Define the disintegration rate or radioactivity of a sample and obtain the relation $R = \lambda N$ and define its different units.

(N/A) The number of disintegrating nuclei per unit time in a radioactive sample is called the decay rate or radioactivity $(R)$.
If the radioactive sample contains $N$ nuclei at time $t$, then the rate of disintegration or activity $R$ is given as follows:
$R = -\frac{dN}{dt}$
The negative sign indicates that as time passes, the number of radioactive nuclei decreases.
From the law of radioactive decay, the rate of decay is proportional to the number of nuclei present:
$-\frac{dN}{dt} = \lambda N$
Therefore, $R = \lambda N$, where $\lambda$ is the decay constant.
Units of radioactivity:
$1$. The $SI$ unit is the becquerel $(Bq)$, where $1 \ Bq = 1 \ \text{disintegration per second}$.
$2$. The older unit is the curie $(Ci)$, where $1 \ Ci = 3.7 \times 10^{10} \ Bq$.