life of $^{131}I$ is $8 \, days$. Given a sample of $^{131}I$ at time $t = 0$,we can assert that

IIT 1998 All IIT

A
No nucleus will decay before $t = 4 \, days$
B
No nucleus will decay before $t = 8 \, days$
C
All nuclei will decay before $t = 16 \, days$
D
$A$ given nucleus may decay at any time after $t = 0$

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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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Half lives of two radioactive substances $A$ and $B$ are respectively $20$ minutes and $40$ minutes. Initially,the sample of $A$ and $B$ have equal number of nuclei. After $80$ minutes,the ratio of the remaining numbers of $A$ and $B$ nuclei is

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The decay constant of a radioactive element is $1.5 \times 10^{-9} \text{ s}^{-1}$. Its mean life in seconds will be:

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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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$A$ radioactive element $A$ converts into another stable element $B$. The half-life of $A$ is $1.5 \ hrs$. After time $t$,the ratio of the number of atoms of $A$ to $B$ is found to be $1:8$. Then $t$ in hours is:

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$Rn$ decays into $Po$ by emitting an $\alpha$-particle with a half-life of $4 \text{ days}$. $A$ sample contains $6.4 \times 10^{10}$ atoms of $Rn$. After $12 \text{ days}$,the number of atoms of $Rn$ left in the sample will be:

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The half-life of $^{131}I$ is $8 \, days$. Given a sample of $^{131}I$ at time $t = 0$,we can assert that

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Half lives of two radioactive substances $A$ and $B$ are respectively $20$ minutes and $40$ minutes. Initially,the sample of $A$ and $B$ have equal number of nuclei. After $80$ minutes,the ratio of the remaining numbers of $A$ and $B$ nuclei is

The decay constant of a radioactive element is $1.5 \times 10^{-9} \text{ s}^{-1}$. Its mean life in seconds will be:

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

$A$ radioactive element $A$ converts into another stable element $B$. The half-life of $A$ is $1.5 \ hrs$. After time $t$,the ratio of the number of atoms of $A$ to $B$ is found to be $1:8$. Then $t$ in hours is:

$Rn$ decays into $Po$ by emitting an $\alpha$-particle with a half-life of $4 \text{ days}$. $A$ sample contains $6.4 \times 10^{10}$ atoms of $Rn$. After $12 \text{ days}$,the number of atoms of $Rn$ left in the sample will be:

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