1. Nuclei of all radioactive elements undergo spontaneous disintegration & from new radioactive element with emission of alpha or beta along with gamma rays.
2. The disintegration is random i.e. which nuclei will disintegrate first is only a matter of chance.
3. Number of nuclei undergoing the decay per unit time is proportional to total number of nuclei present in the sample.
It is independent of all physical & chemical conditions (like temperature, pressure and chemical combination etc.)
Let ‘N’ be number of nuclei in the sample.
where is called radioactive decay constant or disintegration constant.
On integrating both sides, we have
where C is integration constant.
At t=0, N= N_{0}
ln N_{0} = 0 + C or C = ln N_{o}
Put in above equation

NOTE:
The above equation gives exponential decay & it can also be written as
or