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 $.... \, \text{sec}$.

Calculate the time (in $minutes$) interval between $33\%$ decay and $67\%$ decay if the half-life of a substance is $20\, minutes$.

At time $t=0$, a material is composed of two radioactive atoms $A$ and $B$, where $N_{A}(0)=2 N_{B}(0)$. The decay constant of both kinds of radioactive atoms is $\lambda$. However, $A$ disintegrates to $B$ and $B$ disintegrates to $C$. Which of the following figures represents the evolution of $N_{B}(t) / N_{B}(0)$ with respect to time $t$?
$N_{A}(0) = \text{Number of } A \text{ atoms at } t=0$
$N_{B}(0) = \text{Number of } B \text{ atoms at } t=0$

$A$ radioactive sample decays by $\beta$-emission. In the first $2 \ s$,$n$ $\beta$-particles are emitted,and in the next $2 \ s$,$0.25n$ $\beta$-particles are emitted. The half-life of the radioactive nuclei is ...... $s$.

Starting with a sample of pure ${}^{66}Cu$,$\frac{7}{8}$ of it decays into $Zn$ in $15 \ minutes$. The corresponding half-life is .......... $minutes$.

Half-life of a radioactive substance is $20 \text{ min}$. The time between $20 \%$ and $80 \%$ decay will be: (in $\text{ min}$)