For a certain radioactive process,the graph between $\ln R$ and $t \, (\text{sec})$ is obtained as shown in the figure. Then the value of the half-life for the unknown radioactive material is approximately $.... \, \text{sec}$.

Two radioactive nuclei $A$ and $B$ both convert into a stable nucleus $C$. At time $t = 0$,the number of nuclei of $A$ is $4N_0$ and that of $B$ is $N_0$. The half-life of $A$ is $1 \, min$ and that of $B$ is $2 \, min$. Initially,the number of nuclei of $C$ is zero. At what time are the rates of disintegration of $A$ and $B$ equal?

Half-lives of two radioactive elements $A$ and $B$ are $30 \text{ minute}$ and $60 \text{ minute}$ respectively. Initially,the samples have an equal number of nuclei. After $120 \text{ minute}$,the ratio of the number of decayed nuclei of $B$ to that of $A$ will be:

Draw a graph of time $t$ versus the number of undecayed nuclei in a radioactive sample and write its characteristics.

The fossil bone has a ${}^{14}C:{}^{12}C$ ratio,which is $\frac{1}{16}$ of that in a living animal bone. If the half-life of ${}^{14}C$ is $5730 \, years$,then the age of the fossil bone is .......... $years$.

At a given instant,there are $25\%$ undecayed radioactive nuclei in a sample. After $10 \, s$,the number of undecayed nuclei reduces to $6.25\%$. The mean life of the nuclei is...........$ s$.