Q. The half life of radium is 1620 years and its atomic weight is $226\ kg\ per\ kilomol$. The number of atoms that will decay from its $1\ g$ sample $per\ second$ will be (Avogadro’s number $N = 6.02 \times 10^{26}atom/kilomol$)
A) $3.61 \times 10^{10}$
B) $3.6 \times 10^{12}$
C) $3.11 \times 10^{15}$
D) $31.1 \times 10^{15}$
Explanation
(a) $\frac{dN}{dt} = \lambda N;\lambda = \frac{0.6931}{t_{12}} = \frac{0.6931}{1620 \times 365 \times 24 \times 60 \times 60}$
$N = \frac{6.023 \times 10^{23}}{226}$
$\therefore\frac{dN}{dt} = \frac{0.6931 \times 6.023 \times 10^{23}}{1620 \times 365 \times 24 \times 60 \times 60 \times 226} = 3.61 \times 10^{10}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.