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13.Nuclei
medium
If $'f^{\prime}$ denotes the ratio of the number of nuclei decayed $\left(N_{d}\right)$ to the number of nuclei at $t=0$ $\left({N}_{0}\right)$ then for a collection of radioactive nuclei, the rate of change of $'f'$ with respect to time is given as:
$[\lambda$ is the radioactive decay constant]
A
$\lambda\left(1-{e}^{-\lambda t}\right)$
B
$-\lambda e^{-\lambda t}$
C
$\lambda e^{-\lambda t}$
D
$-\lambda\left(1-{e}^{-\lambda . t}\right)$
(JEE MAIN-2021)
Solution
$N = N _{0} e ^{-\lambda t}$
$N _{ d }= N _{0}- N$
$N _{ d }= N _{0}\left(1- e ^{-\lambda t }\right)$
$\frac{ N _{ d }}{ N _{0}}= f =1- e ^{-\lambda t }$
$\frac{ df }{ dt }=\lambda e ^{-\lambda t }$
Standard 12
Physics
