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13.Nuclei
medium
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
$D$
Solution
(b) Number of atoms undecayed $N = {N_0}{e^{ – \lambda t}}$
Number of atoms decayed $ = {N_0} – N = {N_0}(1 – {e^{ – \lambda t}})$
==> Decayed 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 $(B)$.
Standard 12
Physics
