Physics > Advanced Modern Physics > 6.0 Radioactive decay law
Advanced Modern Physics
1.0 X-Rays
2.0 Moseley's Law.
3.0 Nuclear Structure
4.0 Nuclear binding energy
4.1 Binding energy per nucleon
4.2 Variation of Binding energy per nucleon with mass number
4.3 Nuclear stability
5.0 Radioactivity
6.0 Radioactive decay law
6.1 Radioactive equilibrium
4.2 Variation of Binding energy per nucleon with mass number
4.3 Nuclear stability
$$\begin{equation} \begin{aligned} \to J({\lambda _1}) \to K({\lambda _2}) \to L \\ \quad \;{\mkern 1mu} {N_1}\quad \quad {N_2} \\\end{aligned} \end{equation} $$
Rate of disintegration of $J$, ${R_1} = {\lambda _1}{N_1}$
As $J$ decays to $K$, the above relation also gives the formation rate of nuclei of $K$.
Rate of disintegration of $K$, ${R_2} = {\lambda _2}{N_2}$
If at some instant the production rate and decay rate of the element $K$ becomes equal, then the amount of $K$ appears to be constant as the number of nuclei of $K$ appears to be constant as the number of nuclei of $K$ produced per second are equal to the number of nuclei of $K$ disintegrating per second.
This situation for the intermediate element $K$ is called radioactive equilibrium.
So,
Rate of formation of $K$ $=$ Rate of disintegration of $K$
Mathematically, $${\lambda _1}{N_1} = {\lambda _2}{N_2}$$
