Q. The rate of disintegration was observed to be $10^{17}$ disintegrations per sec when its half life period is 1445 years. The original number of particles are
A) $8.9 \times 10^{27}$
B) $6.6 \times 10^{27}$
C) $1.4 \times 10^{16}$
D) $1.2 \times 10^{17}$
Explanation
(b) Rate of disintegration $\frac{dN}{dt} = 10^{17}s^{- 1}$
Halt life $T_{1/2} = 1445\ year$
$= 1445 \times 365 \times 24 \times 60 \times 60 = 4.55 \times 10^{10}s$
Now decay constant
$\lambda = \frac{0.693}{T_{1/2}} = \frac{0.693}{4.55 \times 10^{10}} = 1.5 \times 10^{- 11}$ per s
The rate of disintegration
$\frac{dN}{dt} = \lambda \times N_{0} \Rightarrow 10^{17} = 1.5 \times 10^{- 11} \times N_{0}$
$\Rightarrow N_{0} = 6.6 \times 10^{27}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.