Q. If $\lambda$ is decay constant and N the number of radioactive nuclei of an element , then the decay rate (R) of that element is
A) $\lambda N^{2}$
B) $\lambda N$
C) $\frac{\lambda}{N}$
D) $\lambda^{2}N$
Explanation
(b) At any instant the rate of decay of radioactive atoms is proportional to the number of atoms present at that instant $ie,$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - \frac{dN}{dt}\ \propto N$
Or$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ - \frac{dN}{dt}$ = R =$\ \lambda N$
where$\lambda\ is\ decay\ constant.$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.