Write down the definition and formula of half-life of a radioactive substance.

$A$ sample contains $10^{-2} \ kg$ each of two substances $A$ and $B$ with half-lives $4 \ s$ and $8 \ s$ respectively. The ratio of their atomic weights is $1:2$. The ratio of the amounts (number of atoms) of $A$ and $B$ remaining after $16 \ s$ is $\frac{x}{100}$. The value of $x$ is:

After five half-lives,what will be the fraction of the initial substance remaining?

The activity of a radioactive substance can be represented by various units. Select the correct option.

$A$ radioactive element has a rate of disintegration of $16,000 \text{ disintegrations per minute}$ at a particular instant. After $4 \text{ minutes}$, it becomes $2000 \text{ disintegrations per minute}$. The decay constant per minute is:

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