Q. The half-life of a radioactive substance against $\alpha$-decay is $1.2 \times 10^{7}s$. What is the decay rate for $4 \times 10^{15}$ atoms of the substance
A) $4.6 \times 10^{12}atoms/s$
B) $2.3 \times 10^{11}atoms/s$
C) $4.6 \times 10^{10}atoms/s$
D) $2.3 \times 10^{8}atoms/s$
Explanation
(d) $\frac{dN}{dt} = - \lambda N \Rightarrow \left| \frac{dN}{dt} \right| = \frac{0.693}{T_{1/2}} \times N$
$= \frac{0.693}{1.2 \times 10^{7}} \times 4 \times 10^{15} = 2.3 \times 10^{8}atoms/s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.