The half-life period of a radioactive sample is $3.8 \ days$. After how many days will the sample become $\frac{1}{8}$ of the original substance?

The half-life period of a radioactive element $A$ is $62 \text{ years}$. It decays into another stable element $B$. An archaeologist found a sample in which $A$ and $B$ are in $1 : 15$ ratio. The age of the sample is (in $\text{ years}$)

$A$ sample has a half-life of $10^{33}$ years. If the initial number of nuclei of the sample is $26 \times 10^{24}$,then the number of nuclei decayed in $1$ year is ........... $\times 10^{-7}$.

$A$ radioactive nucleus can decay by two different processes. The half-life for the first process is $3.0 \, hours$ while it is $4.5 \, hours$ for the second process. The effective half-life of the nucleus will be $......... \, hours.$

The half-life of polonium is $140 \, days$. After how many days will $16 \, g$ of polonium be reduced to $1 \, g$ (or $15 \, g$ will decay)?

Two radioactive materials $X_1$ and $X_2$ have decay constants $5 \lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. After time $t$,the ratio of the number of nuclei of $X_1$ to that of $X_2$ is $\frac{1}{e}$. Then $t$ is equal to: