(C) The number of nuclei remaining after time $t$ is given by $N = N_0 (1/2)^n$,where $n = t / T_{1/2}$ is the number of half-lives.For substance $A$:

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(C) The number of nuclei remaining after time $t$ is given by $N = N_0 (1/2)^n$,where $n = t / T_{1/2}$ is the number of half-lives.For substance $A$: $T_{1/2, A} = 20 \ min$. The number of half-lives in $80 \ min$ is $n_A = 80 / 20 = 4$.Remaining nuclei $N_A = N_0 (1/2)^4 = N_0 / 16$.For substance $B$: $T_{1/2, B} = 40 \ min$. The number of half-lives in $80 \ min$ is $n_B = 80 / 40 = 2$.Remaining nuclei $N_B = N_0 (1/2)^2 = N_0 / 4$.The ratio of remaining nuclei is $N_A / N_B = (N_0 / 16) / (N_0 / 4) = 4 / 16 = 1 / 4$.

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

Difficult

Half-lives of two radioactive substances $A$ and $B$ are,respectively,$20 \ min$ and $40 \ min$. Initially,the samples of $A$ and $B$ have an equal number of nuclei. After $80 \ min$,the ratio of the remaining number of $A$ and $B$ nuclei is

A
$1 : 16$
B
$4 : 1$
C
$1 : 4$
D
$1 : 1$

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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 neutron is $693 \ s$. What fraction of neutrons will decay when a beam of neutrons, having kinetic energy of $0.084 \ eV$, travels a distance of $1 \ km$? (mass of neutron $= 1.68 \times 10^{-27} \ kg$, and $\ln 2 = 0.693$)

MediumTS EAMCET 2019

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The half-life of a radioactive sample undergoing $\alpha$-decay is $1.4 \times 10^{17} \; s$. If the number of nuclei in the sample is $2.0 \times 10^{21}$,the activity of the sample is nearly:

MediumNEET 2020

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The half-life of a radioactive sample,where the initial activity of the material was $8 \text{ counts}$ and after $3 \text{ hours}$ it becomes $1 \text{ count}$,is ............... $hours$.

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From $N$ atoms of a radioactive element,$n$ alpha particles are emitted per second. The half-life of the element is ......

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$A$ radioactive sample of half-life $ 10 $ days contains $ 1000x $ nuclei. The number of original nuclei present after $ 5 $ days is: (in $x$)

MediumKCET 2016

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Half-lives of two radioactive substances $A$ and $B$ are,respectively,$20 \ min$ and $40 \ min$. Initially,the samples of $A$ and $B$ have an equal number of nuclei. After $80 \ min$,the ratio of the remaining number of $A$ and $B$ nuclei is

Similar Questions

The half-life of a neutron is $693 \ s$. What fraction of neutrons will decay when a beam of neutrons, having kinetic energy of $0.084 \ eV$, travels a distance of $1 \ km$? (mass of neutron $= 1.68 \times 10^{-27} \ kg$, and $\ln 2 = 0.693$)

The half-life of a radioactive sample undergoing $\alpha$-decay is $1.4 \times 10^{17} \; s$. If the number of nuclei in the sample is $2.0 \times 10^{21}$,the activity of the sample is nearly:

The half-life of a radioactive sample,where the initial activity of the material was $8 \text{ counts}$ and after $3 \text{ hours}$ it becomes $1 \text{ count}$,is ............... $hours$.

From $N$ atoms of a radioactive element,$n$ alpha particles are emitted per second. The half-life of the element is ......

$A$ radioactive sample of half-life $ 10 $ days contains $ 1000x $ nuclei. The number of original nuclei present after $ 5 $ days is: (in $x$)

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