(A) Given: Half-life $T_{1/2} = 30 \ min$. Total time $t = 2 \ \text{hours} = 120 \ min$. Number of half-lives $n = \frac{t}{T_{1/2}} = \frac{120}{30}

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(A) Given: Half-life $T_{1/2} = 30 \ min$. Total time $t = 2 \ \text{hours} = 120 \ min$. Number of half-lives $n = \frac{t}{T_{1/2}} = \frac{120}{30} = 4$. The relationship between initial activity $A_0$ and final activity $A$ is given by $A = \frac{A_0}{2^n}$. Given final activity $A = 5 \ \text{disintegrations/sec}$. Substituting the values: $5 = \frac{A_0}{2^4} = \frac{A_0}{16}$. Therefore, $A_0 = 5 \times 16 = 80 \ \text{disintegrations/sec}$.

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

Medium

The radiation emitted by a radioactive substance with a half-life of $30 \ min$ is measured by a Geiger-Muller counter. If the count rate drops to $5 \ \text{disintegrations/sec}$ in $2 \ \text{hours}$, find the initial disintegration rate.

A
$80$
B
$200$
C
$250$
D
$40$

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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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If the mass of a radioactive sample is doubled,the activity of the sample and the disintegration constant of the sample are respectively

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The half-life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y$. Initially,they have the same number of atoms. Then:

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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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$A$ sample of a radioactive element contains $4 \times 10^{16}$ active nuclei. If the half-life of the element is $10$ days,then the number of decayed nuclei after $30$ days is ........ $\times 10^{16}$.

MediumAIPMT 2002

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The radiation emitted by a radioactive substance with a half-life of $30 \ min$ is measured by a Geiger-Muller counter. If the count rate drops to $5 \ \text{disintegrations/sec}$ in $2 \ \text{hours}$, find the initial disintegration rate.

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 mass of a radioactive sample is doubled,the activity of the sample and the disintegration constant of the sample are respectively

The half-life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y$. Initially,they have the same number of atoms. Then:

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$A$ sample of a radioactive element contains $4 \times 10^{16}$ active nuclei. If the half-life of the element is $10$ days,then the number of decayed nuclei after $30$ days is ........ $\times 10^{16}$.

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