(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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Class 12

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Chapter

Nuclei

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

The half-life of radon is $3.8 \ days$. Three-fourths of a radon sample decays in ............ $days$.

Medium

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In a sample of $^{66}Cu$,$7/8$ of the initial number of nuclei decay into $Zn$ in $15 \ min$. The half-life of the sample is ......... $min$.

Medium

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Define the average life of a radioactive sample and obtain its relation to decay constant and half-life.

Medium

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Using a nuclear counter, the count rate of emitted particles from a radioactive source is measured. At $t = 0$, it was $1600$ counts per second, and at $t = 8 \, s$, it was $100$ counts per second. The count rate observed, in counts per second, at $t = 6 \, s$ is close to:

MediumAIEEE 2012

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At time $t=0$,a container has $N_{0}$ radioactive atoms with a decay constant $\lambda$. In addition,$c$ number of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at $t=T$?

KVPY 2010

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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

The half-life of radon is $3.8 \ days$. Three-fourths of a radon sample decays in ............ $days$.

In a sample of $^{66}Cu$,$7/8$ of the initial number of nuclei decay into $Zn$ in $15 \ min$. The half-life of the sample is ......... $min$.

Define the average life of a radioactive sample and obtain its relation to decay constant and half-life.

Using a nuclear counter, the count rate of emitted particles from a radioactive source is measured. At $t = 0$, it was $1600$ counts per second, and at $t = 8 \, s$, it was $100$ counts per second. The count rate observed, in counts per second, at $t = 6 \, s$ is close to:

At time $t=0$,a container has $N_{0}$ radioactive atoms with a decay constant $\lambda$. In addition,$c$ number of atoms of the same type are being added to the container per unit time. How many atoms of this type are there at $t=T$?

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