At $t = 0$,the number of active nuclei in a sample is $N_0$. How many nuclei will decay in the time interval between its first mean life and second half-life?

Half-life of a radioactive sample is $24 \,h$. If a newly prepared radioactive sample shows $4$ times the allowed and safe value of radioactivity, the minimum time after which one can work safely with the source is (in $\,h$)

$A$ sample contains $10^{-2} \ kg$ each of two substances $A$ and $B$ with half-lives $4 \ s$ and $8 \ s$ respectively. The ratio of their atomic weights is $1:2$. The ratio of the amounts (number of atoms) of $A$ and $B$ remaining after $16 \ s$ is $\frac{x}{100}$. The value of $x$ is:

The relation between the mean life time $\tau$ and the half-life time $T_{1/2}$ of a radioactive substance is:

The activity of a radioactive sample is $1.6 \, curie$ and its half-life is $2.5 \, days$. Its activity after $10 \, days$ will be .......... $curie$.

${ }_{92}^{238} U$ is known to undergo radioactive decay to form ${ }_{82}^{206} Pb$ by emitting alpha and beta particles. $A$ rock initially contained $68 \times 10^{-6} \text{ g}$ of ${ }_{92}^{238} U$. If the number of alpha particles that it would emit during its radioactive decay of ${ }_{92}^{238} U$ to ${ }_{82}^{206} Pb$ in three half-lives is $Z \times 10^{18}$,then what is the value of $Z$?