Radioactive decay process follows first order Kinetics i.e rate of reaction depends upon no. of nucleus raised to power one.  where  disintegration / decay constant.
or 
Integrating both sides
for half life N = N0/2
Activity of a radioactive substance is the rate of decay or the number disintegration per second . it is denoted by A.
Also A = A0 where A0  initial activity.
Dumb Question:
Why has the rate been taken as negative of rate of change of no. of nuclei
Ans:- It is known that in a radioactive decay, the no. of nucleii always decreases,
 itself will be negative, so to get overall rate as a positive quantity R = - 
• no. of nucleii remaining after n half lives is given by
N = 
Illustration:-
Uranium areas on the earth at present time typically have a composition consisting of 99.3% of the isotope 92U235 and 0.7% of the isotope 92U235. The half lives of those isotopes are 4.47 x 109y and 7.04 x 108y respectively. if then isotopes were equally abundant when the earth was formed, estimate the age of earth
Solution:- let no be number of atoms of each isotope at the time of formation of the earth (T = 0) and N1 and N2 the number of atoms at present(t - t) then
N1 = N0 .................................................................(i)
N2 = N0 .................................................................(ii)
Further it is given that 
Equating (iii) and (iv) and taking log on both sides, we have
Substituting the values, we have
(1) Graphical Representation:- Since the radioactive decay process follows experential rate law hence
it has graph as shown in adjacent figure.
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