Q. For a radioactive nucleus, the mean life is $T$, If the number of decays per unit time is n at $t = 0$, the number of decays between time 0 and $t$, is
A) $nTe^{- t/T}$
B) $n(1 - e^{- t/T})$
C) $nT(1 - e^{- t/T})$
D) $ne^{- t/T}$
Explanation
(b) $N = N_{0}e^{- \lambda t}$
$N = ne^{- \lambda t}$
The number of decay between 0 and $t\ N_{0} - N$
$= n - ne^{- \lambda t} = n\left( 1 - e^{- \lambda t} \right) = n(1 - e^{- t/T})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.