(A) The radioactive decay law states that the amount of substance remaining after time $t$ is given by $N(t) = N_0 (1/2)^{t/T_{1/2}}$.Given that the r

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(A) The radioactive decay law states that the amount of substance remaining after time $t$ is given by $N(t) = N_0 (1/2)^{t/T_{1/2}}$.Given that the ratio of Carbon-$14$ to Carbon-$12$ is $\frac{1}{4}$ of the original amount,we have $\frac{N(t)}{N_0} = \frac{1}{4}$.Since $\frac{1}{4} = (1/2)^2$,it implies that the time elapsed $t$ is equal to two half-lives.$t = 2 \times T_{1/2} = 2 \times 5,800$ years.Since $1$ century $= 100$ years,$t = 2 \times 58$ centuries.Therefore,$x = 2 \times 58$.

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

Medium

Carbon-$14$ decays with a half-life of about $5,800$ years. In a sample of bone,the ratio of Carbon-$14$ to Carbon-$12$ is found to be $\frac{1}{4}$ of what it is in free air. This bone may belong to a period about $x$ centuries ago,where $x$ is nearest to:

A
$2 \times 58$
B
$58$
C
$58/2$
D
$3 \times 58$

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Nuclei

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

The half-life of tritium is $ 12.5 $ years. What mass of tritium of initial mass $ 64 \ mg $ will remain undecayed after $ 50 $ years (in $mg$)?

DifficultKCET 2018

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What is the relationship between the decay constant $\lambda$ and the half-life $\tau_{1/2}$?

Easy

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The activities of three radioactive substances $A, B$ and $C$ are represented by the curves $A, B$ and $C$ in the figure. Then their half-lives $T_{\frac{1}{2}}(A) : T_{\frac{1}{2}}(B) : T_{\frac{1}{2}}(C)$ are in the ratio:

DifficultJEE MAIN 2020

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If $3/4$ of a radioactive sample decays in $3/4 \, s$,then the half-life of the sample is ........ .

Medium

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Two species of radioactive atoms are mixed in equal number. The disintegration constant of the first species is $\lambda$ and of the second is $\lambda / 3$. After a long time,the mixture will behave as a species with a mean life of approximately:

MediumKVPY 2013

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Carbon-$14$ decays with a half-life of about $5,800$ years. In a sample of bone,the ratio of Carbon-$14$ to Carbon-$12$ is found to be $\frac{1}{4}$ of what it is in free air. This bone may belong to a period about $x$ centuries ago,where $x$ is nearest to:

Similar Questions

The half-life of tritium is $ 12.5 $ years. What mass of tritium of initial mass $ 64 \ mg $ will remain undecayed after $ 50 $ years (in $mg$)?

What is the relationship between the decay constant $\lambda$ and the half-life $\tau_{1/2}$?

The activities of three radioactive substances $A, B$ and $C$ are represented by the curves $A, B$ and $C$ in the figure. Then their half-lives $T_{\frac{1}{2}}(A) : T_{\frac{1}{2}}(B) : T_{\frac{1}{2}}(C)$ are in the ratio:

If $3/4$ of a radioactive sample decays in $3/4 \, s$,then the half-life of the sample is ........ .

Two species of radioactive atoms are mixed in equal number. The disintegration constant of the first species is $\lambda$ and of the second is $\lambda / 3$. After a long time,the mixture will behave as a species with a mean life of approximately:

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