(A) The law of radioactive decay states that the activity $A$ at time $t$ is given by $A = A_0 (\frac{1}{2})^n$,where $n$ is the number of half-lives.

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(A) The law of radioactive decay states that the activity $A$ at time $t$ is given by $A = A_0 (\frac{1}{2})^n$,where $n$ is the number of half-lives.Given that the activity decays to $\frac{1}{16}$ of its initial value,we have $\frac{A}{A_0} = \frac{1}{16}$.Since $\frac{1}{16} = (\frac{1}{2})^4$,we find that $n = 4$.The total time taken $t$ is given by $t = n \times T_{1/2}$,where $T_{1/2} = 100 \mu s$.Therefore,$t = 4 \times 100 \mu s = 400 \mu s$.

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

Medium

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 .........$\mu s$.

IIT 2002 All IIT

A
$400$
B
$6.3$
C
$40$
D
$300$

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Nuclei

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

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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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