Q. During mean life of a radioactive element, the fraction that disintegrates is
A) $e$
B) $\frac{1}{e}$
C) $\frac{e - 1}{e}$
D) $\frac{e}{e - 1}$
Explanation
(c) By using $N = N_{0}e^{- \lambda t}$ and average life time $t = \frac{1}{\lambda}$
So $N = N_{0}e^{- \lambda \times 1/\lambda} = N_{0}e^{- 1} \Rightarrow \frac{N}{N_{0}} = e^{- 1} = \frac{1}{e}$
Now disintegrated fraction $= 1 - \frac{N}{N_{0}} = 1 - \frac{1}{e} = \frac{e - 1}{e}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.