Explain the decay constant and write down its definition.

(N/A) According to the law of radioactive decay,the rate of disintegration is given by:
$\frac{dN}{dt} = -\lambda N$
Here,$dN$ is the number of nuclei that decay in a small time interval $dt$,$N$ is the number of undecayed nuclei present at time $t$,and $\lambda$ is the decay constant or radioactive constant.
Rearranging the equation for $\lambda$:
$\lambda = -\frac{dN/dt}{N}$
Definition: The decay constant is defined as the ratio of the instantaneous rate of disintegration to the number of undecayed nuclei present at that instant.
Alternatively,it can be defined as the probability of decay per unit time for a radioactive nucleus.