$N$ atoms of a radioactive element emit $n$ number of $\alpha$-particles per second. The mean life of the element in seconds is:

Half-life is measured by

The half-life of a radioactive element $X$ is equal to the mean life of another radioactive element $Y$. Initially, the number of atoms for both is the same. Then:

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 $t$?
$N_{A}(0) = \text{Number of } A \text{ atoms at } t=0$
$N_{B}(0) = \text{Number of } B \text{ atoms at } t=0$

The half-life of a radioactive substance is $20 \ min$. The time taken for the decay to increase from $20\%$ to $80\%$ is ........ $min$.

During the mean life of a radioactive element,the fraction that disintegrates is