Half Life and Mean Life

The expression for the average life of a radionuclide that shows its relationship with the half – life would be:

A radioactive sample contains $\text{2.2} \mathrm{mg}$ of pure ${}_6{}^{11}\mathrm{C}$ which has a half-life period of $1224$ seconds. Calculate the number of atoms present initially, and the activity when $5 \mathrm{\mu g}$ of the sample will be left.

A radioactive isotope has half-life of $5$ years. After how much time is its activity reduced to $3.125\%$ of its original activity? (Answer in years)

If $N_0$ is the initial mass of a substance with half-life $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=5 years$, then the amount of substance left after $15 years$ is

At some instant the ratio of the amount of two radioactive elements is $2:1$. If their half-lives respectively are $12$ hours and $16$ hours, then after two days, the ratio of the amount of two substances is

Half lives of two radioactive nuclei $\mathrm{A}$ and $\mathrm{B}$ are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be:

$Uranium-238$ decays to $Thorium-234$ with half-life $5\times {10}^9\mathrm{ }\mathrm{y}\mathrm{r}$ . The resulting nucleus is in the excited state and hence further emits $\mathrm{\gamma }$ -rays to come to the ground state. It emits $\mathrm{20 }\mathrm{\gamma }$ -rays per second. The emission rate will drop to $\mathrm{5 }\mathrm{\gamma }$-rays per second in

After $280$ days, the activity of a radioactive sample is $600 \mathrm{dps}$. The activity reduces to $300 \mathrm{dps}$ after another $140$ days. The half-life of the radioactive sample is

A radioactive nucleus $A$ with a half-life $T$, decays into a nucleus $B$. At $t=0$, there is no nucleus $B$. At some time $t$, the ratio of the number of $B$ to that of $A$ is $0\text{.}3$. Then, $t$ is given by: $\left({\log }_e\left(x\right)=\log \left(x\right)\right)$

If the nucleus ${}_{13}^{27}\text{Al}$ has a nuclear radius 3.6 fm, then what would be the approximate value of nuclear radius (in fm) of  ${}_{32}^{125}\text{Te}$?

The half lives of radioisotopes $P^{32}$ and $P^{33}$ are $20$ days and $30$ days, respectively. These radio isotopes are mixed in the ratio of $4:1$ of their atoms. If the initial activity of the mixed sample is $7 \mathrm{mCi}$, then the activity of the mixed isotopes after $60$ days will be $\dots \dots \mathrm{mCi}.$

The count rate from $100 {\mathrm{cm}}^3$ of a radioactive liquid is $c$. Some liquid is now discarded. The count rate of the remaining liquid is found to be $\frac{c}{10}$ after three half-lives. The volume of the remaining liquid, when discarded in ${\mathrm{cm}}^3$, is $\left(10n\right) {\mathrm{cm}}^3$ Calculate $n$.

In a sample initially, there are an equal number of atoms of two radioactive isotopes $A$ and $B$. $3$ days later, the number of atoms of $A$ is twice that of $B$. The half-life of $B$ is $1.5$ days. What is the half-life (in days) of isotope $A$?

A rock which is $10,000$ years old initially contains only Uranium nuclei. Uranium is radioactive which decays into $\mathrm{Pb}$ with a half life period $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$. At present, the ratio of Uranium and $\mathrm{Pb}$ nuclei in the rock is found to be $1:31$. The half life period $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ of Uranium is,

Half life of a radioactive substance is $1 \min$ . It is produced at a constant rate $R_0={10}^8$ nuclei per sec. How soon after (in $\min$, to the nearest integer), the beginning of production will its activity be equal to $7.5\times {10}^7$ disintegration per sec.

If the half life of a radio active is $T,$ then the fraction that would remain after a time $\frac{T}{2}$ is

$1$ $\mathrm{curie}$ represents

The half life period of a radioactive element $X$ is same as the mean life time of another radioactive element $Y.$ Initially both of them have the same number of atoms. Then :-