The rate of disintegration was observed to be 1017 disintegrations per sec when its half life period is 1445 years. The original number of particles are

Rate of disintegration dNdt=1017s-1Half life T1/2=1445 year=1445 x 365 x 24 x 60 x 60 =4.55 x 1010secNow decay constantλ=0.693T1/2=0.934.55 x 1010=1.5 x 10-11 per secThe rate of disintegrationdNdt=λ x N0⇒1017=1.5 x 10-11 x N0 ⇒N0=6.6 x 1027.