The radioactive decay law?

Radioactivity is a vital component of Modern Physics. The IIT JEE often picks up questions form this topic and hence, it becomes very essential for the JEE aspirants to master this topic in order to remain competitive in the JEE. Questions may sometimes be asked on the derivation of radioactive decay constant or the derivation of radioactive rate law.
The radioactive decay law explains or clarifies how the number of non-decayed nuclei of a given radioactive substance falls in due course of time.
Derivation of Radioactive Decay Law:
The number of atoms disintegrating per secondγis very small in the SI system it take a large number N (~ Avogadro number, 1023) to get any significant activity.
dN /dt = – γN ….(i)
Whereγis the radioactivity decay constant.
If N0is the number of radioactive atoms present at a time t = 0, and N is the number at the end of time t, then
N = N0e–γt
The term (–dN/dt)is called the activity of a radioactive substance and is denoted by 'A'.