Q. The fraction $f$ of radioactive material that has decayed in time $t$, varies with time $t$. The correct variation is given by the curve
A) $A$
B) $B$
C) $C$
D) $D$
Explanation
(b) Number of atoms undecayed $N = N_{0}e^{- \lambda t}$
Number of atoms decayed $= N_{0} - N = N_{0}(1 - e^{- \lambda t})$
$\Rightarrow$ Decyaed fraction $f = \frac{N_{0} - N}{N_{0}} = 1 - e^{- \lambda t}$
$i.e.,$ fraction will rise up to 1, following exponential path as shown in graph $(B)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.