(B) The fraction of the substance remaining undecayed is given by $\frac{N}{N_0} = 2^{-n}$, where $n = \frac{t}{T_{1/2}}$.Given $t = 20 \, \text{hours

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$\frac{\sqrt{2} - 1}{\sqrt{2}}$

(B) The fraction of the substance remaining undecayed is given by $\frac{N}{N_0} = 2^{-n}$, where $n = \frac{t}{T_{1/2}}$.Given $t = 20 \, \text{hours}$ and $T_{1/2} = 40 \, \text{hours}$, the number of half-lives $n = \frac{20}{40} = 0.5$.Therefore, the fraction remaining is $\frac{N}{N_0} = 2^{-0.5} = \frac{1}{2^{0.5}} = \frac{1}{\sqrt{2}}$.The fraction that has decayed is $1 - \frac{N}{N_0}$.Decayed fraction $= 1 - \frac{1}{\sqrt{2}} = \frac{\sqrt{2} - 1}{\sqrt{2}}$.

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

Medium

The half-life of a radioactive nuclide is $40 \, \text{hours}$. Find the fraction of the substance that has decayed after $20 \, \text{hours}$.

A
$\frac{\sqrt{2} + 1}{\sqrt{2}}$
B
$\frac{\sqrt{2} - 1}{\sqrt{2}}$
C
$\frac{\sqrt{2} - 1}{\sqrt{3}}$
D
$\frac{\sqrt{3}}{\sqrt{2}}$

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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 in a laboratory has a half-life of $2 \text{ hours}$. It is considered safe for laboratory use when its activity reduces to $1/64$ of its initial value. After how many hours will the laboratory be safe?

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Element $X$ decays into element $Y$ with a half-life of $3$ days. On March $1$st,the mass of $X$ is $10 \, g$. What will be the masses of $X$ and $Y$ after $6$ days?

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The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at a later time $t_2$. Its decay constant is $\lambda$. Which of the following relations is correct?

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The radioactivity of a given sample of whisky due to tritium (half-life $12.5 \text{ years}$) was found to be only $3\%$ of that measured in a recently purchased bottle marked "$7 \text{ years}$ old". The sample must have been prepared about:

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$A$ freshly-prepared radioactive source of half-life $2 \, h$ emits radiation of intensity which is $64$ times the permissible safe level. The minimum time after which it would be possible to work safely with this source is ....... $h$.

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The half-life of a radioactive nuclide is $40 \, \text{hours}$. Find the fraction of the substance that has decayed after $20 \, \text{hours}$.

Similar Questions

$A$ radioactive substance in a laboratory has a half-life of $2 \text{ hours}$. It is considered safe for laboratory use when its activity reduces to $1/64$ of its initial value. After how many hours will the laboratory be safe?

Element $X$ decays into element $Y$ with a half-life of $3$ days. On March $1$st,the mass of $X$ is $10 \, g$. What will be the masses of $X$ and $Y$ after $6$ days?

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at a later time $t_2$. Its decay constant is $\lambda$. Which of the following relations is correct?

The radioactivity of a given sample of whisky due to tritium (half-life $12.5 \text{ years}$) was found to be only $3\%$ of that measured in a recently purchased bottle marked "$7 \text{ years}$ old". The sample must have been prepared about:

$A$ freshly-prepared radioactive source of half-life $2 \, h$ emits radiation of intensity which is $64$ times the permissible safe level. The minimum time after which it would be possible to work safely with this source is ....... $h$.

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