(C) The number of days from $January \, 1^{st}$ to $January \, 24^{th}$ is $23 \, days$.The number of half-lives $n$ is calculated as $n = \frac{23}{8

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(C) The number of days from $January \, 1^{st}$ to $January \, 24^{th}$ is $23 \, days$.The number of half-lives $n$ is calculated as $n = \frac{23}{8.04} \approx 2.86$.Since $n After $3$ half-lives,the activity would be $A = A_0 \times (1/2)^3 = 600 \times (1/8) = 75 \, Bq$.Because the elapsed time $(23 \, days)$ is less than $3$ half-lives $(3 \times 8.04 = 24.12 \, days)$,the remaining activity must be greater than $75 \, Bq$.

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

Medium

The nuclide $^{133}I$ is radioactive,with a half-life of $8.04 \, days$. At noon on $January \, 1$,the activity of a certain sample is $600 \, Bq$. The activity at noon on $January \, 24$ will be

A
$75 \, Bq$
B
Less than $75 \, Bq$
C
More than $75 \, Bq$
D
$150 \, Bq$

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Nuclei

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

$A$ count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later,the meter shows a count rate of $30$ per minute. The half-life of the source 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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Half-life of radium is $1620$ years. How many radium nuclei decay in $5$ hours in $5 \, g$ of radium? (Atomic weight of radium $= 223$)

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In a radioactive material,the activity at time $t_{1}$ is $R_{1}$ and at a later time $t_{2}$,it is $R_{2}$. If the decay constant of the material is $\lambda$,then:

MediumMHT CET 2007

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Let $N_{\beta}$ be the number of $\beta$ particles emitted by $1 \, g$ of $^{24}Na$ radioactive nuclei (half-life $= 15 \, hrs$) in $7.5 \, hrs$. $N_{\beta}$ is close to (Avogadro number $= 6.023 \times 10^{23} \, mol^{-1}$)

MediumJEE MAIN 2015

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The nuclide $^{133}I$ is radioactive,with a half-life of $8.04 \, days$. At noon on $January \, 1$,the activity of a certain sample is $600 \, Bq$. The activity at noon on $January \, 24$ will be

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$A$ count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later,the meter shows a count rate of $30$ per minute. The half-life of the source is .......... $min$.

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

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