Q. In a sample of radioactive material, what percentage of the initial number of active nuclei will decay during one mean life
A) 69.3%
B) 63%
C) 50%
D) 37%
Explanation
(b) Number of atoms remains undecayed $N = N_{0}e^{- \lambda t}$
Number of atoms decayed $= N_{0}(1 - e^{- \lambda t})$
$= N_{0}\left( 1 - e^{- \lambda \times \frac{1}{\lambda}} \right) = N_{0}\left( 1 - \frac{1}{e} \right) = 0.63{\ N}_{0} = 63\%$ of $N_{0}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.