(A) The radioactive decay law is given by $\frac{N}{N_0} = (\frac{1}{2})^n$,where $n$ is the number of half-lives.Given $\frac{N}{N_0} = \frac{1}{8}$,

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(A) The radioactive decay law is given by $\frac{N}{N_0} = (\frac{1}{2})^n$,where $n$ is the number of half-lives.Given $\frac{N}{N_0} = \frac{1}{8}$,we have $\frac{1}{8} = (\frac{1}{2})^n$.Since $\frac{1}{8} = (\frac{1}{2})^3$,we find $n = 3$.The total time $t$ is given by $t = n \times T_{1/2}$.Substituting the values,$t = 3 \times 3.8 \ days = 11.4 \ days$.

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

Medium

The half-life period of a radioactive sample is $3.8 \ days$. After how many days will the sample become $\frac{1}{8}$ of the original substance?

A
$11.4 \ days$
B
$3.8 \ days$
C
$3 \ days$
D
None of these

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Nuclei

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

$A$ radioactive substance decays by $10\%$ in $5$ days. What percentage of the original substance will remain after $20$ days (in $\%$)?

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Define the $SI$ unit of radioactivity.

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$A$ $16\, g$ sample of a radioactive element is taken from Bombay to Delhi in $2\, hours$ and it is found that $1\, g$ of the element remains (undisintegrated). The half-life of the element is:

Medium

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Starting with a sample of pure ${}^{66}Cu$, $7/8$ of it decays into $Zn$ in $15 \ minutes$. The corresponding half-life is ................ $minutes$.

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The half-life of $^{215}At$ is $100 \mu s$. The time taken for the radioactivity of a sample of $^{215}At$ to decay to $\frac{1}{16}$ of its initial value is .........$\mu s$.

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The half-life period of a radioactive sample is $3.8 \ days$. After how many days will the sample become $\frac{1}{8}$ of the original substance?

Similar Questions

$A$ radioactive substance decays by $10\%$ in $5$ days. What percentage of the original substance will remain after $20$ days (in $\%$)?

Define the $SI$ unit of radioactivity.

$A$ $16\, g$ sample of a radioactive element is taken from Bombay to Delhi in $2\, hours$ and it is found that $1\, g$ of the element remains (undisintegrated). The half-life of the element is:

Starting with a sample of pure ${}^{66}Cu$, $7/8$ of it decays into $Zn$ in $15 \ minutes$. The corresponding half-life is ................ $minutes$.

The half-life of $^{215}At$ is $100 \mu s$. The time taken for the radioactivity of a sample of $^{215}At$ to decay to $\frac{1}{16}$ of its initial value is .........$\mu s$.

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