Rate of radioactive decay/disintegration:-  Decay of radioactive elements always follow first order kinetics.

Rate of disintegration at time t = (-dN/dt)=KN K = Decay constant      

k = (2.303/t) log (N_o/N)                N = no. of atoms at time t

t_1/2 = 0.993/k

Natural life of radioactive elements is infinite. Average life of radioactive substance (c) depends upon decay constant