(D) The number of half-lives $n$ is given by $n = \frac{t}{T_{1/2}}$,where $t = 12\, days$ and $T_{1/2} = 4\, days$.Thus,$n = \frac{12}{4} = 3$.The nu

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(D) The number of half-lives $n$ is given by $n = \frac{t}{T_{1/2}}$,where $t = 12\, days$ and $T_{1/2} = 4\, days$.Thus,$n = \frac{12}{4} = 3$.The number of atoms remaining $N$ is given by the formula $N = N_0 \times (\frac{1}{2})^n$,where $N_0 = 6.4 \times 10^{10}$.Substituting the values,we get $N = 6.4 \times 10^{10} \times (\frac{1}{2})^3$.$N = 6.4 \times 10^{10} \times \frac{1}{8} = 0.8 \times 10^{10}$ atoms.

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

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

A
$3.2 \times 10^{10}$
B
$0.53 \times 10^{10}$
C
$2.1 \times 10^{10}$
D
$0.8 \times 10^{10}$

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Nuclei

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

An ancient discovery found a sample where $75 \%$ of the original carbon $(C^{14})$ remains. The age of the sample is: $\left(T_{1/2}(C^{14}) = 5730 \text{ years}, \ln 0.5 = -0.7, \ln 0.75 = -0.3\right)$ (in $\text{ years}$)

DifficultAP EAMCET 2022

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Two radioactive isotopes $P$ and $Q$ have half-lives $10 \text{ minutes}$ and $15 \text{ minutes}$ respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After $30 \text{ minutes}$,the ratio $\frac{\text{number of atoms of } P}{\text{number of atoms of } Q}$ will be

Medium

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If the half-life of a substance is $3.8\, days$ and its initial quantity is $10.38\, gm$,then the quantity of the substance remaining after $19\, days$ will be ........$gm$.

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The half-life of a radioactive element is $12.5 \; h$ and its initial quantity is $256 \; g$. After how much time (in $h$) will its quantity remain $1 \; g$?

MediumAIPMT 2001

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$A$ radioactive material whose half-life period is $2$ years weighs $1 \,g$ and is stored in the laboratory for $4$ years. Then the amount of remaining radioactive material is (in $\,g$)

EasyAP EAMCET 2023

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

Similar Questions

An ancient discovery found a sample where $75 \%$ of the original carbon $(C^{14})$ remains. The age of the sample is: $\left(T_{1/2}(C^{14}) = 5730 \text{ years}, \ln 0.5 = -0.7, \ln 0.75 = -0.3\right)$ (in $\text{ years}$)

If the half-life of a substance is $3.8\, days$ and its initial quantity is $10.38\, gm$,then the quantity of the substance remaining after $19\, days$ will be ........$gm$.

The half-life of a radioactive element is $12.5 \; h$ and its initial quantity is $256 \; g$. After how much time (in $h$) will its quantity remain $1 \; g$?

$A$ radioactive material whose half-life period is $2$ years weighs $1 \,g$ and is stored in the laboratory for $4$ years. Then the amount of remaining radioactive material is (in $\,g$)

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