State the law of radioactive decay.

(N/A) The law of radioactive decay states that the rate of disintegration of a radioactive substance at any instant is directly proportional to the number of radioactive nuclei present in the sample at that instant.
Mathematically,if $N$ is the number of radioactive nuclei at time $t$,then the rate of decay is given by:
$\frac{dN}{dt} = -\lambda N$
Where:
$1$. $\frac{dN}{dt}$ is the rate of decay (disintegration per unit time).
$2$. $\lambda$ is the decay constant (or disintegration constant) of the radioactive substance.
$3$. The negative sign indicates that the number of radioactive nuclei decreases with time.
Integrating this equation gives the law of radioactive decay: $N(t) = N_0 e^{-\lambda t}$,where $N_0$ is the initial number of nuclei at $t = 0$.