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.
On integrating both sides, we have
where C is integration constant.
At t=0, N= N0
ln N0 = 0 + C or C = ln No
Put in above equation
The above equation gives exponential decay & it can also be written as