The half-life of a radioactive substance is $48$ hours. How much time will it take to disintegrate to its $\frac{1}{16}$th part?

The half-life of a radioactive substance is $25 \ min$. The time interval between $50 \%$ decay and $87.5 \%$ decay of the substance will be: (in $min$)

$Rn$ decays into $Po$ by emitting an $\alpha$-particle with a half-life of $4 \text{ days}$. $A$ sample contains $6.4 \times 10^{10}$ atoms of $Rn$. After $12 \text{ days}$,the number of atoms of $Rn$ left in the sample will be:

Two radioactive materials $X_1$ and $X_2$ contain the same number of nuclei. If $6\lambda \, s^{-1}$ and $4\lambda \, s^{-1}$ are the decay constants of $X_1$ and $X_2$ respectively,the ratio of the number of undecayed nuclei of $X_1$ to that of $X_2$ will be $\left( \frac{1}{e} \right)$ after a time:

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$.

$A$ radioactive material has a half-life of $10$ days. What fraction of the material would remain after $30$ days?