Q. If $N_{1} = N_{0}e^{- \lambda t_{1}}$, then the number of atoms decayed during time interval from $t_{1}and\ t_{2}(t_{2} > t_{1})$ will be
A) $N_{t_{1}} = N_{t_{2}} = N_{o}\lbrack e^{- \lambda t_{1}} - e^{- \lambda r_{2}}\rbrack$
B) $N_{t_{2}} = N_{t_{1}} = N_{o}\lbrack e^{- \lambda t_{2}} - e^{- \lambda t_{1}}\rbrack$
C) $N_{t_{2}} - N_{t_{1}} = N_{o}\lbrack e^{\lambda t}2 - e^{- \lambda t_{1}}\rbrack$
D) None of the above
Explanation
(a) $N_{t_{1}} = N_{0}e^{\ ^{–\lambda t_{1}}\ }\ \ $
$N_{t_{2}} = N_{0}e^{- \lambda t_{2}}\ $
$\therefore\ N_{t_{1}} - N_{t_{2}} = N_{0}(e^{- {\lambda_{t}}_{2}} - e^{- {\lambda_{t}}_{2}})$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.