(D) The number of half-lives $n$ is calculated by dividing the total time $t$ by the half-life $T_{1/2}$.$n = \frac{t}{T_{1/2}} = \frac{72000}{24000}

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(D) The number of half-lives $n$ is calculated by dividing the total time $t$ by the half-life $T_{1/2}$.$n = \frac{t}{T_{1/2}} = \frac{72000}{24000} = 3$.The fraction of the substance remaining after $n$ half-lives is given by the formula $\frac{N}{N_0} = \left( \frac{1}{2} \right)^n$.Substituting $n = 3$, we get $\frac{N}{N_0} = \left( \frac{1}{2} \right)^3 = \frac{1}{8}$.

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

Easy

Plutonium decays with a half-life of $24000 \, \text{years}$. If the plutonium is stored for $72000 \, \text{years}$, then the fraction of plutonium that remains is

A
$1/2$
B
$1/3$
C
$1/4$
D
$1/8$

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Nuclei

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

The activity of a radioactive sample:

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After $40 \, days$,the $1/16$th part of a radioactive element remains undecayed. What is its half-life (in $, days$)?

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The half-life of radium is about $1600$ years. Of $100 \, g$ of radium existing now, $25 \, g$ will remain unchanged after .......... $years$.

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Half-life of a radioactive element depends upon:

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The half-life of a radioactive substance is $12 \text{ minutes}$. The time gap between $28 \%$ decay and $82 \%$ decay of the radioactive substance is

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Plutonium decays with a half-life of $24000 \, \text{years}$. If the plutonium is stored for $72000 \, \text{years}$, then the fraction of plutonium that remains is

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